S P Decent 1997 Fluid Dyn. Res. 19 201 doi:10.1016/S0169-5983(96)00037-8
S P Decent1
Show affiliationsParametrically excited waves are usually modelled with a nonlinear amplitude equation. It has recently been demonstrated that the behaviour of these waves depends critically upon the coefficient of the cubic damping term in the nonlinear amplitude equation, and especially upon the sign of this coefficient (see Decent and Craik [J. Fluid Mech. 293 (1995) 237]. However, very little work has been carried out on theoretically determining the value of this coefficient. This paper derives the coefficient of cubic damping for the single-mode nonlinear amplitude equation which models two-dimensional gravity waves in a narrow rectangular container. Energy dissipation in the main body of the fluid and in boundary layers at the sidewalls and at the surface is considered. Theoretical results agree fairly well with an experiment carried out by Decent and Craik (1995).
Issue 4 (April 1997)
Received 29 November 1995, revised 25 April 1996, accepted for publication 11 September 1996
S P Decent 1997 Fluid Dyn. Res. 19 201
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