Secondary motions in stratified flows

A simple model for secondary motions over heterogenous surfaces in stably-stratified turbulent flows is presented. The model is an extension to the Meyers et al. (2019) model which considers the neutral case only. Starting from the RANS equations that include buoyancy, the homogenous background is separated from the dispersive secondary motions. The dispersive equations are linearized, and the superposition principle is used to express solutions per wavenumber. The new model is validated against DNS simulations of a stable channel flow with heterogenous surface temperatures (Bon & Meyers, 2022). Including buoyancy improves the model predictions for weak secondary motions and strong secondary motions away from the surface. However, the model fails to predict the strong secondary motions near to the surface if zero background shear is assumed. Allowing the shear to be non-zero enhances the model predictions. The non-zero shear terms lead to a two-way coupling between vertical velocity and temperature, and a one-way coupling between vertical velocity and vorticity, which seem necessary for strong secondary motions.

Meyers J, Ganapathisubramani B & Cal RB 2019 On the decay of dispersive motions in the outer region of rough-wall boundary layers. J Fluid Mech 862.

Bon T & Meyers J 2022 Stable channel flow with spanwise heterogeneous surface temperature. J Fluid Mech 933.