Applying compressible transformations to wall modeled LES of cold wall flat plate boundary layers

Existing near-wall turbulence models for WMLES are usually extended to cold wall, compressible flows with heat transfer by using empirical modifications to the algebraically defined eddy viscosity. This work seeks to define an alternative, rational modification supported by canonical compressible boundary layer scaling laws. Recently developed compressible velocity transformations have been shown to collapse data to the incompressible law of the wall. These transformations also imply a form for the compressible eddy viscosity. We propose to modify the eddy viscosity used by the wall model in accordance with the implied eddy viscosity of the compressible transformation.