Journal of Fluid Mechanics



Papers

A note on the resonant interaction between a surface wave and two interfacial waves


MIRMOSADEGH JAMALI a1, GREGORY A. LAWRENCE a2 and BRIAN SEYMOUR a3
a1 Department of Civil Engineering, Sharif University of Technology, PO Box 11365-9313, Teheran, Iran
a2 Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4
a3 Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2

Abstract

Hill & Foda (1998) and Jamali (1998) have presented theoretical and experimental studies of the resonant interaction between a surface wave and two oblique interfacial waves. Despite many similarities between the findings there is one seemingly major difference. Hill & Foda's (1998) analysis indicated that there are only narrow bands of frequency, density ratio and direction angle within which growth is possible. On the other hand, Jamali (1998) predicted and observed wave growth over wide ranges of frequency and direction angle, and for all the density ratios that he investigated. We show that Hill & Foda's (1998) second-order representation of the dynamic interfacial boundary condition is missing a term proportional to the time derivative of the square of the velocity shear across the interface. When this missing term is included in the analysis, the resulting predictions are consistent with the laboratory experiments.

(Received April 2 2001)
(Revised March 31 2003)



Metrics