Finite Element Simulation of Stratified Turbulent Flows

A two-dimensional, time dependent Finite Element (FE) code for simulating uniform density or thermally stratified flows is developed and applied to cavity flows. The choices of the schemes used for time stepping and for solving the nonlinear equations are discussed. Smagorinsky's model and the vorticity gradient model for Sub-Grid-Scale (SGS) turbulence in uniform density flows are incorporated in the FE code to simulate cavity flows driven by a surface shear stress with a randomly varying component. The general structure of the flow field and its spectral characteristics, as predicted with the two models, are compared. An algebraic model for turbulence in thermally stratified flows is incorporated in the FE code to simulate a shear driven flow in a stratified cavity. The transient development of the circulation under the action of a constant shear and the response to a shear stress with a randomly varying component are simulated. Velocity, and isotherm displacement spectra are presented. The spectra show a sharp drop in the spectral density function near the buoyancy frequency of the thermocline.