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

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 Phys. Rev. Lett. 105 184501), and obtain scaling laws for the whole MVP by generalizing the Monin-Obukhov similarity theory.