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

Forbes, L.K., Hocking, G.C. and Farrow, D.E. (2006) An intrusion layer in stationary incompressible fluids: Part 1: Periodic waves. European Journal of Applied Mathematics, 17 (05). pp. 557-575.

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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.