scholarly journals ESTIMATION OF WATER PARTICLE VELOCITIES OF SHALLOW WATER WAVES BY A MODIFIED TRANSFER FUNCTION METHOD

1986 ◽  
Vol 1 (20) ◽  
pp. 33 ◽  
Author(s):  
Hirofumi Koyama ◽  
Koichiro Iwata
Keyword(s):  
Transfer Function ◽  
Shallow Water ◽  
Approximate Method ◽  
Stream Function ◽  
Water Waves ◽  
Function Method ◽  
Finite Amplitude ◽  
Water Particle ◽  
Irregular Wave ◽  
Particle Velocities

This paper Is intended to propose a simple, yet highly reliable approximate method which uses a modified transfer function in order to evaluate the water particle velocity of finite amplitude waves at shallow water depth in regular and irregular wave environments. Using Dean's stream function theory, the linear function is modified so as to include the nonlinear effect of finite amplitude wave. The approximate method proposed here employs the modified transfer function. Laboratory experiments have been carried out to examine the validity of the proposed method. The approximate method is shown to estimate well the experimental values, as accurately as Dean's stream function method, although its calculation procedure is much simpler than that of Dean's method.

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.

A multiple exp-function method for the three model equations of shallow water waves

2017 ◽  
Vol 89 (3) ◽  
pp. 2291-2297 ◽  
Author(s):  
Yakup Yildirim ◽  
Emrullah Yasar ◽  
Abdullahi Rashid Adem
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Shallow Water Waves ◽  
Model Equations

scholarly journals Shallow water waves in porous medium for coast protection

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 145-151 ◽  
Author(s):  
Yan Wang ◽  
Yufeng Zhang ◽  
Wenjuan Rui
Keyword(s):  
Porous Medium ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Travelling Wave ◽  
Basic Solution ◽  
Solution Properties ◽  
Shallow Water Waves ◽  
Fractional Complex Transform ◽  
Fractional Momentum

This paper extends the Hirota-Satsuma equation in continuum mechanics to its fractional partner in fractal porous media in shallow water for absorbing wave energy and preventing tsunami. Its derivation is briefly introduced using the fractional momentum law and He?s fractional derivative. The fractional complex transform is adopted to elucidate its basic solution properties, and a modification of the exp-function method is used to solve the equation. The paper concludes that the kinetic energy of the travelling wave tends to be vanished when the value of the fractional order is less than one.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

Reflection of a shallow-water soliton. Part 1. Edge layer for shallow-water waves

1984 ◽  
Vol 146 ◽  
pp. 369-382 ◽  
Author(s):  
N. Sugimoto ◽  
T. Kakutani
Keyword(s):  
Boundary Condition ◽  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Equation ◽  
Expansion Method ◽  
Matching Condition ◽  
Finite Amplitude ◽  
Matched Asymptotic Expansion ◽  
Dispersive Waves ◽  
Edge Layer

To investigate reflection of a shallow-water soliton at a sloping beach, the edge-layer theory is developed to obtain a ‘reduced’ boundary condition relevant to the simplified shallow-water equation describing the weakly dispersive waves of small but finite amplitude. An edge layer is introduced to take account of the essentially two-dimensional motion that appears in the narrow region adjacent to the beach. By using the matched-asymptotic-expansion method, the edge-layer theory is formulated to cope with the shallow-water theory in the offshore region and the boundary condition at the beach. The ‘reduced’ boundary condition is derived as a result of the matching condition between the two regions. An explicit edge-layer solution is obtained on assuming a plane beach.

The evolution of time-periodic long waves of finite amplitude

1970 ◽  
Vol 44 (1) ◽  
pp. 195-208 ◽  
Author(s):  
O. S. Madsen ◽  
C. C. Mei ◽  
R. P. Savage
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Finite Amplitude ◽  
Long Waves ◽  
Shallow Water Waves ◽  
Wave Maker ◽  
Steep Waves ◽  
Time Periodic ◽  
Moderate Magnitude ◽  
Approximate Equations

The breakdown of shallow water waves into forms exhibiting several secondary crests is analyzed by numerical computations based on approximate equations accounting for the effects of non-linearity and dispersion. From detailed results of two cases it is shown that when long waves are such that the parameter σ = ν*L*2/h*3 is of moderate magnitude, either due to initially steep waves generated at a wave-maker or due to forced amplification by decreasing depth, waves periodic in time do not remain simply periodic in space. Numerical results are compared with experiments for waves propagating past a slope and onto a shelf.

scholarly journals ON THE RELATION BETWEEN CHANGES IN INTEGRAL QUANTITIES OF SHOALING WAVES AND BREAKING INCEPTION

1982 ◽  
Vol 1 (18) ◽  
pp. 2
Author(s):  
Takeshi Yasuda ◽  
Shintaro Goto ◽  
Yoshito Ysuchiya
Keyword(s):  
Conservation Laws ◽  
Stream Function ◽  
Function Method ◽  
Breaking Waves ◽  
Variable Coefficients ◽  
Shoaling Waves ◽  
Wave Profiles ◽  
Internal Properties ◽  
Particle Velocities ◽  
The Waves

This paper describes a mechanism of breaking waves over sloping bottoms in terms of changes in integral quantities of the waves. Systematic computations are made of wave profiles of shoaling waves up to the numerical unstable points by using the K-dV equation with variable coefficients and internal properties such as horizontal and vertical water particle velocities by a stream function method satisfying the conservation laws of mass and energy. Applicability of the numerical results is examined and a relation between numerical unstable points and actual breaker points is found. Characteristics of the integral quantities of shoaling waves are investigated in relation to the existence of the extremum of the energy of the shoaling waves and their breaking inception.

Amplification and decay of long nonlinear waves

1973 ◽  
Vol 58 (3) ◽  
pp. 481-493 ◽  
Author(s):  
S. Leibovich ◽  
J. D. Randall
Keyword(s):  
Shallow Water ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Vries Equation ◽  
Variable Coefficients ◽  
Finite Amplitude ◽  
Rotating Fluids ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Waves

The interaction of weakly nonlinear waves with slowly varying boundaries is considered. Special emphasis is given to rotating fluids, but the analysis applies with minor modifications to waves in stratified fluids and shallow-water aves. An asymptotic solution of a variant of the Korteweg–de Vries equation with variable coefficients is developed that produces a ‘Green's law’ for the amplification of waves of finite amplitude. For shallow-water waves in water of variable depth, the result predicts wave growth proportional to the $-\frac{1}{3}$ power of the depth.

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