A Linear Model of Back-Sheared Flow over an Isolated Hill in the Presence of Rotation

Abstract

Linearized solutions are derived for the case of constant (negative) shear flow over an isolated, circularly symmetric hill and are evaluated for three characteristic wave regimes. Of particular interest is the three-dimensional structure of the resulting field of inertia?gravity waves near the lower of two levels where the magnitude of the intrinsic frequency is equal to the Coriolis parameter?the inertia critical levels. In contrast to the equivalent nonrotating problem, the critical level height is a function of the horizontal wavenumber for each Fourier mode representing the disturbance. Furthermore the wave field, which consists of a downstream train of inertia waves, exhibits an azimuthal asymmetry about the direction of the flow. When the Rossby number near the mountain is less than unity the wave response consists of an evanescent disturbance and a pattern of neutral baroclinic lee waves that radiate horizontally away from the hill. These too show some cross-flow asymmetry, though in the opposite sense to that found with the inertia?gravity wave field. The spectral distribution of the wave stress is found to be symmetric about the flow direction, and the total stress averaged over the finite domain area decays with height as wave pseudomomentum is carried downstream in the form of quasi-inertial waves.