ScienceAsia 23 (1997): 001-011 |doi: 10.2306/scienceasia1513-1874.1997.23.001

SYMMETRIC WAVES OF A TWO-LAYER FLUID WITH FREE SURFACE OVER AN UNEVEN BOTTOM

J. W. CHOI^a AND J. ASAVANANT^b

ABSTRACT: In this paper we study steady two dimensional waves in a two-layer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction. Two critical speeds for the waves are obtained. Near the smaller critical speed, the derivation of the usual forced KdV equation (FKdV) fails when the coefficient of the nonlinear term in the FKdV vanishes. To overcome this difficulty, a new equation called a Steady Modified KdV equation with forcing term (SFMKdV) governing interfacial wave forms is obtained by a refined asymptotic method. By using SFMKdV we find the traveling solition-like solutions and symmetric wave solutions for different choices of parameters. Existence theorems are proved and numerical results of this equation are presented.

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a Department of Mathematics, College of Science, Korea University, Seoul, 136-701, Korea.
b Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand.

Received June 15, 1996