Secondary Kelvin-Helmholtz Instability In A 3d Stably Stratified Temporal Mixing Layer By Direct Numerical Simulation.

Abstract

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.