Journal of Fluid Mechanics

Localization of gravity waves on a channel with a random bottom

Pierre  Devillard a1, François  Dunlop a1 and Bernard  Souillard a1
a1 Centre de Physique Théorique, Ecole Polytechnique, F-91128 Palaiseau, France

Article author query
devillard p   [Google Scholar] 
dunlop f   [Google Scholar] 
souillard b   [Google Scholar] 


We present a theoretical study of the localization phenomenon of gravity waves by a rough bottom in a one-dimensional channel. After recalling localization theory and applying it to the shallow-water case, we give the first study of the localization problem in the framework of the full potential theory; in particular we develop a renormalized-transfer-matrix approach to this problem. Our results also yield numerical estimates of the localization length, which we compare with the viscous dissipation length. This allows the prediction of which cases localization should be observable in and in which cases it could be hidden by dissipative mechanisms.

(Published Online April 21 2006)
(Received January 3 1986)
(Revised April 29 1987)