摘要：The present work investigates the nature of the transition to turbulence in the
stably stratified mixing layer, which is a complex process with great
importance for geophysical and industrial flows. In the stably stratified
mixing layer, the streamwise density gradient, which corresponds to the
spanwise component of the baroclinic torque in the Boussinesq approximation,
feeds the region between the Kelvin-Helmholtz (KH) vortices with vorticity
and forms a thin vorticity layer, called baroclinic layer. The competition
between buoyancy and inertial forces modifies the dynamics of this layer.
As consequence, two different secondary instabilities are found to develop
upon the baroclinic layer: one originated near the core region of the KH
vortex, called near-core instability, that propagates towards the baroclinic
layer and the other of Kelvin-Helmholtz type developed in the baroclinic layer
itself. The development of these instabilities in the baroclinic layer
depends on the Richardson number, the Reynolds number and the initial
conditions. The main objective of this paper is to investigate the occurrence
of secondary instabilities in the baroclinic layer of a three-dimensional
stably stratified mixing layer using Direct Numerical Simulation (DNS). The
development of streamwise vortices and its interactions with the secondary KH
structures are focused. Typical Richardson numbers ranging from 0.07 to 0.167
are considered while the Reynolds number is kept constant ( 500 or 1000).
White noise and forced perturbation are used as initial conditions. The
Navier-Stokes equations, in the Boussinesq approximation, are solved
numerically using a sixth-order compact finite difference scheme to compute the
spatial derivatives, while the time integration is performed with a
third-order low-storage Runge-Kutta method. The numerical results show the
development of a jet in the baroclinic layer adjacent to vorticity layers of
opposite signs. These layers are created baroclinically by convective motions
inside the primary KH vortex and amplifies the near-core instability. It is
shown that this instability appears due to the formation of a negative
vorticity layer generated between two co-rotating positive vortices. The
negative vorticity layer unstables the baroclinic layer and forms small
vortices of the KH type. The intensity of the negative vorticity layer
depends on the Richardson and Reynolds numbers and defines occurrence or not of
secondary KH structures. Interactions between these secondary KH structures
and streamwise vortices are also observed. They strongly depend on the
initial conditions.
