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Exact Floquet theory for waves over arbitrary periodic topographies

Published online by Cambridge University Press:  28 September 2012

Jie Yu  and
Louis N. Howard
Jie Yu*
Affiliation:
Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC 27695-7908, USA
Louis N. Howard
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: jie_yu@ncsu.edu
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Abstract

We consider linear waves propagating over periodic topographies of arbitrary amplitude and wave form, generalizing the method in Howard & Yu (J. Fluid Mech., vol. 593, 2007, pp. 209–234). By a judicious construction of a conformal map from the flow domain to a uniform strip, exact solutions of Floquet type can be developed in the mapped plane. These Floquet solutions, in an essentially analytical form, are analogous to the complete set of flat-bottom propagating and evanescent waves. Therefore they can be used as a basis for the solutions of boundary value problems involving a wavy topography with a constant mean water depth. Various concrete examples are given and quantitative results are discussed. Comparisons with experimental data are made, and qualitative agreement is achieved.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 451 - 470
Copyright
©2012 Cambridge University Press

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