Internal Waves of Arbitrary Shape in the Ocean

Abstract

Internal gravity waves of arbitrary shape in a water of finite depth with a stable vertical density stratification are studied within the realm of the linear theory. It is shown that the dispersion relations of such kind of internal waves are entirely controlled by the vertical component of the field equations. An explicit solution is obtained for a special density variation obeying a power law in terms of confluent hypergeometric functions, and the asymptotic forms of the dispersion relations are determined for very long and very short waves.