An Alternative Eddy-Viscosity Model for the Horizontally Uniform Atmospheric Boundary Layer

Abstract

This paper explores the utility of specifying the eddy viscosity for the horizontally uniform boundary layer as the product \({K=\sigma_w^2 \tau_w}\) of the variance of vertical velocity and an empirical time scale τ w , as opposed to the more usual formulation \({K = \sqrt{\alpha k}\lambda_k}\) where k is the turbulent kinetic energy (TKE), λ k is a length scale and α is a dimensionless coefficient. Simulations were compared with the observations on Day 33 of the Wangara experiment, and with a plausible specification of τ w (or λ k ) each model simulated convective boundary-layer development reasonably well, although the \({K=\sqrt{\alpha k}\lambda_k}\) closure produced a more realistic width for the entrainment layer. Under the light winds of Day 33, and with the onset of evening cooling, an excessively shallow and strongly-stratified nocturnal inversion developed, and limited its own further deepening. Boundary-layer models that neglect radiative heat transport and parametrize convective transport by eddy viscosity closure are prone to this runaway (unstable) feedback when forced by a negative (i.e. downward) surface flux of sensible heat.