An Euler Solver for Nonlinear Water Waves Simulation Using a Modified Staggered Grid and Gaussian Quadrature Approach

2011 ◽  
Author(s):  
Q. J. Chen ◽  
Q. Fan ◽  
S. H. Ko ◽  
H. Huang ◽  
G. Allen ◽  
...  
Keyword(s):  
Water Waves ◽  
Gaussian Quadrature ◽  
Staggered Grid ◽  
Nonlinear Water Waves ◽  
Euler Solver

scholarly journals Study on the Interaction of Nonlinear Water Waves considering Random Seas

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Marten Hollm ◽  
Leo Dostal ◽  
Hendrik Fischer ◽  
Robert Seifried
Keyword(s):  
Water Waves ◽  
Nonlinear Water Waves ◽  
Random Seas

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

Meshless numerical simulation for fully nonlinear water waves

2005 ◽  
Vol 50 (2) ◽  
pp. 219-234 ◽  
Author(s):  
Nan-Jing Wu ◽  
Ting-Kuei Tsay ◽  
D. L. Young
Keyword(s):  
Numerical Simulation ◽  
Water Waves ◽  
Nonlinear Water Waves ◽  
Fully Nonlinear

scholarly journals Nonlinear water waves

2012 ◽  
Vol 370 (1964) ◽  
pp. 1501-1504 ◽  
Author(s):  
Adrian Constantin
Keyword(s):  
Water Waves ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Recent Developments

This introduction to the issue provides a review of some recent developments in the study of water waves. The content and contributions of the papers that make up this Theme Issue are also discussed.

scholarly journals On the short-wavelength stabilities of some geophysical flows

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170090 ◽  
Author(s):  
Delia Ionescu-Kruse
Keyword(s):  
Water Waves ◽  
Short Wavelength ◽  
Travelling Wave ◽  
Geophysical Flows ◽  
Rotating Flows ◽  
Steady Flows ◽  
Azimuthal Direction ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Stability Method

This paper is a survey of the short-wavelength stability method for rotating flows. Additional complications such as stratification in the flow or the presence of non-conservative body forces are considered too. This method is applied to the specific study of some exact geophysical flows. For Gerstner-like geophysical flows one can identify perturbations in certain directions as a source of instabilities with an exponentially growing amplitude, the growth rate of the instabilities depending on the steepness of the travelling wave profile. On the other hand, for certain physically realistic velocity profiles, steady flows moving only in the azimuthal direction, with no variation in this direction, are locally stable to the short-wavelength perturbations. This article is part of the theme issue ‘Nonlinear water waves’.

A new Boussinesq method for fully nonlinear waves from shallow to deep water

2002 ◽  
Vol 462 ◽  
pp. 1-30 ◽  
Author(s):  
P. A. MADSEN ◽  
H. B. BINGHAM ◽  
HUA LIU
Keyword(s):  
Laplace Equation ◽  
Infinite Series ◽  
Deep Water ◽  
Water Waves ◽  
Modulational Instability ◽  
Surface Boundary ◽  
Nonlinear Water Waves ◽  
Finite Series ◽  
Starting Point ◽  
Highly Nonlinear

A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain. The starting point is an exact solution to the Laplace equation given in terms of infinite series expansions from an arbitrary z-level. We replace the infinite series operators by finite series (Boussinesq-type) approximations involving up to fifth-derivative operators. The finite series are manipulated to incorporate Padé approximants providing the highest possible accuracy for a given number of terms. As a result, linear and nonlinear wave characteristics become very accurate up to wavenumbers as high as kh = 40, while the vertical variation of the velocity field becomes applicable for kh up to 12. These results represent a major improvement over existing Boussinesq-type formulations in the literature. A numerical model is developed in a single horizontal dimension and it is used to study phenomena such as solitary waves and their impact on vertical walls, modulational instability in deep water involving recurrence or frequency downshift, and shoaling of regular waves up to breaking in shallow water.

scholarly journals Dynamic-pressure distributions under Stokes waves with and without a current

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170103 ◽  
Author(s):  
Motohiko Umeyama
Keyword(s):  
Water Waves ◽  
Dynamic Pressure ◽  
Water Pressure ◽  
Travelling Waves ◽  
Stokes Wave ◽  
Front Face ◽  
Nonlinear Water Waves ◽  
Near Surface ◽  
Stokes Waves ◽  
A Current

To investigate changes in the instability of Stokes waves prior to wave breaking in shallow water, pressure data were recorded vertically over the entire water depth, except in the near-surface layer (from 0 cm to −3 cm), in a recirculating channel. In addition, we checked the pressure asymmetry under several conditions. The phase-averaged dynamic-pressure values for the wave–current motion appear to increase compared with those for the wave-alone motion; however, they scatter in the experimental range. The measured vertical distributions of the dynamic pressure were plotted over one wave cycle and compared to the corresponding predictions on the basis of third-order Stokes wave theory. The dynamic-pressure pattern was not the same during the acceleration and deceleration periods. Spatially, the dynamic pressure varies according to the faces of the wave, i.e. the pressure on the front face is lower than that on the rear face. The direction of wave propagation with respect to the current directly influences the essential features of the resulting dynamic pressure. The results demonstrate that interactions between travelling waves and a current lead more quickly to asymmetry. This article is part of the theme issue ‘Nonlinear water waves’.

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