Linear internal waves generated by density and velocity perturbations in a linearly stratified fluid

Abstract

A generalized theoretical analysis and finite-difference solutions of the Navier-Stokes equations of the initial-value problem are applied to obtain the linear internal wave fields generated by a density perturbation and two rotational velocity perturbations in an inviscid linearly stratified fluid. The velocity perturbations are those due to an axisymmetric swirl and a vortex pair. Solutions obtained correspond to the strong stratification limit.The theoretical results of the rotational perturbation cases show an oscillating non-propagating disturbance, which is absent in the density-perturbation case. The swirl-flow solution shows an oscillatory behaviour in both the angular momentum deposited in the fluid and in the torque exerted by the external gravitational force field. The vortex-flow solution shows a vertical ray pattern.The equi-partitioning of energy is reached at about 0.4 of a Brunt-Väisälä (B.V.) period. The potential energy-kinetic energy conversion, or vice versa, takes place between 0.15 and 0.3 B.V. periods.