Note on Turbulent Kinetic Energy Production for Reynolds-Averaged Navier–Stokes Models

Linear eddy-viscosity Reynolds-Averaged Navier–Stokes (RANS) turbulence models are based on the Boussinesq approximation that asserts the Reynolds stresses to be linearly dependent on the mean strain rate. Using the Boussinesq approximation for the Reynolds stress yields a production term in the turbulent kinetic energy equation that is proportional to the square of the magnitude of the strain rate tensor. For some flows, this relation to the strain causes overproduction of turbulence. Widely used ad hoc modifications of the production term using vorticity lead to an inconsistent energy balance in the mean flow kinetic energy equation, violating the energy conservation. In this note, how to obtain a consistent RANS framework for a given production term modification is shown.