Second-order analysis of shallow-water wave spectra

1988 ◽  
Vol 11 (5-6) ◽  
pp. 723-737
Author(s):  
M. Petti
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Second Order ◽  
Wave Spectra ◽  
Order Analysis ◽  
Shallow Water Wave

scholarly journals TRANSFORMATION OF SHALLOW WATER WAVE SPECTRA

1988 ◽  
Vol 1 (21) ◽  
pp. 44
Author(s):  
Genowefa Bendykowska ◽  
Gosta Werner
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Peak Frequency ◽  
Wave Spectra ◽  
Linear Dispersion ◽  
Mean Frequency ◽  
Wave Flume ◽  
Strongly Nonlinear ◽  
Shallow Water Wave ◽  
The Mean

Investigations are presented, on some effects of nonlinearity in the motion of shallow water wave spectra. The waves were generated, mechanically in a laboratory wave flume with fixed bottom. Essential differences with the linear dispersion relation are found, showing vanishing dispersivity of higher frequency spectral components in strongly nonlinear spectra. The mean frequency increases with decreasing water depth. The relation of the peak frequency to the mean frequency varied in the experiments from 0.9 to 0.5, for deep to shallow water wave spectra respectively.

scholarly journals Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1439
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Elliptic Integral ◽  
Momentum Conservation ◽  
Two Dimensional ◽  
Order Ordinary Differential Equation ◽  
Closed Form Solutions ◽  
Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

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