Rate of decay of turbulent kinetic energy in abruptly stabilized Ekman boundary layers

Under statically stable conditions in wall-bounded flows, turbulence is generated by shear and dissipated by buoyancy and viscosity. Most studies have focused on the steady-state balance of this budget, but the time evolution of the turbulence when the stabilizing buoyancy flux is first imposed is as important in many geophysical applications. In this paper, we utilize a new paradigm on the critical role of shear production damping by buoyancy to develop a quantitative model for the rate of decay of turbulent kinetic energy (TKE), at early and intermediate times, after buoyancy is abruptly imposed on a steady neutrally stratified Ekman boundary-layer flow. Scaling analyses and reduced models are developed to obtain an expression for this rate of decay, which is then validated using results from direct numerical simulation. We further show that the TKE production term persists as a parameter outside of the classic stability parameter term (the flux Richardson number) under unsteady conditions, and is therefore needed to describe the dynamics of evolving stable boundary layers. The long-time steady dissipation-production-buoyancy balance is also analyzed using the same modeling framework and confirms that the damping of shear TKE production by buoyancy is the main agent for the reduction in TKE, while the direct role of buoyancy destruction is secondary.