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

Published online by Cambridge University Press:  21 April 2006

James C. S. Meng  and
James W. Rottman
James C. S. Meng
Affiliation:
Gould Defense Systems, Inc., Ocean Systems Division, One Corporate Place, Newport Corporate Park, Middletown, RI 02840, USA
James W. Rottman
Affiliation:
Department of Marine, Earth & Atmospheric Sciences, North Carolina State University, Raleigh, NC 27695, USA
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 419 - 444
Copyright
© 1988 Cambridge University Press

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