Inertia–Gravity Wave and Neutral Eady Wave Trains Forced by Directionally Sheared Flow over Isolated Hills

Abstract

Analytical solutions are obtained to the linearized equations describing a particular class of directionally sheared flow over isolated hills or ridges. The flows are characterized by constant buoyancy frequency and vertical wind shear, though the wind direction changes with height due to the presence of a constant, horizontal wind component normal to the wind shear vector. The inclusion of a constant Coriolis parameter permits the formation of inertia wave trains and neutral baroclinic wave trains. A particular focus of this study is the nature of the selective critical level absorption process that results from varying wind direction with height in the presence of an azimuthal spectrum of forced wave modes. It will be shown that the stationary disturbance generated by circular and elliptical hills of mesoscale dimensions comprises an inertia wave train that trails downwind at all heights in the form of a horizontal wind perturbation, and a baroclinic wave train that extends in the direction of the surface flow. Unlike the equivalent nonrotating problem, these calculations suggest that the kinetic energy density of the inertia wave train does not decay downstream but asymptotes to a constant value, as recently inferred by Broutman. The form of the downstream wave train is also shown to be very different in the rotating and nonrotating cases, implying that wave breakdown will occur much nearer to the orographic wave source in the presence of rotation (though still potentially a long way from the source). The results support the general notion that three-dimensionality, directional wind shear, and rotation promote horizontal energy dispersion into a background inertia?gravity wave ?soup.?