European Journal of Applied Mathematics



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An intrusion layer in stationary incompressible fluids: Part 1: Periodic waves


LAWRENCE K. FORBES a1, GRAEME C. HOCKING a2 and DUNCAN E. FARROW a3
a1 School of Mathematics and Physics, University of Tasmania, Hobart 7001, Tasmania, Australia email: larry.forbes@utas.edu.au
a2 School of Mathematics and Statistics, Division of Science, Murdoch University, Murdoch 6150, Western Australia
a3 Mathematics and Statistics, DSE, Murdoch University, Murdoch 6150, Western Australia

Article author query
forbes lk   [Google Scholar] 
hocking gc   [Google Scholar] 
farrow de   [Google Scholar] 
 

Abstract

Waves on a neutrally buoyant intrusion layer moving into otherwise stationary fluid are studied. There are two interfacial free surfaces, above and below the moving layer, and a train of waves is present. A small amplitude linearized theory shows that there are two different flow types, in which the two interfaces are either in phase or else move oppositely. The former flow type occurs at high phase speed and the latter is a low-speed solution. Nonlinear solutions are computed for large amplitude waves, using a spectral type numerical method. They extend the results of the linearized analysis, and reveal the presence of limiting flow types in some circumstances.

(Received November 30 2005)
(Revised June 1 2006)