The Effect of Rotation and Surface Friction on Orographic Drag

Abstract

A numerical, hydrostatic model is used to investigate the form and magnitude of the pressure drag created by 3D elliptical mountains of various heights (h) and aspect ratios (R) in flows characterized by uniform upstream velocity (U) and stability (N). Three series of simulations, corresponding to increasing degrees of realism, are performed: (i) without rotation and surface friction; (ii) with rotation, but no surface friction; (iii) with rotation and surface friction. For the simulations with rotation, the Coriolis parameter has a typical midlatitude value and the upstream flow is geostrophically balanced. The surface friction is introduced by the use of a typical roughness length. For low values of the nondimensional height (Nh/U), the pressure drag is reduced by the effect of rotation, in agreement with well-known results of linear theory. This seems to be valid until Nh/U ? 1.4, that is, in the high drag regime. On the other hand, for large values of Nh/U, that is, in the blocked flow regime, rotation has the opposite effect and increases the drag. The authors propose a simple interpretation of these results: that geostrophic adjustment acts to first order as a relaxation toward the upstream velocity. For low Nh/U, the acceleration above the mountain is a dominating feature of the flow and here the flow is slowed by the presence of rotation. For high Nh/U, when upstream blocking is dominant, the flow is slowed by the mountain and therefore accelerated by rotation. For values of Nh/U ? 1.4, the rotation is sufficient to force a transition from the blocked state to the unblocked state. The influence of rotation may therefore extend the range of usefulness of linear theory. Surface friction dramatically suppresses wave breaking at all values of Nh/U. The induced effect on the drag is negligible for Nh/U > 3, but there is a strong reduction at smaller values of Nh/U. In fact, the high-drag regime is nearly suppressed. The overall combined effect of rotation and surface friction is to constrain the drag (and to some extent, the flow patterns) to values remarkably close to the linear prediction. This sheds some light on recent, but as yet unexplained, results from the PYREX field experiment. The authors conclude this paper by running a real case drawn from this experiment, which reveals a behavior consistent with the idealized scenarios.