k-ε Model for Density Preserving and Boussinesq Fluids
In this chapter a simple turbulence model of first order — called the k-ε model — will be developed, which merely uses evolution equations for the specific turbulent kinetic energy, k and the specific turbulent dissipation rate, ε. In the derivation concepts will become known, which illustrate how also higher order models might be handled. This so-called k-ε model shall in the subsequent paragraphs be developed for a density preserving fluid and is then extended for a Boussinesq fluid i.e., a fluid in which density variations are only accounted for in the body (gravity) force. In particular the Coriolis acceleration and the buoyancy effects play often a role in combination in such geophysical applications, e.g. in a stratified atmosphere or in the ocean which are typical configurations in meteorology, oceanography and limnology.
KeywordsTurbulent Kinetic Energy Dissipation Rate REYNOLDS Stress Isotropic Turbulence Turbulent Dissipation
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