Pressure Gradient Parameters for Turbulent Boundary Layers Capturing Non-Equilibrium Effects in Steady and Unsteady Flows

Kurzfassung

We present two pressure gradient parameters designed to capture history effects in strongly nonequilibrium steady turbulent boundary layers, as well as history and memory effects in unsteady turbulent boundary layers where unsteady inertia forces are not dominant. The first parameter is defined as the Lagrangian (material) time average of the pressure gradient parameter βZS, computed for a fictitious particle traveling through the ensemble-averaged flow field. The second parameter is derived from a transport-relaxation differential equation. As the transport–relaxation parameter has not yet been extensively validated, the paper primarily focuses on the Lagrangian-based parameter. This cumulative parameter is assessed using seven strongly non-equilibrium TBLs, comprising four steady and three unsteady cases. In the steady cases, it captures the history effects of the pressure force reasonably well, outperforming two cumulative parameters from the literature and performing comparably to the one proposed by Gomez and McKeon (J. Fluid Mech., 1002:A20, 2025). Its main advantage, however, lies in its ability to capture history and memory effects in unsteady cases, provided that unsteady inertia forces remain secondary. Regarding the transport-relaxation pressure-gradient parameter, an initial application to a strongly decelerated boundary layer indicates behavior similar to that of the Lagrangian-based parameter.