A Wall Function for Turbulent Boundary Layers under Rotation via Symbolic Regression

This study employs symbolic regression to derive physically interpretable, white-box wall-function expressions for turbulent boundary layers under system rotation. Flows in a rotating frame are subject to Coriolis forces, which deflect the boundary layer profile from static case. The classical law of the wall, formulated under non-rotating conditions, is ill-suited to describing the effects of rotation. To obtain the wall function under rotation, we examine the deflection behavior of the turbulent boundary layers on the leading and trailing sides, and construct wall functions that are valid over a wide range of rotation numbers. The analytical expressions show that, as the rotation effect intensifies, the boundary layer on the leading side contracts whereas that on the trailing side expands, and the leading side exhibits a tendency towards relaminarization, consistent with high-fidelity numerical results. The resulting symbolic expressions are compact and interpretable. The wall functions obtained in this study complement conventional wall functions, and provide a new avenue for turbulence model closure subject to system rotation.