Scaling thermal convection of stratified fluid over sloping surfaces

Abstract:

A set of scaling relations are proposed for thermal convection of stably stratified fluid down a thermally perturbed, smooth, sloping surface. Apparent universal functions of the dimensionless similarity parameters are also presented based on results from direct numerical simulations (DNS). These simulations allow the variability of the low-level jet (LLJ) height and its speed to be specified along with the height of both the dynamic and the thermal boundary layers. Such scaling relations are of interest for numerical and experimental communities, given that they facilitate the design of experiments and the parameterization of thermally driven flows over a broad range of scales and applications. Normalized DNS profiles show a remarkable collapse of the proposed flow features and suggest the LLJ could be regarded as a transition layer separating the inner (laminar) wall regions from the outer (turbulent) flow. A dynamic and a thermodynamic identity – to be employed in assessing convergence of averaging operations is also proposed and tested using the DNS.