The recovery of the Brunt–Väisälä frequency using dispersion curves

The coefficients of the Taylor expansion of the square of the Brunt–Väisälä frequency (BVF) are found, assuming its analyticity and certain symmetry conditions, using a well-known model [Miropol'skii YuZ. The Dynamics of Internal Gravitational Waves in are Ocean. Leningrad: Gidrometeoizdat; 1981.] employing an integral equation for the BVF constructed using a sequence of dispersion curves of internal gravitational waves in a vertically stratified ocean of constant depth. Assuming that the square of the BVF can be represented in the form of a fourth-order polynomial of the depth of the liquid layer being considered, it is shown that no more than two such polynomials correspond to one and the same sequence of dispersion curves. The coefficients of these polynomials are found.