A Topographic Drag Closure Built on an Analytical Base Flux

Abstract

Topographic drag schemes depend on grid-scale representations of the average height, width, and orientation of the subgrid topography. Until now, these representations have been based on a combination of statistics and dimensional analysis. However, under certain physical assumptions, linear analysis provides the exact amplitude and orientation of the drag for arbitrary topography. The author proposes a computationally practical closure based on this analysis. Also proposed is a nonlinear correction for nonpropagating base flux. This is patterned after existing schemes but is better constrained to match the linear solution because it assumes a correlation between mountain height and width. When the correction is interpreted as a formula for the transition to saturation in the wave train, it also provides a way of estimating the vertical distribution of the momentum forcing. The explicit subgrid height distribution causes a natural broadening of the layers experiencing the forcing. Linear drag due to simple oscillating flow over topography, which is relevant to ocean tides, has almost the same form as for the stationary atmospheric problem. However, dimensional analysis suggests that the nonpropagating drag in this situation is mostly due to topographic length scales that are small enough to keep the steady-state assumption satisfied.