Geophys. Astrophys. Fluid Dynamics,
vol. 66, p. 133-167, 1992
A two-dimensional numerical model is
used to investigate the nonlinear dissipative interaction between a
disturbance and an unbounded stratified shear flow. The disturbances
considered are Kelvin Helmholtz instabilities and forced gravity waves.
The nonlinear stabilization (destabilization) of Kelvin Helmholtz
instabilities at Prandtl number, Pr<1 (Pr>1) found by Brown and
Stewartson (1981) is recovered. The model confirms that it is
mostly due to a stabilization (destabilization) of the mean flow by the
wave. The nonlinear evolution of instabilities existing when thermal
disspation is large and when the Richardson number is everywhere larger
than 0.25 is also investigated. It is shown that such a mode
stops growing when the nonlinear distorsion of the mean flow becomes
significant.
For forced gravity waves, and when the initial minimum Richardson
number, J=0.25, it is found that mean flow stabilization
(destabilization) also occurs at the critical level for Pr<1
(Pr>1). More generally, the value of Pr above (below) which critical
level destabilization (stabilization) occurs increases (decreases) when
J increases (decreases). The nonlinear reflection and transmission of a
wave are partly related to those stability changes. They are also
related to the mean flow distorsions, located below the critical level,
and where the incident wave can be strongly reflected.
In the present study, the critical level interaction is weakly
nonlinear, quasi-steady and disspative. The amplitude of the
fundamental mode is such that the nonlinear effects are significant
while secondary modes remain small and convective overturning does not
occur.
Back