A Formula for Vertical Flux of Horizontal Momentum Generated by Topography

Abstract

   An approximate formula for the vertical flux of horizontal momentum (momentum flux for brevity) generated by topography is derived. A steady non-rotating hydrostatic 3-dimensional linear problem is considered. The height of topography is a function of both horizontal coordinates, and its environmental flow has vertical shears of both magnitude and direction. Because of the directional shear, critical levels are present continuously in the vertical direction. In the presence of the critical levels, the momentum flux vector is azimuthally filtered continuously in the vertical direction, and becomes a function of the vertical coordinate.
   The formula shows that, except for the azimuthal filtering, the momentum flux vector is approximately the same as that for a uniform environmental flow, whose velocity is equal to the original environmental flow velocity at the ground.