Shape and scaling of the mean-velocity profile in thermally-stratified plane-Couette flows

Abstract

It has long been known from measurements that buoyant motions cause the mean-velocity profile (MVP) in thermally-stratified, wall-bounded turbulent flows to significantly deviate from its constant-density counterpart. Theoretical analysis has restricted attention to an “intermediate layer” of the MVP, akin to the celebrated “log layer” in the constant-density case. Here, for thermally-stratified plane-Couette flows, we study the shape and scaling of the whole MVP. We elucidate the mechanisms that dictate the shape of the MVP by using the framework of the spectral link (Gioia et al.; 2010), and obtain scaling laws for the whole MVP by generalizing the Monin-Obukhov similarity theory.

Spectral link and wave breaking enhanced dissipation of turbulent kinetic energy

“…We employ the theoretical framework of the spectral link, originally proposed for MVP in sheared flows (Gioia et al 2010) and later extended to stratified flows (Katul et al 2011, Zhang 2021). An eddy of size s transfers momentum across the wetted surface w y at a depth y below the ocean surface will span a momentum contrast ρ(u(y − s) − u(y + s)) ≈ −2ρs du dy and thus produce the turbulent shear stress acting on w y with the rate of momentum transfer set by the velocity of the eddy v s (figure 2).…”