Internal Generation of Waves for Time-Dependent Mild-Slope Equations

The technique of generating waves internally is studied for two time-dependent mild-slope equations developed by Copeland (1985) and by Radder and Dingemans (1985) the velocity of disturbances caused by the incident wave is the phase velocity from the viewpoint of mass transport and it is the energy velocity from the viewpoint of energy transport. For Radder and Dingemans' equations. the desired energy of incident wave cannot be obtained from the viewpoint of mass transport from which the desired energy was successfully obtained by Larsen and Dancy (1983) in the Boussinesq equations and by Madsen and Larsen (1987) in Copeland's equations. However for all the two equations developed by Copeland and Radder and Dingemans. the desired energy of incident wave can be obtained from the viewpoint of energy transport. For horizontally two-dimensional case. an efficient technique of internal generation of multi-directional mono-chromatic waves is suggested.

[1]  G. Copeland,et al.  A practical alternative to the “mild-slope” wave equation , 1985 .

[2]  N. Hashimoto,et al.  ESTIMATION OF DIRECTIONAL SPECTRA FROM THE MAXIMUM ENTROPY PRINCIPLE , 1986 .

[3]  M. Isobe.  Time-Dependent Mild-Slope Equations for Random Waves , 1993 .

[4]  Per A. Madsen,et al.  An efficient finite-difference approach to the mild-slope equation , 1987 .

[5]  P. A. Madsen,et al.  A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry , 1992 .

[6]  A. Radder,et al.  Canonical equations for almost periodic, weakly nonlinear gravity waves , 1985 .

[7]  Jang-Won Chae,et al.  Boundary Treatment Techniques of Numerical Model for the Prediction of Harbor Oscillation , 1996 .

[8]  D. Peregrine.  Long waves on a beach , 1967, Journal of Fluid Mechanics.

[9]  James T. Kirby,et al.  A note on linear surface wave‐current interaction over slowly varying topography , 1984 .

[10]  Taerim Kim,et al.  Comparisons of Directional Wave Analysis Methods , 1994 .

[11]  N. Booij,et al.  Gravity waves on water with non-uniform depth and current , 1981 .

[12]  J. Berkhoff,et al.  Computation of Combined Refraction — Diffraction , 1972 .

[13]  T. Sprinks,et al.  Scattering of surface waves by a conical island , 1975, Journal of Fluid Mechanics.

[14]  TIME-DEPENDENT SOLUTIONS OF THE MILD-SLOPE WAVE EQUATION , 1993 .

[15]  P. A. Madsen,et al.  A new form of the Boussinesq equations with improved linear dispersion characteristics , 1991 .

[16]  J. Larsen,et al.  Open boundaries in short wave simulations — A new approach , 1983 .

[17]  O. Nwogu.  Alternative form of Boussinesq equations for nearshore wave propagation , 1993 .