Analysis of Numerical Oscillation Problems in a Non Linear Time Dependent Mild Slope Model and First Developments for the Implementation of Wave Breaking

2008 ◽  
Author(s):  
Ana Catarina Zo´zimo ◽  
Conceic¸a˜o Fortes
Keyword(s):  
Energy Dissipation ◽  
Wave Breaking ◽  
Linear Time ◽  
Momentum Equation ◽  
Time Dependent ◽  
Theoretical Formulation ◽  
Dissipative Term ◽  
Mild Slope Equation ◽  
Non Linear ◽  
Work Done

In this paper, a description of the numerical model NMLSE is presented. This model solves the time dependent non linear mild slope equation, without including energy dissipation due to wave breaking [1]. Some modifications are made in the boundary conditions of the original version of the model in order to overcome the numerical oscillation problems detected in the work done by [2]. To evaluate the effectiveness of the new versions of the model, they are applied to test cases of the bibliography and to a bar-trough profile beach for which there are data from physical model tests. The basic theoretical formulation of a new momentum equation that includes energy dissipation due to wave breaking is also presented. The energy dissipation due to wave breaking is included through the addition of a dissipative term based in the eddy viscosity concept.

scholarly journals A Modified k – ε Turbulence Model for a Wave Breaking Simulation

Water ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 2282
Author(s):  
Giovanni Cannata ◽  
Federica Palleschi ◽  
Benedetta Iele ◽  
Francesco Gallerano
Keyword(s):  
Energy Dissipation ◽  
Turbulence Model ◽  
Wave Breaking ◽  
A Priori ◽  
Time Dependent ◽  
Breaking Wave ◽  
Vertical Coordinate ◽  
Initial Wave ◽  
Proposed Model ◽  
Curvilinear Coordinate

We propose a two-equation turbulence model based on modification of the k − ε standard model, for simulation of a breaking wave. The proposed model is able to adequately simulate the energy dissipation due to the wave breaking and does not require any “a priori” criterion to locate the initial wave breaking point and the region in which the turbulence model has to be activated. In order to numerically simulate the wave propagation from deep water to the shoreline and the wave breaking, we use a model in which vector and tensor quantities are expressed in terms of Cartesian components, where only the vertical coordinate is expressed as a function of a time-dependent curvilinear coordinate that follows the free surface movements. A laboratory test is numerically reproduced with the aim of validating the turbulence modified k − ε model. The numerical results compared with the experimental measurements show that the proposed turbulence model is capable of correctly estimating the energy dissipation induced by the wave breaking, in order to avoid any underestimation of the wave height.

Modified Extended Hyperbolic Mild-Slope Equations

2014 ◽  
Vol 522-524 ◽  
pp. 995-999
Author(s):  
Hua Chen Pan ◽  
Zhi Guang Zhang
Keyword(s):  
Wave Propagation ◽  
Energy Dissipation ◽  
Wave Breaking ◽  
Nonlinear Dispersion ◽  
Modifying Factors ◽  
Nonlinear Dispersion Relation ◽  
Mild Slope Equation ◽  
Breaking Mechanism ◽  
Wind Input ◽  
Rapidly Varying Topography

A form of hyperbolic mild-slope equations extended to account for rapidly varying topography, nonlinear dispersion relation, wind input and energy dissipation during the process of wave propagation, has been derived from the mild-slope equation modified first in this paper. With the inclusion of the input of wind energy, the resultant model can be applied in some areas where the effect of wind could not be neglected. The wave-breaking mechanism which will cause energy dissipation remarkably, as well as the bottom friction, is introduced and discussed during this derivation. Since the modifying factors have taken plenty of aspects into consideration, the extended equations hold enlarged application and increased accuracy.

New features of non-linear time-dependent two-level atoms

2019 ◽  
Vol 105 ◽  
pp. 171-181
Author(s):  
Mehdi Akremi ◽  
S.T. Korashy ◽  
T.M. El-Shahat ◽  
R. Nekhili ◽  
Inamuddin ◽  
...  
Keyword(s):  
Linear Time ◽  
Time Dependent ◽  
Non Linear

scholarly journals DYNAMICS OF T=0 BCS CONDENSATES

1995 ◽  
Vol 09 (11) ◽  
pp. 1359-1373 ◽  
Author(s):  
MICHAEL STONE
Keyword(s):  
Fermi Surface ◽  
Order Parameter ◽  
Schrodinger Equation ◽  
Linear Time ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Long Wavelength ◽  
Non Linear ◽  
Bose Superfluid ◽  
Galilean Invariant

Fermi-surface bosonization is used to show that the long-wavelength, T=0, dynamics of a BCS superfluid or superconductor is described by a galilean invariant non-linear time-dependent Schrödinger equation. This equation is of same form as the Gross-Pitaevskii equation for a Bose superfluid, but the “wavefunction” is not the superfluid order parameter.

scholarly journals Second-Order Time-Dependent Mild-Slope Equation for Wave Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Ching-Piao Tsai ◽  
Hong-Bin Chen ◽  
John R. C. Hsu
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Surf Zone ◽  
Linear Time ◽  
Second Order ◽  
Time Dependent ◽  
Wave Transformation ◽  
Stokes Wave ◽  
Perturbation Scheme ◽  
Mild Slope Equation

This study is to propose a wave model with both wave dispersivity and nonlinearity for the wave field without water depth restriction. A narrow-banded sea state centred around a certain dominant wave frequency is considered for applications in coastal engineering. A system of fully nonlinear governing equations is first derived by depth integration of the incompressible Navier-Stokes equation in conservative form. A set of second-order nonlinear time-dependent mild-slope equations is then developed by a perturbation scheme. The present nonlinear equations can be simplified to the linear time-dependent mild-slope equation, nonlinear long wave equation, and traditional Boussinesq wave equation, respectively. A finite volume method with the fourth-order Adams-Moulton predictor-corrector numerical scheme is adopted to directly compute the wave transformation. The validity of the present model is demonstrated by the simulation of the Stokes wave, cnoidal wave, and solitary wave on uniform depth, nonlinear wave shoaling on a sloping beach, and wave propagation over an elliptic shoal. The nearshore wave transformation across the surf zone is simulated for 1D wave on a uniform slope and on a composite bar profile and 2D wave field around a jetty. These computed wave height distributions show very good agreement with the experimental results available.

Numerical Simulation of Wave Transformation Across the Surf Zone Over a Steep Bottom

2010 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Ta-Yuan Lin ◽  
Hwung-Hweng Hwung ◽  
Yaron Toledo ◽  
Aron Roland
Keyword(s):  
Energy Dissipation ◽  
Wave Breaking ◽  
Surf Zone ◽  
Numerical Models ◽  
Dissipation Factor ◽  
Wave Transformation ◽  
Bottom Slope ◽  
Mild Slope Equation ◽  
Efficient Scheme ◽  
Sloping Beach

The combined effect of shoaling, breaking and energy dissipation on a sloping bottom was investigated. Based on the conservation principle of wave motion, a combined shoaling and bottom slope coefficient is included in the mild-slope equation (MSE) which is derived as a function of the bottom slope perturbed to the third-order. The model incorporates the nonlinear shoaling coefficient and energy dissipation factor due to wave breaking to improve the accuracy of the simulation prior to wave breaking and in the surf zone over a steep bottom. The evolution equation of the MSE is implemented in the numerical solution which provides an efficient scheme for describing wave transformation in a large coastal area. The model validity is verified by comparison to accurate numerical models, laboratory experiments and analytical solutions of waves travelling over a steep sloping beach.

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