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Scattering of internal tides by irregular bathymetry of large extent

Published online by Cambridge University Press:  17 April 2014

Yile Li  and
Chiang C. Mei
Yile Li
Affiliation:
Katy, TX 77450, USA
Chiang C. Mei*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: ccmei@mit.edu
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Abstract

We present an analytical theory of scattering of tide-generated internal gravity waves in a continuously stratified ocean with a randomly rough seabed. Based on a linearized approximation, the idealized case of constant mean sea depth and Brunt–Väisälä frequency is considered. The depth fluctuation is assumed to be a stationary random function of space, characterized by small amplitude and a correlation length comparable to the typical wavelength. For both one- and two-dimensional topographies the effects of scattering on the wave phase over long distances are derived explicitly by the method of multiple scales. For one-dimensional topography, numerical results are compared with Bühler & Holmes-Cerfon (J. Fluid Mech., vol. 678, 2011, pp. 271–293), computed by the method of characteristics. For two-dimensional topography, new results are presented for both statistically isotropic and anisotropic cases.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 481 - 505
Copyright
© 2014 Cambridge University Press 

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