Fully Nonlinear Dispersive HAWASSI-VBM for Coastal Zone Simulations

2016 ◽  
Author(s):  
Didit Adytia ◽  
Lawrence
Keyword(s):  
Gravity Waves ◽  
Laboratory Experiments ◽  
Hamiltonian Structure ◽  
Wave Model ◽  
Nonlinear Property ◽  
Irregular Waves ◽  
Boussinesq Model ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Finite Element Implementation

The accuracy of a wave model for simulating waves in deep and coastal areas is highly determined by the dispersive properties as well as by the nonlinearity of the model. The Variational Boussinesq Model (VBM) for waves [1–4], available publicly as HAWASSI-VBM software [5], is based on the Hamiltonian structure of surface gravity waves. The model has tailor-made dispersive properties, which can be set to be sufficiently accurate for simulating a desired wave field. In this paper, we extend the nonlinear property of the HAWASSI-VBM from weakly nonlinear to be fully nonlinear. To show the improvement in nonlinearity, simulations of the model with a Finite Element implementation is tested against laboratory experiments, of regular and irregular waves propagating above a submerged bar and the dam-break problem.

On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves

1994 ◽  
Vol 272 ◽  
pp. 1-20 ◽  
Author(s):  
Vladimir P. Krasitskii
Keyword(s):  
Power Series ◽  
Surface Waves ◽  
Gravity Waves ◽  
Hamiltonian Structure ◽  
Classical Method ◽  
Weakly Nonlinear ◽  
Integral Power ◽  
Reduced Equations ◽  
Nonlinear Surface Waves ◽  
Nonlinear Surface

Many studies of weakly nonlinear surface waves are based on so-called reduced integrodifferential equations. One of these is the widely used Zakharov four-wave equation for purely gravity waves. But the reduced equations now in use are not Hamiltonian despite the Hamiltonian structure of exact water wave equations. This is entirely due to shortcomings of their derivation. The classical method of canonical transformations, generalized to the continuous case, leads automatically to reduced equations with Hamiltonian structure. In this paper, attention is primarily paid to the Hamiltonian reduced equation describing the combined effects of four- and five-wave weakly nonlinear interactions of purely gravity waves. In this equation, for brevity called five-wave, the non-resonant quadratic, cubic and fourth-order nonlinear terms are eliminated by suitable canonical transformation. The kernels of this equation and the coefficients of the transformation are expressed in explicit form in terms of expansion coefficients of the gravity-wave Hamiltonian in integral-power series in normal variables. For capillary–gravity waves on a fluid of finite depth, expansion of the Hamiltonian in integral-power series in a normal variable with accuracy up to the fifth-order terms is also given.

scholarly journals Effects of an abrupt depth change on weakly nonlinear surface gravity waves: deterministic and stochastic analysis

2020 ◽  
Author(s):  
Yan Li ◽  
Samuel Draycott ◽  
Yaokun Zheng ◽  
Thomas A.A. Adcock ◽  
Zhiliang Lin ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Second Order ◽  
Surface Gravity ◽  
Irregular Waves ◽  
Wave Steepness ◽  
Weakly Nonlinear ◽  
Wave Statistics ◽  
Surface Gravity Waves ◽  
Seabed Topography ◽  
Nonlinear Surface

<p>This work focuses on two different aspects of the effect of an abrupt depth transition on weakly nonlinear surface gravity waves: deterministic and stochastic. It is known that the kurtosis of waves can reach a maximum near the top of such abrupt depth transitions. The analysis is based on three different approaches: (1) a novel theoretical framework that allows for narrow-banded surface waves experiencing a step-type seabed, correct to the second order in wave steepness; (2) experimental observations; and (3) a numerical model based on a fully nonlinear potential flow solver. To reveal the fundamental physics, the evolution of a wave envelope that experiences an abrupt depth transition is examined in detail; (a) we show the release of free waves at second order in wave steepness both for the super-harmonic and sub-harmonic or ‘mean’ terms; (b) a local wave height peak that occurs near the top of a depth transition – whose exact position depends on several nondimensional parameters – is revealed; (c) furthermore, we examine which parameters affect this peak. The novel physics has implications for wave statistics for long-crested irregular waves experiencing an abrupt depth transition. We show the connection of the second-order physics at work in the deterministic and stochastic cases: the peak of wave kurtosis and skewness occurs in the neighborhood of the deterministic wave peak in (b) and for the same parameters set composed of a seabed topography, water depths, primary wave frequency and steepness, and bandwidth.</p>

scholarly journals Two-dimensional generalized solitary waves and periodic waves under an ice sheet

2011 ◽  
Vol 369 (1947) ◽  
pp. 2957-2972 ◽  
Author(s):  
Jean-Marc Vanden-Broeck ◽  
Emilian I. Părău
Keyword(s):  
Solitary Waves ◽  
Gravity Waves ◽  
Ice Sheet ◽  
Periodic Waves ◽  
Two Dimensional ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Dimensional Gravity ◽  
Nonlinear Solutions

Two-dimensional gravity waves travelling under an ice sheet are studied. The flow is assumed to be potential. Weakly nonlinear solutions are derived and fully nonlinear solutions are calculated numerically. Periodic waves and generalized solitary waves are studied.

A FULLY NONLINEAR BOUSSINESQ MODEL FOR WATER WAVE PROPAGATION

2011 ◽  
Vol 1 (32) ◽  
pp. 12
Author(s):  
Hong-sheng Zhang ◽  
Hua-wei Zhou ◽  
Guang-wen Hong ◽  
Jian-min Yang
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Nonlinear Boundary Conditions ◽  
Boussinesq Model ◽  
Linear Dispersion ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Sea Bed ◽  
Nonlinear Version ◽  
Nicolson Scheme

A set of high-order fully nonlinear Boussinesq-type equations is derived from the Laplace equation and the nonlinear boundary conditions. The derived equations include the dissipation terms and fully satisfy the sea bed boundary condition. The equations with the linear dispersion accurate up to [2,2] padé approximation is qualitatively and quantitatively studied in details. A numerical model for wave propagation is developed with the use of iterative Crank-Nicolson scheme, and the two-dimensional fourth-order filter formula is also derived. With two test cases numerically simulated, the modeled results of the fully nonlinear version of the numerical model are compared to those of the weakly nonlinear version.

scholarly journals Wave Directions in a Narrow Bay

2010 ◽  
Vol 40 (1) ◽  
pp. 155-169 ◽  
Author(s):  
Heidi Pettersson ◽  
Kimmo K. Kahma ◽  
Laura Tuomi
Keyword(s):  
Wave Model ◽  
Wave Climate ◽  
Spectral Peak ◽  
Step Size ◽  
Weakly Nonlinear ◽  
Spectral Wave Model ◽  
Directional Coupling ◽  
Directional Wave ◽  
The Baltic ◽  
The Waves

Abstract In slanting fetch conditions the direction of actively growing waves is strongly controlled by the fetch geometry. The effect was found to be pronounced in the long and narrow Gulf of Finland in the Baltic Sea, where it significantly modifies the directional wave climate. Three models with different assumptions on the directional coupling between the wave components were used to analyze the physics responsible for the directional behavior of the waves in the gulf. The directionally decoupled model produced the direction at the spectral peak correctly when the slanting fetch geometry was narrow but gave a weaker steering than observed when the fetch geometry was broader. The method of Donelan estimated well the direction at the spectral peak in well-defined slanting fetch conditions, but overestimated the longer fetch components during wave growth from a more complex shoreline. Neither the decoupled nor the Donelan model reproduced the observed shifting of direction with the frequency. The performance of the third-generation spectral wave model (WAM) in estimating the wave directions was strongly dependent on the grid resolution of the model. The dominant wave directions were estimated satisfactorily when the grid-step size was dropped to 5 km in the gulf, which is 70 km in its narrowest part. A mechanism based on the weakly nonlinear interactions is proposed to explain the strong steering effect in slanting fetch conditions.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

scholarly journals The role of constant vorticity on weakly nonlinear surface gravity waves

Wave Motion ◽  
2020 ◽  
pp. 102702
Author(s):  
M.A. Manna ◽  
S. Noubissie ◽  
J. Touboul ◽  
B. Simon ◽  
R.A. Kraenkel
Keyword(s):  
Gravity Waves ◽  
Surface Gravity ◽  
Weakly Nonlinear ◽  
Surface Gravity Waves ◽  
Constant Vorticity ◽  
Nonlinear Surface

Fully Nonlinear Potential/RANSE Simulation of Wave Interaction With Ships and Marine Structures

2008 ◽  
Author(s):  
Pierre Ferrant ◽  
Lionel Gentaz ◽  
Bertrand Alessandrini ◽  
Romain Luquet ◽  
Charles Monroy ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Fully Nonlinear ◽  
Nonlinear Potential ◽  
6 Degrees Of Freedom

This paper documents recent advances of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach, a method for simulating fully nonlinear wave-body interactions including viscous effects. The methods efficiently combines a fully nonlinear potential flow description of undisturbed wave systems with a modified set of RANS with free surface equations accounting for the interaction with a ship or marine structure. Arbitrary incident wave systems may be described, including regular, irregular waves, multidirectional waves, focused wave events, etc. The model may be fixed or moving with arbitrary speed and 6 degrees of freedom motion. The extension of the SWENSE method to 6 DOF simulations in irregular waves as well as to manoeuvring simulations in waves are discussed in this paper. Different illlustative simulations are presented and discussed. Results of the present approach compare favorably with available reference results.

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