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A crucial step in understanding compressible turbulent boundary layers is to relate mean compressible profiles with their incompressible counterparts. The seminal work of Van Driest relied on re-mapping of the mean velocity profile, which worked only for adiabatic wall conditions. An improved transformation for internal flows by Trettel and Larsson followed in 2016. The transformation presented here relies on re-mapping both the wall-normal space coordinate and velocity profile, achieving excellent universality for both internal and boundary-layer flows across a wide range of flow parameters.
Volpiani et al. (Wed,) studied this question.