Resolving nonhydrostatic effects in oceanic lee waves

Abstract

With increased computing power, the horizontal grid-spacing of regional ocean models is decreasing to the point where they can directly simulate lee waves. Although oceanic lee waves can be inherently nonhydrostatic, such as in the abyssal ocean or in the Gulf Stream, regional ocean models are frequently run in hydrostatic mode to avoid the computational expense of solving the nonhydrostatic pressure. However, the effects of the nonhydrostatic pressure and the numerical error on the accuracy of the simulated lee waves is not immediately obvious. To quantify these effects, this paper presents hydrostatic and nonhydrostatic simulations of an idealized lee wave over both linear and nonlinear height and varying length bathymetry utilizing a range of horizontal grid-spacings. We present an analysis of the numerical error arising from the discrete linear, stratified Euler equations to identify the numerically induced physics in lee wave simulations. As expected for the second-order accurate model, the numerical error in the lee wave drag decreases quadratically with respect to horizontal grid refinement, although the error arises from two primary sources. The first is related to discretization of the kinematic bottom boundary condition, which acts to decrease the lee wave drag. The second is related to discretization of the nonhydrostatic pressure, which acts to increase the drag. Together, the results offer a regional ocean modeler several cautionary notes for calculating and interpreting properties of simulated lee waves, namely, that a hydrostatic model can produce the correct form drag due simply to numerical error, and attempting to employ a nonhydrostatic model to correct for this error can require prohibitively fine grid resolution.