Detailing History and Non-equilibrium Effects in Adverse Pressure Gradient Turbulent Boundary Layers

Utilizing the stress balance and a wall shear stress and pressure based velocity scale, \(u_{hyb}\) , introduced in Romero et al. (2022) non-equilibrium effects in adverse pressure gradient turbulent boundary layers are studied. Data from canonical flows, i.e. zero pressure gradient turbulent boundary layers, are used to provide context for this adverse pressure gradient turbulent boundary layer analysis. Adverse pressure gradient flows at varying Clauser pressure-gradient parameter \(\beta \) are studied. This parameter can be defined as the ratio of time-scales, \(\beta = t_\Delta /t_{PG}\) , characteristic of the turbulence and pressure gradient. Here, \(t_\Delta = \Delta / u_\tau \) , where \(\Delta = (U_\infty /u_\tau )\delta ^*\) is the Rotta-Clauser thickness, \(\delta ^*\) is the displacement thickness, and \(u_\tau \) is the friction velocity. \(t_{PG} = -(dU_\infty /dx)^{-1}\) , where \(U_\infty \) is the free-stream velocity. For the adverse pressure gradient flow to achieve self-similarity, \(\beta \) , the ratio of two time-scales, has to be a constant. Therefore, under a non-constant \(\beta \) the flow takes time to reach self-similarity and history effects become apparent. From studying non-constant \(\beta \) cases, this study hypothesizes a link between the cross-over from equilibrium to non-equilibrium with a corresponding qualitative change to the internal leading order stress balance.