Neutral and stratified turbulent boundary‐layer flow over low mountains

Abstract

AbstractA theory for flow over gentle hills using a mixing‐length turbulence closure is developed to describe the transition from turbulent orographic form drag to gravity wave drag. It confirms that the first is associated with downstream sheltering, and the second with upstream blocking and strong downslope winds. It shows that the altitude at which the incident flow needs to be taken to calculate the drag is the inner layer scale at which dissipation equilibrates disturbance advection. It also shows that the parameter that controls the transition, here a Richardson number, compares the mountain length with the altitude of the turning points above which the upward‐propagating gravity waves become evanescent. Our solutions are also used to show that the downslope winds penetrate well into the inner layer and that a good fraction of the drag is deposited in the inner layer: all of it in the neutral case, a large fraction in the intermediate cases when there are trapped lee waves, and even in stable situations without trapping part of the gravity wave drag is eroded in the inner layer. Some discussion on how to combine neutral and stratified effects in the parametrization of subgrid scale orography in large‐scale models is given.