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Linear waves in two-layer fluids over periodic bottoms

Published online by Cambridge University Press:  06 April 2016

Jie Yu  and
Leo R. M. Maas
Jie Yu*
Affiliation:
Department of Civil Engineering, and School of Marine and Atmospheric Sciences, Stony Brook University, Stony Brook, NY 11794, USA
Leo R. M. Maas
Affiliation:
Royal Netherlands Institute for Sea Research, PO Box 59, 1790 AB Texel, The Netherlands Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Princetonplein 5, 3584 CC, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

A new, exact Floquet theory is presented for linear waves in two-layer fluids over a periodic bottom of arbitrary shape and amplitude. A method of conformal transformation is adapted. The solutions are given, in essentially analytical form, for the dispersion relation between wave frequency and generalized wavenumber (Floquet exponent), and for the waveforms of free wave modes. These are the analogues of the classical Lamb’s solutions for two-layer fluids over a flat bottom. For internal modes the interfacial wave shows rapid modulation at the scale of its own wavelength that is comparable to the bottom wavelength, whereas for surface modes it becomes a long wave carrier for modulating short waves of the bottom wavelength. The approximation using a rigid lid is given. Sample calculations are shown, including the solutions that are inside the forbidden bands (i.e. Bragg resonated).

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 794 , 10 May 2016 , pp. 700 - 718
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Copyright
© 2016 Cambridge University Press 

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