Extended Mild-Slope Equation

HUANG Hu; DING Ping-xing; LÜ Xiu-hong

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(6): 645-650

HUANG Hu, DING Ping-xing, LÜ Xiu-hong. Extended Mild-Slope Equation[J]. Applied Mathematics and Mechanics, 2001, 22(6): 645-650.

Citation:

HUANG Hu, DING Ping-xing, LÜ Xiu-hong. Extended Mild-Slope Equation[J]. Applied Mathematics and Mechanics, 2001, 22(6): 645-650.

Citation:

HUANG Hu, DING Ping-xing, LÜ Xiu-hong. Extended Mild-Slope Equation[J]. Applied Mathematics and Mechanics, 2001, 22(6): 645-650.

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Extended Mild-Slope Equation

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, Shanghai 200072, P R China

Received Date: 1999-07-30
Rev Recd Date: 2001-01-15
Publish Date: 2001-06-15

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.
- mild-slope equation,
- slowly varying three-dimensional currents,
- rapidly varying topography,
- Hamiltonian formalism for surface waves

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References(14)

References

[1]	Dingemans M W. Water Wave Propagatio n Over Uneven Bottoms[M]. Singapore: World Scientific,1997.
[2]	Kirby J T. Nonlinear, dispersive long waves in water of va riable depth[A]. In: Hunt J N Ed. Gravity Waves in Water of Finite Depth[C]. Southampt on: Computational Mechanics Publications,1997,55-126.
[3]	Kirby J T. A note on linear surface wave-current interaction[J]. J Geophys Res,1984,89(C1):745-747.
[4]	Yoon S B, Liu P L-F. Interaction of currents and weakly no nlinear water waves in shallow water[J]. J Fluid Mech,1989,205:397-419.
[5]	Liu P L-F. Wave transformation[A]. In: LeMehaute B, Hane s D M Ed s. The Sea, Ocean Engineering Science[C]. New York: J Wiley and Sons,1990, 27-63.
[6]	Kirby J T. A general wave equation for waves over rippled beds[J]. J Fluid Mech,1986,162:171-186.
[7]	Chamberlain P G, Porter D. The modified mild-slope equation[J]. J Fluid Mech,1995,291:393-407.
[8]	Chandrasekera C N, Cheung K F. Extended linear refraction-diffraction model[J]. J Wtrwy Port Coast and Oc Engrg,1997,123(5) :280-286.
[9]	Lee C, Park W S, Cho Y-S, et al. Hyperbolic mild-slope equations extended to account for rapidly varying topography[J]. Coastal Eng,1998,34:243-257.
[10]	Thomas G P, Klopman G. Wave-current interactions in the near shore region[A]. In: Hunt J N Ed. Gravity Waves in Water of Finite Depth[C]. Southampton: Computational Mechanics Publications,1997,255-319.
[11]	Zakharov V E. Stability of periodic waves of finite amplitude on the surface of a deep fluid[J]. J Appl Mech Tech Phys,1968,2:190-194.
[12]	Broer L J F. On the Hamiltonian theory of surface waves[J]. Appl Sci Res,1974,30(5):430-446.
[13]	Miles J W. On Hamilton's principle for surface waves[J]. J Fluid Mech,1977,83:153-158.
[14]	Berkhoff J C W. Computation of combined refraction-diffraction[A]. In: 13th Inte Conf on Coastal Engng[C]. New York: ASCE,1972,471-490.