EXTENDED MILD-SLOPE EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (6): 724-729.

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EXTENDED MILD-SLOPE EQUATION

HUANG Hu^1,2, DING Ping-xing¹, LÜ Xiu-hong ¹

1. State Key Laboratory of Estuarine & Coastal Research, East China Normal University, Shanghai 200062, P.R.China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shang

Received:1999-07-03 Revised:2000-01-15 Online:2001-06-18 Published:2001-06-18
Supported by:
the National Outstanding Youth Science Foundation of China (49825161),Shanghai Postdoctoral Science Foundation

Abstract

Abstract: The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom, thus leading to an extended mild-slope equation. The bottom topography consists of two components: the slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the amplitude being smaller than that of the surface wave. The frequency of the fast varying depth component is, however, comparable to that of the surface waves. The extended mild-slope equation is more widely applicable and contains as special cases famous mild-slope equations below: the classical mild-slope equation of Berkhoff, Kirby’s mild-slope equation with current, and Dingemans’s mild-slope equation for rippled bed. The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.

2010 MSC Number:

O353.2

HUANG Hu;DING Ping-xing;L�Xiu-hong . EXTENDED MILD-SLOPE EQUATION. Applied Mathematics and Mechanics (English Edition), 2001, 22(6): 724-729.

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References

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