TY - JOUR
T1 - The nonlinear damping of parametrically excited two-dimensional gravity waves
AU - Decent, S.P.
N1 - Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 1997/4
Y1 - 1997/4
N2 - Parametrically 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).
AB - Parametrically 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).
UR - http://www.scopus.com/inward/record.url?scp=0031127713&partnerID=8YFLogxK
U2 - 10.1016/S0169-5983(96)00037-8
DO - 10.1016/S0169-5983(96)00037-8
M3 - Article
AN - SCOPUS:0031127713
SN - 0169-5983
VL - 19
SP - 201
EP - 217
JO - Fluid Dynamics Research
JF - Fluid Dynamics Research
IS - 4
ER -