Surface Pressure Drag for Hydrostatic Two-Layer Flow over Axisymmetric Mountains

Abstract

The effect of partial reflections on surface pressure drag is investigated for hydrostatic gravity waves in two-layer flow with piecewise constant buoyancy frequency. The variation of normalized surface pressure drag with interface height is analyzed for axisymmetric mountains. The results are compared 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 analytical expression for the normalized drag of axisymmetric mountains is derived from 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 pressure drag is examined in a series of experiments with different interface and mountain heights. The focus is on the linear regime and the nonlinear regime of nonbreaking gravity waves. The entire spectrum of gravity waves can be in resonance in hydrostatic flow over infinitely long ridges. This cannot occur in 3D flow over isolated mountains due to the dispersion of gravity waves. In consequence, the oscillation of the normalized drag with interface height is smaller for axisymmetric mountains than for infinitely long ridges. However, even for a reflection coefficient as low as ⅓ the drag of an axisymmetric mountain can be amplified 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 with the prediction of linear theory if the linear drag is computed for a slightly lowered interface.