ON COMPUTING UNIFORMLY VALID APPROXIMATIONS FOR VISCOUS WAVES ON A PLANE BEACH

[摘要] Existing expansions for the near- and far-field flow of linear waves in a viscous liquid on a plane beach are supplemented by an approximation in the intermediate region which enables the flow to be matched from the shore line to infinity. Methods of computation are discussed and incorporated are recent improvements on the performance of numerical computation of oscillatory integrals. Sidi's user-friendly W-transform (1988) and Kohler's parameter optimisation (this journal, 1993) for generalised Newton-Cotes quadrature are found to be significant elements particularly with regard to the inversion of the Kontorovich-Lebedev transform. Comprehensive computations are undertaken and diagrams shown to display the behaviour of the stream function for all depths. An attempt is also made to construct a composite expansion of the vorticity and this is computed on a ray bisecting the wedge.

[发布日期] 1994-05-20

[效力级别]  Proceedings Paper

[关键词] OSCILLATORY INTEGRALS;W-TRANSFORMATION;GENERALIZED NEWTON-COTES QUADRATURE;KONTOROVICH-LEBEDEV AND MELLIN TRANSFORMS;KELVIN FUNCTION;ASYMPTOTIC EXPANSIONS;FREDHOLM EQUATION;STREAM FUNCTION;VORTICITY;STOKES FLOW