HORIZONTAL BUOYANCY FLUX OF INTERNAL GRAVITY-WAVES IN VERTICAL SHEAR

The equations of motion describing two-dimensional internal gravity waves were analyzed to derive an expression for the horizontal buoyancy flux-i.e., the correlation between buoyancy (or temperature) and horizontal velocity-in various cases involving vertical shear. It is shown that, although this correlation vanishes at zeroth order for a single wave, its first order contribution is nonzero due to shear, even for steady, conservative, incompressible waves. Departures from steady, conservative motion or quasi-compressibility also cause a nonzero correlation. Several cases were analyzed and some numerical results obtained for waves approaching a critical layer of reduced intrinsic phase speed. With weak shear, the buoyancy flux is small relative to vertical momentum flux, as expected from the perturbation theory. Strong vertical shear enhances the buoyancy flux within the shear zone and causes partial reflection beneath, producing a nonzero correlation (at zeroth order) in this region. These effects may explain recent observations of zonal wind and temperature cospectra in the equatorial lower stratosphere.