Far-field vessel wakes in Tallinn Bay/ Laevalainete kaugmojust Tallinna lahel.
Parnell, Kevin ; Delpeche, Nicole ; Didenkulova, Ira 等
1. INTRODUCTION
The importance of the contribution of ship traffic to the local
hydrodynamic activity in confined waters has been recognized for a long
time. Heavy ship traffic has the potential to cause environmental damage
in the vicinity of vulnerable areas such as wetlands or low-energy
coasts where wake-waves can cause extensive shoreline erosion, resuspend
bottom sediments, trigger ecological disturbance and harm the aquatic
wildlife [1-3].
The hydrodynamic influence of ship traffic on the marine and
coastal environment is usually negligible in areas of high natural wave
energy but becomes evident in small, micro-tidal lagoons and bays,
straits and inner waters of archipelagos. Examples of effects are the
enhancement of vertical mixing along the fairway that may intensify
eutrophication effects and result in harmful algae blooms by causing the
transport of nutrients from sediments into the euphotic layer [4], the
enhanced resuspension of fine sediments and changes to the coastal
processes in areas affected by ship wakes [1,3,5-7], and the direct
impact on fish [8] and marine mammals [9]. Several aspects of the impact
of ship traffic have been extensively studied in the Aland archipelago,
the Baltic Sea, over several decades [10-13].
The increase in the number, speed and size of ships over the last
few decades has led to the situation where ship wakes may be a
significant driver of hydrodynamics on some coasts that are exposed to
relatively high natural hydrodynamic loads. Such a situation was first
identified a few years ago for several sections of Tallinn Bay [14,15].
This area is characterized by an overall mild, but largely intermittent,
wave regime. While the annual mean significant wave height [H.sub.s] is
well below 0.5 m, rough seas with [H.sub.s] exceeding 3-4 m occasionally
occur in the inner sections of the bay. The daily highest ship waves
(with a typical height of slightly over 1 m) are equivalent to the
annual highest 1%-5% of wind-generated waves. Ship traffic is so intense
that ship-generated waves contribute, at least, 5%-8% of the total wave
energy, and about 18%-35% of the energy flux (the transport rate of the
wave energy, frequently called wave power in the coastal engineering
literature) even in those coastal areas of Tallinn Bay that are exposed
to dominant winds [16].
While the local influence of intense ship traffic on the water
column and sediments has been understood to some extent, the potential
for remote impacts is largely unknown. The basic concern is that the
waves, excited by strongly powered ships sailing at high speeds at
moderate depths, can result in a significant energy increase not only in
the vicinity of the sailing line, but also in the far-field, kilometres
from the vessel track [14,16,17]. In areas of generally low natural
waves, comparatively massive amounts of energy, released far from the
sailing line a long time after the ship has passed, can be spectacular,
but can also be a danger to lives and result in unusually high
hydrodynamic loads in the marine environment [18,19]. The breaking of
long ship waves, coming from atypical directions, may be responsible,
for example, for drastic thermal changes in shallow inlets several
kilometres away from the fairway [20] and even in the open sea [21]. The
breaking of unexpectedly high wave humps (formed in the process of
interaction of an incoming and reflected ship wave, or during crossing
of two ship wave systems) can be a significant human hazard in shallow
water [22].
After wide recognition of the effects of vessel wakes, efforts have
been made to reduce their impact in areas of intense ship traffic. In
some places fast ferries have ceased operation (for example, in Denmark
[3] and Washington State, USA), or there have been significant speed
limits introduced for sensitive sections of the vessel routes (for
example, in New Zealand [23], Finland and Sweden). In other places,
there have been attempts to optimize vessel operation or encourage
operation in water depths (normally deeper water) that avoid critical
(1) speeds [24]. New generations of vessels with ship hulls carefully
optimized to reduce the wave resistance (and therefore the height of
ship-induced waves) at specific speeds, have entered into service.
There have been significant changes in the types of vessels
operating in the traditional 'fast-ferry' market on the route
between Tallinn (Estonia) and Helsinki (Finland) and elsewhere in the
world. Firstly, the vessels that produced very dangerous and damaging
waves (for example, the largest of the high-speed catamarans sailing
between Tallinn and Helsinki in the late 1990s and early 2000s, which
produced the highest waves [14]) have been taken out of service.
Secondly, a new generation of high-powered conventional ferries with
service speeds 25-30 knots (~45-55 km/h, see Table 1 below) has replaced
the older conventional ferries that sailed at 15-20 knots (~ 25-35
km/h). Thirdly, the small hydrofoils have been replaced by much larger
ships. As sailing lines have remained largely unchanged and no
limitations have been imposed on the speed, the new ships may operate at
near-critical speeds in areas where older ships were clearly
subcritical. With these changes, the number of large vessels that are
able to travel at near-critical speeds has almost doubled in Tallinn Bay
since about the year 2000. The properties of the wakes of these vessels
are largely unknown. Although earlier studies have indicated or
hypothesized that ship wakes may serve as a major driver of sediment
transport at certain depths [5] and directly or indirectly impact the
coastal processes near the waterline [6,16,17,25], almost no unambiguous
evidence exists about the behaviour and impact of ship wakes on
realistic medium-or high-energy coasts.
The main aim of this study is to provide a brief overview of
experiments undertaken in Tallinn Bay in the spring and summer of 2008
in order to (i) update the understanding of ship induced hydrodynamic
activity in Tallinn Bay with respect to the new classes of ships that
are now operating, and to (ii) re-assess the properties and overall
changes of the wake wave climate in this bay based on systematic
measurements over a longer time interval. A novel aspect of this study
is an attempt to relate the properties of measured ship waves before
significant shoaling to their character and the resulting runup at the
shoreline.
The paper is organized as follows. The environment of Tallinn Bay,
the reasons for the choice of the experiment site and the details of the
fast ferry operations are described in Section 2. The experimental setup
at the Island of Aegna in spring and summer 2008 and the basic
geological and morphological features of the site are discussed in
Section 3. The procedure of recording and analysis of the wake
parameters and the typical and extreme features of wakes of individual
ships are described in Section 4. Section 5 contains an analysis of the
properties of the wave fields extracted from the water surface time
series (such as an estimate of the daily maximum ship wave height and
the shape of the energy spectrum of ship wakes) and from typical daily
and average characteristics of the ship-induced waves. This is followed
by a discussion of the results and an indication of further studies in
Section 6.
2. WIND WAVES AND SHIP WAKES IN TALLINN BAY
Tallinn Bay is a semi-enclosed body of water, approximately 10 x 20
km in size, with the City of Tallinn located at its southern end. The
bay belongs to a family of semi-sheltered bays that penetrate deep into
the southern coast of the Gulf of Finland (Fig. 1), an elongated
sub-basin of the Baltic Sea. The overall hydrodynamic activity is fairly
limited in this almost tideless area. There are, however, extensive
water level variations driven primarily by weather systems, with a
maximum recorded range of 2.47 m. As very high (more than 1 m above the
mean sea level) water level events are rare, the wind wave impact is
concentrated into a relatively narrow area in the coastal zone.
[FIGURE 1 OMITTED]
The complex shape of the Baltic Sea, combined with the anisotropy
of predominant winds, results in a particular local wave climate in
Tallinn Bay. Most storms blow from SW but occasionally very strong NNW
storms occur. Long and high waves, created in the Baltic Proper during
SW storms, usually do not enter the Gulf of Finland owing to geometrical
blocking [26]. Bottom refraction at the mouth of the Gulf of Finland may
cause waves to enter the gulf under some circumstances [27]. However, on
entering they keep propagating along the axis of the Gulf of Finland,
and affect only very limited sections of the coast of Tallinn Bay, the
northern part of which is additionally sheltered by the islands of Aegna
and Naissaar (Fig. 2). The same is also true for the waves excited in
the Gulf of Finland by easterly winds. The roughest seas in Tallinn Bay
occur during NNW storms that have fetch length of the order of 100 km
and thus only produce waves with relatively short periods. These
features severely limit the periods of the wave components. The peak
periods of wind waves are usually well below 3 s, reaching 4-6 s in
strong storms and only in exceptional cases do they exceed 7-8 s [28].
As a result of these factors, the local wave climate is relatively
mild in Tallinn Bay compared with the adjacent sea areas. The
significant wave height exceeds 0.5-0.75 m in the bay with a probability
of 10% and 1.0-1.5 m with a probability of 1% [28]. On the other hand,
very high (albeit relatively short) waves occasionally occur during
strong NW-NNW winds, to which Tallinn Bay is fully open. The significant
wave height typically exceeds 2 m at some time each year and may reach 4
m in extreme NNW storms in the central part of the bay. As a
consequence, most of the coast of Tallinn Bay has preserved features
indicative of periods of intense erosion [29,30] and as such it can be
considered to be a medium-or high-energy coastal environment.
The sea area between Tallinn and Helsinki is one of the most
intense ship traffic regions in the world with about 65 000 ship
crossings annually. Tallinn Bay is one of the few places in the world
where high-speed ferries continue to operate at, or close to, service
speeds close to the shoreline. High-speed (fast) ferries are interpreted
here as the vessels, the regular sailing regime of which contains
extensive sections with the depth Froude number 0.6. [F.sub.h] V/[square
root of (gh)] > 6 When this threshold is exceeded, the classical,
linear Kelvin wave system is modified and specific, non-linear
components of wakes frequently exist [31,32].
During the high (summer) season, the number of passenger ferries
and hydrofoils, servicing the Tallinn-Helsinki route cumulatively
traversing Tallinn Bay, was up to 70 per day around the year 2000 [15].
The most common high-speed ferries were large (~80 m in length, ~1200 t
displacement when fully loaded) and medium-sized (~60 m in length, ~600
t displacement) catamarans, and quite small hydrofoils [14]. There was
only one monohull high-speed ship, and a large conventional, but
extremely high-powered ferry Finnjet which crossed the bay a few times a
week. The number of conventional ferry sailings at low Froude numbers
was about 20 per day.
[FIGURE 2 OMITTED]
[FIGURE 6 OMITTED]
The structure of the fleet has changed considerably in the last
five years. The largest catamarans AutoExpress are not in operation any
more. The fleet now consists of a range of vessel types (Table 1). There
are two high-speed monohulls (SuperSeaCat, until 2006 operated by Silja
Line, since then by SeaContainers, operating speed ~65 km/h), and two
medium-sized twin hull vessels (Nordic Jet and Baltic Jet, operating
speeds ~60 km/h) which have been used on the route for several years.
Small monohull hydrofoils have been replaced by a twin-hull hydrofoil
Merilin, operated by Linda Line.
The number of conventional ferries (operating at speeds at or below
~30 km/h) has decreased considerably. The biggest change is the
introduction of several vessels of a new class of large, mostly
conventional ships operating at relatively high speeds (~50 km/h).
During this experiment, the vessels operating were Star, Superstar, and
Superfast (Tallink), and Viking XPRS.
The total number of departures of passenger ships from Tallinn to
Helsinki was 22-25 per day in summer 2008 (Table 1, Fig. 3). The
decrease in the frequency of departures from a peak of around 35 per day
in the early 2000s was mostly due to a significant reduction in the
number of conventional ferry and hydrofoil crossings. However, the
number of departures of large ships occasionally entering the
nearcritical regime has almost doubled.
The basic properties of the waves of the largest ships, sailing at
speeds below critical, can be adequately estimated with the use of the
classical theory of Kelvin wakes. The largest waves usually occur at the
border of the Kelvin wedge. Their period
T = 2 [pi][Vg.sup.-1][square root of (1+sin [alpha]/2)], (1)
increases linearly with the increase in the ship speed . V Here,
[alpha] is the apex half-angle of the Kelvin wedge (that also reflects
the dependence of the wake system on the water depth), V is the ship
speed and g is the acceleration due to gravity [31,32]. In deep water,
sin [alpha] 1/3 and Eq. (1) is approximately
T = 2[pi]/[square root of (6g)]V [congruent to] 0.523V, (2)
where the proportionality coefficient has the dimension of
[s.sup.2]/m. From Eq. (2) it follows that the periods of the largest
waves, excited by ships sailing faster than 6 m/s (~20 km/h or ~12
knots), exceed the typical periods of wind waves in Tallinn Bay. Periods
of waves of ships, sailing over 12 m/s (~45 km/h or ~24 knots), match
those of wind waves in strong storms whereas ships sailing faster than
about 50 km/h may excite waves of periods that are extremely seldom
found under natural conditions in Tallinn Bay, even if they sail at low
depth Froude numbers over the deepest part of the bay. This estimate is
slightly modified in water of finite depth , h where the Kelvin wake
apex half-angle is
sin [alpha] = (1+Q/(3-Q), (3)
Q = 2kh/sinh(2kh), (4)
where k is the wave number and the product kh is determined from
the transcendental equation [31]
(3-Q)tan(kh) = 2kh[F.sup.2.sub.h] (5)
[FIGURE 3 OMITTED]
The relevant corrections to Eqs. (1), (2) are of the order of a few
per cent unless the depth Froude number reaches about 0.95 [33,34].
For much of the time ships in Tallinn Bay operate in the so-called
low speed sub-critical regime ([F.sub.h] < 0.84). However, there are
sections both on the inbound and outbound tracks where many of the
vessels travel in the near-critical regime. The depth Froude number
exceeds 0.84 in some places for all tracked ships (Figs. 2, 4). At these
speeds, ships tend to generate packets of large, solitonic, very long
and long-crested waves [24,31]. The periods of the leading waves,
excited at near-critical speeds, may be much larger than those of
conventional ferries or vessels travelling at even slightly slower
speeds [34].
Another important parameter of the sailing regime is the length
Froude number, [F.sub.L] = V/[square root of (gL)], where L is usually
interpreted as the length of the ship waterline. A specific regime
called hump speed occurs when the wavelength of transverse Kelvin waves,
propagating along the sailing line, is about twice the ship's
length 2L. This happens when [F.sub.Lhump] = 1/[sqaure root ([pi])]
[congruent to] 0.56. Sailing at this speed means that the ship is
continuously moving 'upwards' along the slope of its own wake.
Wave resistance is usually relatively high for 0.4 [F.sub.L] 0.6 and
increases fast when [F.sub.L] [right arrow] [[pi].sup.-1/2] The increase
is particularly significant in shallow water conditions [31].
Approaching either the critical speed or the hump speed is commonly
accompanied by a drastic increase of wave resistance, or equivalently,
released wave energy. The highest waves eventually occur when the hump
and the critical speed coincide [24,31]. For the ships operating in
Tallinn Bay (Table 1), the SuperSeaCats operate near the upper limit of
the length-based range of generation of high waves. Baltic Jet and
Nordic Jet, and Merilin operate in the range of [F.sub.L] about 0.8-0.9,
whereas the conventional-hulled ships operate with 0.35. [F.sub.L] <
0.35.
[FIGURE 4 OMITTED]
The observed periods of the highest vessel waves are up to T
[congruent to] 15 s in Tallinn Bay [14], much larger than the wave
periods of 3-8 s typically found for conventional ship wakes or for
wind-generated waves in this sheltered body of water [28]. The high peak
period of these ship waves is the main reason for the large difference
between the shares of ship-induced and wind-wave generated waves in the
annual mean wave energy and power (5%-8% versus 18%-35%, respectively
[16]). Wind waves, similar to the leading ship waves (with a height of
about 1 m and a period exceeding 10 s), occur very infrequently in this
semisheltered bay, and for this reason ship wakes form a qualitatively
new component of marine hydrodynamic activity in this environment [16].
The typical ship tracks in Tallinn Bay were determined based on the
information from the sailing directions [35] and verified by means of
direct GPS-measurements onboard several randomly chosen ships (Fig. 2).
A total of eight track records have been collected, six of which contain
enough data to reconstruct the ship position and velocity along the
entire length of the bay. The three incoming leg records are in fairly
good agreement, whereas significant differences appear for the three
outgoing leg records in terms of location of the track and the speed of
the ship along the track (Fig. 4).
Ships, proceeding towards Tallinn, mostly sail along a deep trench
in the section between the islands of Aegna and Naissaar (Fig. 2). The
most sensitive section of the incoming leg is located at the southern
end of the trench at a distance of 2-4 km from the port, where operation
in the supercritical regime (defined as sailing at the depth Froude
numbers larger than 1) is possible. The near-and supercritical wakes
mostly impact the southern coast of the bay, extending from the Kopli
and Paljassaare peninsulas to Pirita [34]. Some fairly large waves may
also reach the southern end of Naissaar.
Vessels, departing from Tallinn towards Helsinki, sail along the
eastern slope of the trench, where they may frequently enter the
near-critical regime (Fig. 2). The slope causes asymmetry of the wake
system [36]. Detailed simulations of wake patterns have been made based
on a recorded SuperSeaCat sailing to Helsinki on 29 June 2008, using the
long wave model COULWAVE. This extension of previous work [34] takes
full advantage of the parallelization of the model that enables us to
include the entire Tallinn Bay area in the computational domain. In
contrast to the results presented in [36], a larger wedge apex angle
appears at the right-hand side of the wave fan in the relatively shallow
area [37].
The southern part of the Viimsi Peninsula receives relatively
little wake-wave energy from outbound ships because of the finite
extension of the wave fan. The highest waves for ships on the outgoing
leg are generated at the SW and W coast of Aegna. Some locations along
the Viimsi Peninsula (Pringi Jetty and to the north of Miiduranna) also
receive fairly large waves. Ship travel direction varies to a degree and
this results in significant spatial variability in the important ship
wake parameters [37]. However, intense wakes from outbound ships reach
the SW shore of Aegna in most cases. Details of the relevant research
and comparisons between measured and simulated wave properties can be
found in [37].
3. STUDY SITE, EXPERIMENTAL SET-UP AND OBSERVATIONS AT THE COAST
The northern Viimsi Peninsula and the WSW end of Aegna are
protected by very shallow waters. No such protection exists adjacent to
Aegna jetty on the SW coast of the island. The SW coast of Aegna and the
isobaths in its vicinity are predominantly (albeit not perfectly)
oriented perpendicular to the ship wave rays (Fig. 5) and it is
therefore a suitable place for measurements of both ship wave parameters
in the nearshore and wave-induced impact on the coast (including wave
runup patterns). This area has also been an object of several previous
studies [5,14].
The measurement site was located on the SW coast of Aegna, at a
small mixed gravel-sand beach immediately west of the jetty (Figs. 5,
6b,c, 59[degrees]34'50'N, 24[degrees]45'28'E). The
island, about 1.5 x 2 km in size, is located 1.5 km north of the Viimsi
Peninsula, at the northern entrance of Tallinn Bay. It is separated from
the Viimsi Peninsula by a shallow-water (typical depth 1-1.5 m) channel
with two small islands. Effectively, no wave energy enters Tallinn Bay
from the east.
The study site for this research was determined using two criteria.
The site had to be mostly open to the ship wakes and the slope in the
immediate vicinity of the shoreline and beachface had to be
approximately linear in order to adequately record the runup height.
These conditions excluded the western coast of Aegna, the southern
section of which has a significant scarp near the waterline, and the
northern section of which is sheltered by an area of boulders in the
nearshore.
The experimental site is fully open to the south. The maximum fetch
length in this direction, however, is only some 10 km. Although the
majority of storms blow from the SW, they produce no large waves.
Moreover, these waves approach the shore perpendicularly and result in
negligible longshore sediment transport. Owing to their small lengths,
they only affect sediments at the coastline and in very shallow water.
Significant wave energy enters Tallinn Bay from the north but the study
site is sheltered from these waves by the island and shallow water about
300 m to the west. The most significant waves at the study site and
along the adjacent shore to the west, come from the west, entering
Tallinn Bay between the mainland and the Island of Naissaar. Waves from
the NW are effectively blocked by Talneem Point (the WSW end of Aegna,
Fig. 5) and even if they reach the SW coast owing to refraction, they
impact the coast in a way similar to waves approaching from the west.
The western side of the jetty is protected by tetrapods which
effectively damp wave energy so that there is no visible reflection of
wave energy back to the study beach.
The littoral drift, therefore, is from west to east. Along the
shoreline to the west of the study site there is an evident sediment
deficit (Fig. 6a) and coastal erosion [30]. Long-term accretion occurs
only in a short section immediately adjacent to the jetty, where the
beach is much wider (up to 25 m, Fig. 6b) than along the rest of the SW
coast. This deposit consists of a relatively thin coating of finer
sediment, with cobbles and boulders (~20-50 cm in diameter) permanently
visible (Fig. 6c), indicating that the beach immediately adjacent to the
jetty is not currently accreting.
A belt of boulders at water depth of 0.5-3 m, 50-150 m from the
shoreline, is found between the jetty and Talneem. This belt occurs in
other areas around Aegna, becoming visible when sea levels are low. The
seabed at 2-4 m depth in the vicinity of the wave recording device
comprises some cobbles and boulders (some > 1 m height above the
seabed), interspersed amongst sand and small gravel. While cobbles,
pebbles and boulders dominate the rest of the beach and to depths of a
few (usually 6-10) metres, the seabed in deeper waters (from 7 to at
least 16 m) SW of Aegna comprises a relatively thin (usually 0.2-0.3 m)
but almost continuous sheet of mixed finer sediments, dominated by sand
(finer in deeper areas), with gravel sized sediment being less than 15%
(decreasing with depth [38]), at times containing small pebbles, and
overlying postglacial clay or till. Ripples on sand-covered areas at
depths of 10-12 m indicate that wave activity regularly reaches these
depths [30].
Towards Talneem from the study site, a very shallow area extends up
to 300 m from the coast, seaward of which water depths increase over a
short distance. In the vicinity of the jetty, water depths increase over
a short distance to approximately 2 m (Fig. 5), beyond which there is a
more or less linear slope from the position of the tripod down to depths
of 6-8 m and a gently sloping terrace 0.5-1 km wide to about 15 m water
depth. Beyond this is a steep slope on the edge of the trench referred
to in Section 2 above.
The bathymetric variability causes significant differences in the
nature of ship wakes reaching the SW shore of Aegna. At the western end
of the coastal section, waves break at 100-300 m from the beach whereas
in the immediate vicinity of the jetty they propagate to within a few
tens of metres of the beach without breaking.
The Aegna study site is appropriate for this investigation as it
receives significant wave energy from vessels that may be operating in
the near-critical regime and the waves shoal and break at, or very near
to, the shoreline, thus permitting measurement of the unbroken wave
forms (including their shape and asymmetry) close to shore. The site
also allows comparison of the runup with the unbroken wave
characteristics, which is difficult on beaches where both broken and
unbroken waves meet the beach face. Experiments performed in 2002-2006
used sub-surface pressure sensors, which were able to adequately
distinguish the wave periods and average properties of wave fields, but,
due to pressure attenuation with depth, single wave heights and the
shape of the water surface during ship wake events could be estimated
only approximately. In the present study, approaching waves were
measured by tracking sea-surface elevations of unbroken waves using an
ultrasonic echosounder. We used a LOG_aLevel[R] device (General
Acoustics), designed as a complete, stand-alone remote sensing water
level gauge. The standard configuration was modified by adding a
standard car battery and larger memory card, so that the system was able
to operate without attention or external connections for about two
weeks. The measurement range of the sensor is 0.5-10 m to the water
surface with a field accuracy of 1 cm and a resolution of single
measurements of [+ or -] 1 mm. According to the manufacturers, the
systems needs no calibration or on-site maintenance. The typical time
scale of factors, potentially affecting the reading of the device caused
by changes of the local air density (such as temperature, humidity,
barometric pressure, and salinity), are usually much longer (a few
hours) than the duration of a single wake (15-20 min). Moreover, such
changes in atmospheric conditions are accounted for internally using
sound velocity compensation. The device was mounted on top of a heavy
tripod (Fig. 6d), constructed and manufactured by AS Dimentio, Tallinn,
at a location about 100 m from the shore and the southern end of the
jetty (59[degrees]34.259'N, 24[degrees]45.363'E). The tripod
legs were made of 60.3 x 2.6 mm zinc-coated steel tube. The total weight
of the structure is about 150 kg. The legs were equipped with 20 cm long
spikes that penetrate into the seabed sediments and prevent horizontal
shift of the entire structure. Plates with a diameter of about 25 cm
prevented the tripod's legs from sinking deeper into soft
sediments. The tripod was made more rigid by horizontal braces halfway
up the legs. The device was mounted in an area with gently sloping
gravel bottom so that the water depth at the location of the sensor
(Fig. 6b) was approximately 2.6-2.7 m with respect to the long-term
average sea level. In the essentially tideless Tallinn Bay, maximum
water level variation over the experimental period was 37 cm (+ 30 cm on
25 June and -7 cm on 7 July).
During the first few days of measurements at Aegna, the ultrasonic
transducer was mounted directly at the tripod apex at a distance of
about 1.5 m from the calm water surface. The combined effect of
relatively high water level at the end of June, intense ship waves and
considerable wind wave background resulted in a too low clearance to the
water surface. The system failed to adequately measure distances less
than about 60 cm from the sensor, which led to underestimation of the
largest elevations in measurements. This was corrected on 7 July by
increasing the clearance between the sensor and the water surface by
adding a 1 m high extension to the platform at the tripod apex.
The vessel(s) associated with a wake event were determined either
from the operating schedules (Fig. 3) or by observation. When possible,
a Newcon LRB 3000PRO Laser Range Finder was used to estimate the vessel
speed and distance to the track. This binocular device is equipped with
an eye-safe laser and FMC optics enabling ranging targets up to a
distance of 3 km with a measurement accuracy of 1 m in good visibility.
The distance and bearing to a fixed point on the vessel was measured on
at least two occasions from the most landward tetrapod of the sea wall
(59[degrees]34.301'N, 24[degrees]45.431'E) and from these
data, speed and track were calculated. At times, due primarily to
atmospheric conditions, the range finder did not operate.
Besides providing data to measure and understand the far-field wake
events, and to fix the changes that have occurred since previous studies
[5,14], a number of other experiments were conducted, the results of
which will be reported elsewhere. These include (i) measurement of wave
runup and its correlation with measurements made at the tripod, in order
to empirically test the semi-analytical solutions derived in [39-42] and
to identify a relationship between wave shape (primarily the asymmetry)
and wave runup in realistic conditions of partially breaking waves, (ii)
examination of the effect of wakes on bottom sediments using optical
methods, extending the work described in [5,43], (iii) studies detailing
the effect of the wave events on shoreline geomorphology [6,17,25], and
(iv) numerical simulations of wave properties for typical ship tracks
and the spatial variability of the ship wave patterns [34,37].
4. WAVE RECORDINGS
The surface water elevation data were collected almost continuously
over 30 days during the period from 21 June to 20 July 2008 at a
recording frequency of 5 Hz. The recording was only stopped for short
time intervals (typically a few tens of minutes) for maintenance reasons
on 26 June and on 2, 7 and 15 July. The total record contains more that
650 outbound wake events from fast ferries, about 400 of which can be
adequately separated from the wind wave background and attributed to
particular vessels, and several hundred distinguishable smaller wakes
from other ships and vessels sailing to Tallinn.
The raw record from the water level gauge (Fig. 7) was first
quality-checked and reformatted so that each data point could be
time-synchronized with the runup measurements. The record contained only
one short unreliable section with a duration of 5 min and less than ten
unrealistic negative spikes with a duration of a few seconds, which were
excluded from the analysis.
Single wakes (or groups of wakes) were separated manually from a
spectrally filtered record (in which the long components of wakes from
fast ferries were usually easily identifiable) and related to particular
ships with the use of the timetable and visually recorded data. An
attempt was made to separate each single wake and to specify a section
of the record of pure background wind waves with a duration of 10-20 min
adjacent to the wake in the record, if possible, just before the start
of the wake. The properties of this background were used to quantify the
mean water level during the wake and the spectral composition of the
wind-wave field.
A low-pass spectral filter (an elliptical filter in the Matlab
environment) was adjusted as the occasion required in order to remove
the wind wave background and to adequately define the start and end of
the wake event. The wake event data were then adjusted to a mean of 0
and detrended. Approximately 6-10 waves in each wake were very high and
long, with periods about 10 s or larger. Their shape was usually
asymmetric (Fig. 8a).
A Matlab low-pass elliptic filter of 9th order with at most 0.1 dB
passband ripple, 60 dB stopband attenuation, [+ or -] 10% width of the
cutoff band and 2.5 s cutoff frequency was used to remove most of the
wind wave components from the recorded signal. As the proportion of wave
components from fast ferries with periods less than 2.5 s is very small
[14], such a filtering almost exactly conserves the energy of the wake.
On the other hand, the majority of wind wave components on relatively
calm days have periods below 2 s and are effectively removed from the
signal.
The filtering process caused a certain phase shift of the wave
forms and frequently led to unrealistic wave shapes with deep troughs
and moderate elevations (Fig. 8b). This distortion is not unexpected,
because similar effects are customary in filtering of elevation data,
derived from narrow wave groups, where the use of high-order filters
result in a large phase shift of the signal. For exactly periodic
signals the phase shift has no dynamic relevance, but for highly peaked
and/or asymmetric waves the large phase shifts may cause substantial
changes of the wave shape and (for phase shifts of the order of [pi])
even an inversion of the wave shape. While the unfiltered signal
correctly reflects the short-term changes of the position of the water
surface and related characteristics (such as the wave shape or
asymmetry), the filtered signal frequently gives much better information
about the role of long wave components in a particular wake in terms of
both their local height and duration of presence, and in many cases
allows more exact determination of the end of the wake.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
For the listed reasons, further analysis of each wake event was
performed in parallel for the original recording and for the filtered
signal. Single waves and their properties in each wake were extracted
with the use of both zero-upcrossing and zero-downcrossing methods. To
the first approximation, the maximum wave height is defined as the
maximum of wave heights obtained by the zero-upcrossing and
zero-downcrossing method. For the largest waves in each wake, this
quantity almost always coincides with the maximum variation of the water
surface within a 30 s interval.
The largest ship waves have, as expected, an asymmetric shape: the
magnitude of the increase in water level above the mean at their crests
considerably (in extreme cases up to three times) exceeds the magnitude
of the decrease in the trough area (Fig. 9). This feature is probably
caused by non-linear effects, the influence of which usually tends to
reshape the wave profile so that it resembles a cnoidal wave [44]. In
many cases, the high, asymmetric waves were interspersed with much lower
waves of the same period, as noted in [45].
[FIGURE 9 OMITTED]
The shape of the largest waves was frequently strongly asymmetric
in another sense also. The front of the wave was much steeper than the
back. This is also an expected feature, however, in our experiment it
was not clear beforehand whether it simply reflected the effects of
shoaling in the shallow nearshore, or whether it was partially caused by
the process of non-linear steepening of long waves over a horizontal
bottom. The observed asymmetry is almost certainly one of the reasons
why waves within ship wake events produce higher runup than one might
expect based on the wave height data alone. This feature of long waves
has been predicted in [41,42].
The energy of each wake was also calculated from both the original
and filtered water level data. The difference between the results was
compared with the energy of the background waves in order to estimate
the adequacy of the method of separation of the wake events. Finally,
the wave power was calculated for each wake by means of summing the
power, carried by each wave for the given water depth.
As during most of the measurements there was considerable wind-wave
background, the wake separation process usually allowed adequate
identification of the first two wave groups (out of a characteristic
three in near-critical wakes [14,24,32]) in each wake event (Fig. 8b),
the typical periods of which were much larger (>5 s) than the periods
of wind waves in weak and moderate wind conditions (2-4 s). This is
acceptable from the viewpoint of wake energy and power, because the
third group of almost monochromatic waves with periods close to 3 s is
present only occasionally and usually contains only a few per cent of
the energy and power of a wake event [14].
The typical durations of the identified single wake events varied
from 15 to 20 min, depending on the particular ship (Table 2). Events
containing waves from two or more ships were even longer. Such complex
wakes usually happened two times a day at 14:00 and 19:30 (Fig. 3) and
sometimes at 08:00, when some ferries were delayed. The largest duration
(25-30 min) was usually from those wakes in which the third group was
identifiable. The largest duration in these cases had the second wave
group (that consisted of waves that generally are attached to the
classical Kelvin wake) with typical periods of 5-7 s. A part of these
waves may represent transverse elements of the Kelvin wake. Such a long
duration of wake events is remarkable, given the small size of the water
body and the distance of the study site from the sailing line. Wakes
with such a long duration evidently have been created not only at a
relatively large distance from the study site (as is expected), but also
at speeds close to critical (2).
The distance between the source of the waves and the measurement
site can be roughly estimated based on the difference in group speeds of
different components of the wake and a reasonable assumption that all
the wake components have been excited in a small sea area adjacent to
the ship. For example, the highest waves of a typical wake from
SuperSeaCat have typical periods ~13 s whereas the usual period of
components of the third group is about 3 s. For an average water depth
about 20 m along the wave rays from the sailing line to the measurement
site, the wake must have propagated over a distance of 6-8 km. The
nearshore, shallow area adds very little to the duration of the wake,
because the difference of the group speed of different components is
small.
An analogous estimate for many wakes of relatively small height and
duration (6-7 min) corresponds to the propagation distance of about 2 km
over a water depth of about 20 m. This estimate matches well with the
theoretical properties of propagation of the classical Kelvin wake with
an apex half-angle close to 20[degrees].
The ships mostly follow the same sailing line (Fig. 2). The typical
distance from the study site to the sailing line (measured by the
rangefinder as the distance to the ships in the direction of the
southern end of Naissaar) was 2.5-3 km. The apex half-angle of the
Kelvin wedge under these conditions apparently was much larger. This
means that ships were frequently sailing in the near-critical regime
over extensive sections of the route (Fig. 2). In reality, different
wake components propagate in different directions whereas the crests of
the longest, long-crested waves of the first group form the largest
angle with the sailing line. Therefore, the longest wake components have
covered the longest distance to the study site.
As several wake events come in groups (due to the sailing times of
various ships) (Table 1, Fig. 3), each day usually has about 15 strong
wake-wave events. These events, which occur at almost exactly the same
time each day, are clearly distinguishable not only in the record of the
water surface, but also in the record of optical properties of
near-bottom water that to some extent reflects the reaction of bottom
sediments. This reaction was estimated by means of measurements of the
changes of the diffuse attenuation coefficient [K.sub.d] in the
near-bottom water column at the tripod, located at a distance of
0.25-0.75 m from the bottom. Although the values of [K.sub.d] also
contain some noise (created, for example, by changing clouds and
small-scale light reflection by waves), it usually characterizes quite
well the optical properties of sea water and their (at times drastic)
reaction to ship waves in terms of an increase in the amount of
(re)suspended matter [5,43]. An important consequence of intense vessel
traffic is that over the course of a day, the values of [K.sub.d]
gradually increase, commonly by 0.2-0.4 1/m, which corresponds to an
increase in the suspended matter concentration of about 4-8 g/[m.sup.3]
[5].
Wake events have even more clearly discernible impact on the
shoreline. An attempt to quantify this impact was made through recording
of the runup of individual ship-induced waves on the beach face using
survey staff (Fig. 6c) and a video recorder. Wind waves with the height
of < 0.5 m produced runup events up to 20-30 cm above the still water
level. As expected, the largest ship waves produced substantial runup
heights that commonly exceeded the height of measured non-broken waves
(Fig. 10). Typically, the highest and longest ship waves from the first
group reached over 1 m above the still water level with several examples
going over the berm crest, over 1.5 m above the still water level. Waves
from the second group, however, in many cases produced runups equivalent
to those of wind-waves.
An attempt was also made to quantify the reaction of the beach to
the joint influence of wind and ship waves in terms of changes of the
dry beach profile. The beach at the study site was stable under moderate
wind wave conditions that gradually refilled the study site with sand
and gravel overnight, after sediment was removed by vessel wakes during
the day. Typically a small gravel berm of 15-30 cm height formed
overnight under the impact of wind waves. This berm was usually
completely removed by the first ship waves the following morning. On
several calm days when ship-generated waves dominated, we observed very
rapid loss of sediment (see Fig. 6c). A more detailed description of the
procedure and results of runup measurements, and details of the
evolution of the beach profile will be reported elsewhere.
[FIGURE 10 OMITTED]
5. WAKE HEIGHT, SPECTRUM, ENERGY AND POWER
The daily maxima of ship wave heights occurred exclusively for the
longest waves of the wakes, with periods >10 s. The daily maxima,
extracted from non-filtered data, all exceeded 1 m and were typically
approximately 1.2 m (Fig. 11). The largest ship wave heights in more or
less calm conditions were 1.5 m. The combined ship and wind wave heights
reached 1.7 m on a few days, with the significant height of the
background about 0.3-0.4 m. The maxima extracted from the spectrally
filtered signal are typically about 15% smaller, but on many days these
values almost coincide (Fig. 11). The lowest daily maxima correspond to
weekends (Sunday, 6 July, and the weekend 19-20 July) when the number of
ships is somewhat smaller and the loadings are likely to be less. The
low height of the echosounder above the water surface may have caused
some erroneously low values for the maximum elevations before 7 July, in
particular, on the relatively windy days, 25-26 June.
One of the largest challenges in the analysis of ship wakes in open
sea areas is the separation of ship waves from the wind wave background.
A benchmark can be obtained through the analysis of wave records on calm
days. During the experiment, the relatively calm days of 4-6 July were
the most favourable for the comparison of the total wave energy spectra
(over 72 h of continuous wave recording) with spectra of wind waves
during the nights (00:30-07:30). The anthropogenic contribution to the
wave field almost totally dominated on these days (Fig. 12). The overall
mean energy density of the wave field was 15.3 J/[m.sup.2] (15.4, 16.4
and 14.0 J/[m.sup.2] on 4, 5 and 6 July, respectively), which
corresponds to a significant wave height of 0.176 m. The wind wave field
contributed from 1.2 J/[m.sup.2] on 4 July to 2.3 J/[m.sup.2] on 5 July.
Moreover, a part of the energy (~0.6 J/[m.sup.2]) of these weak waves at
night was excited by ships. As 6 July was Sunday, with somewhat less
intense ship traffic than on weekdays, the weekly mean energy density of
ship waves apparently is close to 15 J/[m.sup.2].
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
As in previous experiments in this area, the major component (about
70%) of ship wave energy is concentrated in the frequency range of
0.06-0.2 Hz (periods T = 5-16 s). The energy spectrum within this range
contains four peaks. The highest peak is located at T = 9.2 s. A peak of
comparable height is at T = 12.3 s. Two minor peaks are located at T =
7.6 and T = 6.6 s.
The two peaks for longer waves apparently reflect the typical
properties of leading waves of ship wakes whereas the two peaks around 7
s represent wave components from the second group of high-speed ferry
wakes that usually have periods of 6-8 s [14]. The presence of two
clearly separated peaks for both long waves and for periods around 7 s
suggests that the high-speed ships sailing in Tallinn Bay represent two
families, the members of which produce leading waves with similar
properties (and which apparently travel at more or less equal speeds).
Comparison of the cruise speeds of different ships (Table 1)
suggests that SuperSeaCat, Nordic and Baltic Jet, and possibly the twin
hull hydrofoil Merilin (the wakes of which were not always separable
from other wake events, but which is expected to contribute some very
long wave energy) belong to the faster group, the wakes of which mostly
form the peak at T = 12.3. Ships sailing at 25- 30 knots (~45-55 km/h)
are apparently responsible for the other, slightly higher peak. Note
that the numbers of departures of ships of both groups are approximately
equal each day.
The largest ship wakes were frequently preceded by relatively small
amplitude waves (typically below 5 cm) with very long periods (20-30 s).
This part of the wake may be associated with the precursor solitons
(long solitary waves propagating ahead of high-speed ships) that are
customary for near-critical speeds but which may be produced at as low
depth Froude numbers as 0.2 [46]. At least one disturbance of this type
was normally (in about 70% of cases) present in the wakes of faster
ships whereas in the wakes of Viking XPRS and Superfast and in
unidentified wakes they occurred in very few cases (about 10%).
Typically, 1-2 such structures were present, but in some cases up to
five were observed. A small peak at T [cogruent to] 20s in the spectrum
in Fig. 12 may be interpreted as reflecting the energy of these
solitonic waves.
The range of frequencies 0.2-0.4 Hz (T = 2.5-5 s) also contains an
appreciable amount (close to 25%) of the total ship wave energy. As the
sampling rate is quite high, a part of the wave energy (about 5% in the
case in question) is attributed by the Fourier transform to
high-frequency waves with periods well below 2 s, but which apparently
do not exist in reality.
Data, collected on 4-6 July, with low wind-wave energy, makes it
possible to approximately estimate the distribution of ship wave energy
between different wave components through identification of the portion
of ship wave energy on days with considerable wind wave background under
the reasonable assumption that the distribution of wave energy between
different wake components does not change significantly. A natural
separation frequency of different ship wave components is 0.125 Hz. On
the one hand, the long-wave components of wakes with periods exceeding 8
s carry about 38% of the total wake energy in the analysed data on all
three days. This share is almost constant over these days although the
number of departures varies. On the other hand, appreciable wind waves
with periods exceeding 8 s occur very infrequently in Tallinn Bay, and
are virtually non-existent in midsummer [28].
The variation of daily average ship wake energy at the study site
(Fig. 13) shows that the overall mean ship wake energy is about 16 J/m2.
This estimate shows that the annual mean of the ship-induced wave energy
at this site, estimated as 15.8 J/[m.sup.2] in [14], has remained
basically the same. Although one may expect some increase of the
nearshore wave heights and energy due to the shoaling process, given the
relatively uneven seabed and considerable attack angle of ship waves
with respect to the isobaths in the experiment area, the effects of
shoaling are apparently balanced by the wave energy damping and
spreading due to refraction. More reliable estimates of the potential
changes can be made based on the analysis of the set of single waves. As
mentioned above, the variations of the water level were typically about
10-15 cm (the full range within the measurement period was 37 cm). This
variation insignificantly alters the shoaling and breaking properties of
waves at the site, where the water depth mostly varied between 2.6 and
2.7 m and reached 2.8 m for a short period.
While the daily average ship wave energy varies insignificantly,
the energy contained in a single wake of a particular ship may vary
considerably (Table 2). In general, the most energetic wakes are those
from SuperSeaCat, Superstar, and Star. This is consistent with
experience gathered from the observations from Aegna jetty with the
largest visually observed breaking waves usually produced by these
ships. The wakes of Nordic Jet, Baltic Jet and Superfast are (by about
50%) less energetic than wakes of Superstar (Table 2). The wakes from
Viking XPRS are usually much smaller than wakes from the above ships.
The total energy of wakes from a specific ship typically varies by
factors up to 6 times, but even larger variability (up to an order of
magnitude) exists for wakes from Viking XPRS and Superfast.
A large part of the variability of wave patterns occurred owing to
the simultaneous arrival of waves from two vessels that leave Tallinn at
the same time (Fig. 3, 14:00 Star and SuperSeaCat, and 19:30 SuperSeaCat
and Baltic Jet or Nordic Jet). Usually energy of such a
"double" wave pattern was approximately equal to the sum of
typical wave energies of single wakes from these ships. In many cases
such combined wave systems resulted in the highest waves of the day.
[FIGURE 13 OMITTED]
The variability of the non-broken wave heights and wake energy is
not necessarily correlated with the associated variability of breaking
waves, wave runup and the impact of waves on the coast. The observers at
the coast noted that, as a rule, waves from Viking XPRS were frequently
so small that they were completely masked by about 20-30 cm high wind
waves. On one occasion, however (27 June 2008 at 08:00), the waves
excited by this ship detached the measurement staffs from the buried
anchors and knocked over the field personnel working on the beach. The
non-broken wave parameters recorded for this case were not exceptional
and these waves were not even the highest of the day.
An estimate of the daily mean wake power has been also made for the
time interval of 4-6 July, during which the wind wave background was
small and the separation of ship and wind waves was straightforward. The
mean distance from the sensor to the water surface varied from 1.49 to
1.54 m. Given the full height of the tripod (without the leg spikes) was
4.1 m and the height of the mounting point of the sensor at the body of
the LOG_aLevel[R] device about 20 cm from the tripod apex, it is safe to
say that the mean water depth (taken as the basis for calculation of
group velocity) was 2.7 m on these days.
The properties of the very low wind wave background (significant
wave height between 6-8 cm) were almost unchanged during the night and
day within these days. This allowed the estimation of the ship-induced
wave power as the difference between the daily average wave power and
the mean wave power during the night (from midnight to 07:30). As the
waves produced by ships sailing at night were much shorter than the
leading waves from high-speed ships, the share of ship wakes in the
night-time wave power can be neglected. This procedure resulted in the
estimate of the daily average ship wake power for 4-6 July as 78, 45,
and 57 W/m, respectively. The night-time average wave power was 17, 8,
and 8.6 W/m on these days. As 5-6 July were weekend days, with fewer
departures of ships, the weekly average of ship wave power is probably
close to 70 W/m. These results suggest that the average ship wave energy
(Fig. 13) is not necessarily correlated with the ship wave power on the
same day.
6. DISCUSSION AND FURTHER STUDIES
The use of a continuous water surface profiling technique, which
allows direct and high resolution measurement of incident wave
properties (including asymmetry), mostly well before breaking, and the
analysis of a large number of wakes from different high-speed ships has
advanced our knowledge of the wave-making potential of new, high-powered
ships operating on the Tallinn to Helsinki route. Both direct
measurements of speed made onboard several vessels [37] and the analysis
of ship wakes confirm that an increasing number of ships sail in the
near-critical regime along extensive sections of the ferry route in
Tallinn Bay. Although some ships that previously created the largest
waves in this bay [14] are no longer in service, the maxima of ship wave
heights have not decreased. Assuming no loss or spreading of wave
energy, a 1.08 m high wave with a period of 11 s, detected at Aegna in
2002 with the use of a pressure sensor at the depth of 6.7 m [14], would
evolve to about a 1.3 m high wave at the location of the water surface
profiler used in this experiment at the depth of 2.7 m. In this light,
several recorded wave heights close to 1.5 m suggest that the maximum
ship wave heights have, instead, increased.
The continuous recordings also led to much more reliable estimates
of the contribution of ship wakes to the total wave energy and power.
Earlier estimates have been based on a few hours of recordings a day at
each site in the burst mode and extended to the annual scale, based on
the assumption that the rest of the ship wakes of these days are
equivalent to the average of measured wakes [14]. The estimates
presented in this study rely on weeks of continuous recordings of
hundreds of ship wakes; among them many on almost perfectly calm days.
The central result of this study is that the overall amount of ship wave
energy received by the coast of north-eastern Tallinn Bay has not
decreased since 2002 (when the annual mean energy was estimated as 15.8
J/[m.sup.2] [14]), although the ships that produced the largest and
longest waves in the past are no longer in service. As the wind wave
activity has decreased during the last decade [47,48], the relative
share of ship wave energy with respect to wind wave energy (5%-8% in
2002 [15]) may have even increased since then.
The estimate obtained for the average wake power is clearly smaller
than the one derived in 2002 (110 W/m [14]). A part of this difference
may result from the changes of the fleet with increasing share of large
conventional ships with increased cruise speed tending to generate
shorter waves than the classical high-speed ships, and thus contributing
less to the wave power. On the other hand, the loss of wave energy and
spreading due to refraction when waves propagated from the measurement
site, used in 2002, to the current measurement site could cause an
equivalent decrease in the observed wave parameters. Moreover, the
measurement site in 2008 was very well sheltered from wakes generated by
incoming ships, while the measurement site in 2002 received an
appreciable amount of incoming ship wave energy. Although the magnitude
of these changes cannot be adequately estimated based on the existing
data, it is clear that despite the introduction of new classes of
vessels and reduced sailing frequency, ship wave generated wave energy
and power has not been significantly reduced, and the adverse effects of
ship waves on coastal processes have almost certainly not been
mitigated.
Many ship wakes are effectively long waves over large parts of the
bay. Tallinn Bay thus appears to be an ideal "natural
laboratory" to study the behaviour and impact of long waves. The
regular presence of such wave trains, generated by high-speed ferries,
although with varying properties from departure to departure, but still
with remarkable intensity and asymmetry, can be used to develop and
validate calculation methods for runup characteristics of long,
potentially hazardous (tsunami, surge, sneaker etc.) waves. The
location, geometry, and motion of their sources are known and thus
incident (offshore) wave parameters can be modelled with great accuracy.
The resulting data set can be used to test and calibrate both numerical
and semi-analytical models, and may contribute to optimal methodologies
for the forecast of all kinds of long-waveinduced marine natural hazards
in the coastal zone, and to estimate limitations of the models.
The continuing high level of ship wave activity means that there
remains a concern about the potential impact of ship wakes on vulnerable
coasts. On many sea coasts the presence of such high and steep,
soliton-like waves, which are accompanied by significant beach run-up is
believed to be an additional agent of coastal erosion even if they have
periods of only about 7 s and occur only twice a day [7]. In addition,
the regular presence of such high wakes, occasionally containing
strongly asymmetric components, may be used to understand the sediment
transport induced by transient wave trains, which is an important driver
of the morphology and evolution of the coastline. Most research in this
field is focused on the net transport due to a large number of waves.
Much less is known about sediment transport due to a single wave or a
short wave group. Since the long-wave components of the ship waves
arrive at the shore as a group of a few waves, this approach enables the
study of the impact of virtually single waves on sediment transport
processes (including net and bulk bedload transport of sediments by
single wakes) in the coastal zone.
ACKNOWLEDGEMENTS
This study was supported by the Marie Curie RTN SEAMOCS
(MRTN-CT-2005-019374), TK project CENS-CMA (MC-TK-013909), Marie Curie
Reintegration Grant ESTSpline (PERG02-GA-2007-224819), Estonian Science
Foundation (grants Nos. 7000 and 7413), and EEA grant EMP41. Ira
Didenkulova thanks grants of RFBR (08-02-00039, 08-05-00069,
08-05-91850) and Scientific School of V. A. Zverev. We gratefully
acknowledge the contribution of Dr. rer. nat. Heiko Herrmann during
preparation and performing the experiment, divers Tiia Moller and
Kristjan Herkul from Estonian Marine Institute, and frequent help from
volunteers under the command of Liis Aadla during the experiments at
Aegna. Professional comments by Prof. Efim Pelinovsky, Dr. Phil Osborne
and an anonymous reviewer were particularly useful for improving the
paper and are gratefully appreciated. The aerial photo was provided by
Maa-amet (www.maaamet.ee).
Received 14 October 2008, in revised form 10 November 2008
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(1) The characteristics of ship-generated waves are highly
dependent on the depth Froude number [F.sub.h] V[square root of (gh)]
where V is the ship's speed and h is the water depth. The speed at
which [F.sub.h] = 1 is called critical. Subcritical speeds are
characterized by [F.sub.h] < 1 and supercritical speeds by [F.sub.h]
> 1 The near-critical regime corresponds to the vessel speed within
[+ or -] 15% of the maximum phase speed [square root of (gh)] of surface
waves, or 0.84 < [F.sub.h] < 1.16.
(2) A small duration wake may occur in two cases: when the ship is
sailing close to the measurement site or when the ship is sailing at an
almost critical speed. In this case the wake energy is concentrated in a
few high waves.
Kevin Parnell (a,e), Nicole Delpeche (a), Ira Didenkulova (a,g),
Tony Dolphin (a,b), Ants Erm (c), Andres Kask (d), Loreta Kelpsaite (a),
Dmitry Kurennoy (a), Ewald Quak (a), Andrus Raamet (d), Tarmo Soomere (*
a), Anna Terentjeva (a), Tomas Torsvik (f) and Inga Zaitseva-Parnaste
(a)
* Corresponding author, soomere@cs.ioc.ee
(a) Centre for Nonlinear Studies, Institute of Cybernetics, Tallinn
University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia
(b) Coastal Processes Research Group, School of Environmental
Sciences, University of East Anglia, Norwich NR4 7TJ, United Kingdom
(c) Marine Systems Institute, Tallinn University of Technology,
Akadeemia tee 21, 12618 Tallinn, Estonia
(d) Department of Mechanics, Faculty of Civil Engineering, Tallinn
University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia
(e) School of Earth and Environmental Sciences, James Cook
University, Townsville, Queensland 4811, Australia
(f) Bergen Centre for Computational Science, UNIFOB, University of
Bergen, Thormohlensgate 55, N-5008 Bergen, Norway
(g) Department of Nonlinear Geophysical Processes, Institute of
Applied Physics, Russian Academy of Sciences, 46 Uljanov Street, Nizhniy
Novgorod, 603950 Russia
Table 1. Ships operating the Tallinn-Helsinki ferry link in summer
2008. Data from www.tallink.ee, www.superseacat.com, www.eckeroline.ee,
www.lindaliini.ee, and from the relevant ship operators. The displace-
ment data for the hydrofoil and the conventional ferries are given in
terms of net tonnage (NT) and gross tonnage (GT)
Ship Type Departures, Length, Width,
daily per m m
direction
High-speed ferries
SuperSeaCat Monohull 6 100.3 17.1
(2 ships)
Baltic Jet, Catamaran 3-6 60 16.5
Nordic Jet **
Hydrofoil
Merilin Twin hull 3 52.6 13
hydrofoil
Conventional ferries with increased cruise
Star *** Monohull 5 186.1 27.7
Superstar *** Monohull 176.9 27.6
Viking XPRS Monohull 2 185 27.7
Superfast **** Monohull 1 203.3 25
Conventional ferries
Norlandia Monohull 1 153.4 24.7
(Eckero Line)
Baltic Princess Monohull 1 212.1 29
(Tallink)
Ship Type Draught, Displa- Displa- Opera-
m cement cement ting
light, loaded, speed *,
t t knots
SuperSeaCat Monohull 2.6 + 1.4 900 1296 35/40
(2 ships)
Baltic Jet, Catamaran 2.22 515 635 36/38
Nordic Jet **
NT GT
Merilin Twin hull 1.51 299 963 40
hydrofoil
Conventional ferries with increased cruise
Star *** Monohull 6.75 13316 36249 27.5
Superstar *** Monohull 7.1 14073 36277 27.5
Viking XPRS Monohull 6.55 14165 35778 25
Superfast **** Monohull 6.5-6.67 10703- 30285- 25.5-
10793 30441 27.1/
30.4
Conventional ferries
Norlandia Monohull 5.8 14990 20
(Eckero Line)
Baltic Princess Monohull 6.4 30860 48915 24.5
(Tallink)
* Cruise/maximum speed, if given.
** Nordic Jet was moved to another service from 21 July 2008.
*** Star and Superstar are sister ships, and operate on alternating
schedules each day.
**** Three sister ships in the family, typically travelling at
speeds ~ 20 knots (~ 35 km/h) near the measurement site.
Table 2. Properties of wakes from single ships and double wakes during
days with comparatively low wind wave background (1-9, 12, 13 and 20
July 2008). Wake energy and power reflect the total energy and power
of the signal, integrated over the duration of the wake. Unidentified
wakes belong to smaller or slower ships sailing to Helsinki, or to
incoming ships
Vessel No. of Minimum, maximum and average properties
iden-
tified Wake duration, Wake energy,
wakes min [10.sup.4]J.s/
[m.sup.2]
Min Max Av Min Max Av
Star 21 12.1 25.8 19.1 2.92 9.66 4.92
Superstar 25 13 26.8 19.1 4.07 9.1 6.58
SuperSeaCat 48 5.8 28 16.2 2.96 10.9 5.37
Viking XPRS 21 8.4 20.4 15.8 0.41 3.41 1.84
Nordic/Baltic Jet 59 9 26.4 16.6 1.48 8.06 2.86
Superfast 11 6.5 32.3 19.2 0.82 4.92 3.22
Unidentified 126 4.2 28 12.4 0.05 4.42 0.78
wakes
SuperSeaCat + 4 19.5 27.8 22.9 11.1 13 12.2
Star
SuperSeaCat + 3 18.5 29.3 22.8 6.77 12.5 9.48
Star
SuperSeaCat + 7 18.8 27 22.4 5.95 8.6 7.82
Star
Vessel No. of Minimum, maximum and average properties
iden-
tified Wake power,
wakes [10.sup.4]W.s/m
Min Max Av
Star 21 13.1 50.4 23.8
Superstar 25 18.3 45 30.5
SuperSeaCat 48 14.5 54.2 27.3
Viking XPRS 21 1.73 15.6 7.83
Nordic/Baltic Jet 59 7.04 42 13.9
Superfast 11 3.49 22.8 14.6
Unidentified 126 0.18 17.5 3.25
wakes
SuperSeaCat + 4 58.2 65.4 61.7
Star
SuperSeaCat + 3 30.7 60.6 46.3
Star
SuperSeaCat + 7 28.1 45.6 40.5
Star
