Summary: J. Fluid Mech. (2009), vol. 624, pp. 191­224. c 2009 Cambridge University Press
doi:10.1017/S0022112008005478 Printed in the United Kingdom
191
Bragg resonance of waves in a two-layer fluid
propagating over bottom ripples.
Part I. Perturbation analysis
MOHAMMAD-REZA ALAM,
YU M IN G LIU AND DICK K. P. YUE
Department of Mechanical Engineering, Center for Ocean Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139, USA
(Received 29 November 2007 and in revised form 2 December 2008)
We investigate, via perturbation analyses, the mechanisms of nonlinear resonant
interaction of surface-interfacial waves with a rippled bottom in a two-layer density-
stratified fluid. As in a one-layer fluid, three classes of Bragg resonances are found
to exist if nonlinear interactions up to the third order in the wave/ripple steepness
are considered. As expected, the wave system associated with the resonances is more
complicated than that in a one-layer fluid. Depending on the specifics of the resonance
condition, the resonance-generated wave may be a surface or internal mode and may
be transmitted or reflected. At the second order, class I Bragg resonance occurs

Source: Alam, Mohammad-Reza - Department of Mechanical Engineering, Massachusetts Institute of Technology (MIT)

Collections: Engineering