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Oscillatory nature and dissipation of of the internal waves energy spectrum in the deep ocean

Published online by Cambridge University Press:  13 December 2007

R. N. Ibragimov
R. N. Ibragimov*
Affiliation:
Department of Applied Mathematics, New Mexico Institute of Mining and Technology Socorro, NM 87801, USA
*
[email protected]
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Abstract

In this paper the new approach is proposed to consider a large number ofresonantly interacting internal waves in order to investigate the evolutionof the energy spectrum in the ocean. The approach is based on a new methodfor deriving and solving the system of coupled differential equations thatgovern the evolution of the waves on the interaction time scale. Allprevious analytical models are based on studying of three resonant internalwaves and under hydrostatic approximation. The case of eight resonant waveshas been studied experimentally in [J. Fluid Mech. 30, 723 (1967)]. To study the oceanic energy spectrum, only statistical models has been used which are not precise enoughto provide estimates of energy exchange in the ocean. The model reported inthis paper, provides an illustrative example involving 140 000 resonantinternal waves. In this model we don't need to assume the hydrostaticapproximation. So our model involves internal waves with frequenciesspanning the range of possible frequencies, i.e., between a maximum of thebuoyancy frequency N to a minimum of the inertial frequency f. Periodicnature of the spectrum (which has never been reported in previous studies)is investigated. The possible application of this model to investigation ofinternal waves energy dissipation is discussed.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 40 , Issue 3 , December 2007 , pp. 315 - 334
Copyright
© EDP Sciences, 2007

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