Wentzel–Kramers–Brillouin solutions of the equation of internal gravitational waves in a stratified medium with slowly varying shear flows

Model buoyancy frequency distribution and the Wentzel–Kramers–Brillouin method are used to obtain an asymptotic solution to a problem of constructing solutions that describe internal gravity waves in a stratified medium with a background shear flow slowly varying in depth. Dispersion relation asymptotics are expressed in terms of the Airy functions. Asymptotics for various model distributions of background shear flows are used to obtain analytical representations of dispersion relations and eigenfunctions. Exact and asymptotic results are compared for various distributions of background shear flows and generation regimes typical of a real ocean.