The dispersion relation for internal acoustic-gravity waves in a baroclinic fluid

Abstract

The dispersion relation for internal waves in a fluid is generalized from the barotropic approximation to the baroclinic case to allow for the inclination of surfaces of constant density to surfaces of constant pressure. This generalization allows the barotropic approximation to be tested in a variety of situations. The dispersion relation applies to both acoustic waves and internal gravity waves propagating in either the ocean or the atmosphere. Imaginary terms in the dispersion relation proportional to the baroclinic vector indicate energy exchange between the wave and the mean flow, a result of buoyancy being a nonconservative force in a baroclinic fluid. A buoyancy calculation shows that the baroclinic generalization of the Brunt–Väisälä frequency N is given by N2=∇ρθ⋅∇p/ρ2, where ρ is density, ρθ is potential density, and p is pressure. The baroclinicity in a weather front or cyclonic ring can sometimes have as large an effect as the Earth’s rotation on the propagation of internal gravity waves.