Estimation of Water Particle Velocities of Shallow Water Waves by a Modified Transfer Function Method

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.

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Estimation of Water Particle Velocities by a Modified Transfer Function Method

Coastal Engineering in Japan ◽

10.1080/05785634.1985.11924401 ◽

1985 ◽

Vol 28 (1) ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Hirofumi Koyama ◽

Koichiro Iwata

Keyword(s):

Transfer Function ◽

Function Method ◽

Water Particle ◽

Transfer Function Method ◽

Particle Velocities

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

Nonlinear Dynamics ◽

10.1007/s11071-017-3588-9 ◽

2017 ◽

Vol 89 (3) ◽

pp. 2291-2297 ◽

Cited By ~ 15

Author(s):

Yakup Yildirim ◽

Emrullah Yasar ◽

Abdullahi Rashid Adem

Keyword(s):

Shallow Water ◽

Water Waves ◽

Function Method ◽

Shallow Water Waves ◽

Model Equations

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Shallow water waves in porous medium for coast protection

Thermal Science ◽

10.2298/tsci17s1145w ◽

2017 ◽

Vol 21 (suppl. 1) ◽

pp. 145-151 ◽

Cited By ~ 4

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.

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

Open Physics ◽

10.1515/phys-2016-0007 ◽

2016 ◽

Vol 14 (1) ◽

pp. 37-43 ◽

Cited By ~ 8

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.

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