Surface pressure drag for hydrostatic two-layer flow over axisymmetric mountains

The effect of partial reflections on surface pressure drag is investigated for hydrostatic gravity waves in two-layer flow with piecewise constant buo yancy frequency. The variation of normalized surface pressure drag with int erface height is analyzed for axisymmetric mountains. The results are compa red with the familiar solution for infinitely long ridges. The drag for the two-layer flow is normalized with the drag of one-layer flow. An analytica l expression for the normalized drag of axisymmetric mountains is derived f rom linear theory of steady flow. Additionally, two-layer flow over finite- height axisymmetric mountains is simulated numerically for flow with higher stability in the upper layer. The temporal evolution of the surface pressu re drag is examined in a series of experiments with different interface and mountain heights. The focus is on the linear regime and the nonlinear regi me of nonbreaking gravity waves. The entire spectrum of gravity waves can be in resonance in hydrostatic flo w over infinitely long ridges. This cannot occur in 3D flow over isolated m ountains due to the dispersion of gravity waves. In consequence, the oscill ation of the normalized drag with interface height is smaller for axisymmet ric mountains than for infinitely long ridges. However, even for a reflecti on coefficient as low as 1/3 the drag of an axisymmetric mountain can be am plified by 50% and reduced by 40%. The nonlinear drag becomes steady in the numerical experiments in which no wave breaking occurs. The steady-state nonlinear drag agrees quite well wit h the prediction of linear theory if the linear drag is computed for a slig htly lowered interface.