The purpose of this study is to develop a numerical model that can be used to describe
stably stratified shear flows in the presence of a turbulent mixed layer. The model
flow consists of two layers of fluid. The upper layer is turbulent and moving with a
velocity U0 and density rho. The lower layer is stationary with a density of
rho + Delta rho. At the interface a stably stratified shear layer develops.
An existing spectral code was used for this work.
Three methods were considered to implement turbulence in the upper layer. Method I
implements the turbulent data everywhere in the top half of the computational domain.
This flow is not consistent with the upper vertical boundary conditions and led to
a source of numerical instability. Method II employs smoothing of the turbulence at
both the interface and the top boundary. This method resolves the boundary condition
problem but reduces the fluctuations at the shear interface so that no instability could form.
Method III smooths the turbulence data at the top boundary only. This method solved
the upper boundary issue while allowing for instability growth. The results of this
method were compared with two-dimensional known results. Method III proved to be
the best method of the three tried in this study.