Surface drag on deformed topographic boundaries: Tests using a semi-idealized model

The physics of the surface drag (or surface stress) boundary condition is explored in the context of semi-idealized flows past realistic terrain. Numerical experiments are presented to explore the impact of the drag condition on flows past a region of complex topography, with a particular focus on the dependence on terrain geometry. Arguments are presented to show that the drag condition depends on the geometry of the terrain in two respects: (i) a dependence on terrain slope, as represented by a normal gradient term; and (ii) a dependence on the curvature, which appears in the drag condition as a Dirichlet term. The dependence on the geometry is illustrated through a series of numerical experiments in which simulations using the full form of the drag condition are compared to companion simulations using one of two widely used approximations: (a) the normal gradient condition, which accounts for the terrain slope but neglects curvature; and (b) the flat boundary assumption, which neglects both slope and curvature. The results show that the role of the terrain geometry in the drag condition is strongly dependent on grid spacing, with more highly resolved topography leading to a stronger dependence on the slope and curvature. For sufficiently high resolutions, the dependence on the geometry becomes significant, to the extent that simulations using the approximate drag conditions fail to capture important aspects of the flow. Some basic implications of these results for the problem of high resolution wind energy forecasting are discussed.