scholarly journals On the breaking of water waves on a sloping beach of arbitrary shape

1975 ◽  
Vol 33 (2) ◽  
pp. 187-189 ◽  
Author(s):  
Morton E. Gurtin
Keyword(s):  
Water Waves ◽  
Arbitrary Shape ◽  
Sloping Beach

scholarly journals WATER WAVES PROPAGATING ON BEACHES OF ARBITRARY SHAPE

1982 ◽  
Vol 1 (18) ◽  
pp. 51
Author(s):  
Y.Y. Chen ◽  
H.H. Hwung
Keyword(s):  
Water Waves ◽  
Small Amplitude ◽  
Arbitrary Shape ◽  
Water Surface ◽  
Wave Motion ◽  
Progressive Wave ◽  
Amplitude Wave ◽  
Theoretical Derivation ◽  
Beach Slope ◽  
Sloping Beach

When a small amplitude wave climbing along an arbitrary sloping beach from deep water toward the shore, the variation of characteristics in the process of wave motion has been described in this paper. From the results of theoretical derivation, it is found out that the variation of water surface and amplitude are function of beach slope) and dimensionless distance (kx~) from the shore. And under the condition of the beach slope is a = 0 and a = °o that the solution will become a progressive wave and a standing wave respectively.

Water waves of finite amplitude on a sloping beach

1958 ◽  
Vol 4 (1) ◽  
pp. 97-109 ◽  
Author(s):  
G. F. Carrier ◽  
H. P. Greenspan
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Finite Amplitude ◽  
Explicit Solutions ◽  
Shallow Water Theory ◽  
Non Linear ◽  
Wave Forms ◽  
Time Histories ◽  
Sloping Beach

In this paper, we investigate the behaviour of a wave as it climbs a sloping beach. Explicit solutions of the equations of the non-linear inviscid shallow-water theory are obtained for several physically interesting wave-forms. In particular it is shown that waves can climb a sloping beach without breaking. Formulae for the motions of the instantaneous shoreline as well as the time histories of specific wave-forms are presented.

scholarly journals A Regular Integral Equation Formalism for Solving the Standard Boussinesq’s Equations for Variable Water Depth

2017 ◽  
Vol 75 (3) ◽  
pp. 1721-1756 ◽  
Author(s):  
T. S. Jang
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Nonlinear Wave ◽  
Water Depth ◽  
Water Waves ◽  
Numerical Solutions ◽  
Derivative Free ◽  
Sloping Beach ◽  
Wave Phenomena ◽  
Variable Water

Abstract This paper begins with a question of existence of a regular integral equation formalism, but different from the existing usual ones, for solving the standard Boussinesq’s equations for variable water depth (or Peregrine’s model). For the question, a pseudo-water depth parameter, suggested by Jang (Commun Nonlinear Sci Numer Simul 43:118–138, 2017), is introduced to alter the standard Boussinesq’s equations into an integral formalism. This enables us to construct a regular (nonlinear) integral equations of second kind (as required), being equivalent to the standard Boussinesq’s equations (of Peregrine’s model). The (constructed) integral equations are, of course, inherently different from the usual integral equation formalisms. For solving them, the successive approximation (or the fixed point iteration) is applied (Jang 2017), whereby a new iterative formula is immediately derived, in this paper, for numerical solutions of the standard Boussinesq’s equations for variable water depth. The formula, semi-analytic and derivative-free, is shown to be useful to observe especially the nonlinear wave phenomena of shallow water waves on a beach. In fact, a numerical experiment is performed on a solitary wave approaching a sloping beach. It shows clearly the main feature of nonlinear wave characteristics, which has reached good agreement with the known (numerical) solutions. Hence, while being theoretical but fundamental in nonlinear computational partial differential equations, the question raised in the study may be solved.

scholarly journals Linear water waves over a gently sloping beach

1994 ◽  
Vol 52 (2) ◽  
pp. 243-259 ◽  
Author(s):  
S. M. Sun ◽  
M. C. Shen
Keyword(s):  
Water Waves ◽  
Sloping Beach ◽  
Linear Water Waves

scholarly journals Conservation laws for shallow water waves on a sloping beach

1986 ◽  
Vol 9 (2) ◽  
pp. 387-396
Author(s):  
Yilmaz Akyildiz
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Water Waves ◽  
Simple Wave ◽  
Shallow Water Waves ◽  
Linear Partial Differential Equations ◽  
Wave Solutions ◽  
Hodograph Plane ◽  
Sloping Beach ◽  
Linear Nature

Shallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conservation laws and hodograph solutions as well as Bäcklund transformations by using the linear nature of the problems on the hodogrpah plane.

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