Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ANALYTIC EXPRESSION OF HYDRAULIC FALL IN THE FREE SURFACE FLOW OF A TWO-LAYER FLUID OVER A BUMP

  • Park, Jeong-Whan (Department of Mathematics, College of Science, Korea University) ;
  • Hong, Bum-Il (Department of Mathematics and Institute of Natural Science, Kyung Hee University) ;
  • Ha, Sung-Nam (Department of Mathematics and Institute of Natural Science, Kyung Hee University)
  • Published : 1997.04.01
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Abstract

We consider long nonlinear waves in the two-layer flow of an inviscid and incompressible fluid bounded above by a free surface and below by a rigid boundary. The flow is forced by a bump on the bottom. The derivation of the forced KdV equation fails when the density ratio h and the depth ratio $\rho$ yields a condition $1 + h\rho = (2-h)((1-h)^2 + 4\rho h)^{1/2}$. To overcome this difficulty we derive a forced modified KdV equation by a refined asymptotic method. Numerical solutions are given and hydraulic fall solution of a two layer fluid is expressed analytically in the case that derivation of the forced KdV (FKdV) equation fails.

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References

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