Stationary gravity‐wave structure in flows with directional wind shear

Most theoretical studies of flow over mountains assume that the wind direction is constant. For two‐dimensional orographic ridges this is not an issue, since only the component of the wind across the ridge forces internal gravity waves. A special case of rectilinear flow is when the wind component changes sign (i.e. the wind direction changes discontinuously through 180 degrees): such a point is a critical level for all stationary gravity waves. For isolated three‐dimensional mountains the gravity‐wave response comprises waves of all azimuthal orientations, and each of these may have a different critical‐level height‐depending on whether the wind backs or veers with height. Using a combination of ray‐tracing methods and stationary‐phase solutions, the structure of the stationary, hydrostatic gravity‐wave field generated by an isolated mountain is studied for a simple wind field which backs with height. In contrast to the behaviour for unidirectional flow, wave action does not accumulate indefinitely beneath the critical level but is continuously advected downwind by the component of the wind parallel to the phase lines. Instead of the wave energy becoming unbounded following a ray as in the 2D case, the wave energy decays to zero along a trailing wake zone downwind of the mountain along phase lines. This is just an extension of the ‘asymptotic wake’ found in the linear solutions of Smith for constant flow over an isolated mountain. The work described here underlines the desirability of including the effects of selective critical‐level absorption in the gravity‐wave drag parametrization schemes of numerical weather‐prediction models.