Surface gravity waves from direct numerical simulations of the Euler equations: A comparison with second-order theory

2008 ◽  
Vol 35 (3-4) ◽  
pp. 367-379 ◽  
Author(s):  
A. Toffoli ◽  
M. Onorato ◽  
E. Bitner-Gregersen ◽  
A.R. Osborne ◽  
A.V. Babanin
Keyword(s):  
Numerical Simulations ◽  
Euler Equations ◽  
Gravity Waves ◽  
Order Theory ◽  
Second Order ◽  
Direct Numerical Simulations ◽  
Surface Gravity ◽  
Surface Gravity Waves

Verification of Hasselmann's energy transfer among surface gravity waves by direct numerical simulations of primitive equations

2001 ◽  
Vol 444 ◽  
pp. 199-221 ◽  
Author(s):  
MITSUHIRO TANAKA
Keyword(s):  
Energy Transfer ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Direct Numerical Simulations ◽  
Rate Of Change ◽  
Surface Gravity ◽  
Primitive Equations ◽  
Surface Gravity Waves ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

The temporal evolution of nonlinear wave fields of surface gravity waves is studied by large-scale direct numerical simulations of primitive equations in order to verify Hasselmann's theory for nonlinear energy transfer among component gravity waves. In the simulations, all the nonlinear interactions, including both resonant and non-resonant ones, are taken into account up to the four-wave processes. The initial wave field is constructed by combining more than two million component free waves in such a way that it has the JONSWAP or the Pierson–Moskowitz spectrum. The nonlinear energy transfer is evaluated from the rate of change of the spectrum, and is compared with Hasselmann's theory. It is shown that, in spite of apparently insufficient duration of the simulations such as just a few tens of characteristic periods, the energy transfer obtained by the present method shows satisfactory agreement with Hasselmann's theory, at least in their qualitative features.

scholarly journals Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin

2009 ◽  
Vol 627 ◽  
pp. 235-257 ◽  
Author(s):  
M. ONORATO ◽  
L. CAVALERI ◽  
S. FOUQUES ◽  
O. GRAMSTAD ◽  
P. A. E. M. JANSSEN ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Order Theory ◽  
Second Order ◽  
Statistical Properties ◽  
Surface Elevation ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
Wave Basin ◽  
Dimensional Wave

A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30° at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests. Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

Resonant interactions between planetary waves

1967 ◽  
Vol 299 (1456) ◽  
pp. 120-144 ◽  
Keyword(s):  
Energy Transfer ◽  
Gravity Waves ◽  
Second Order ◽  
Planetary Waves ◽  
Surface Gravity ◽  
Third Wave ◽  
Surface Gravity Waves ◽  
Resonant Interactions ◽  
Harmonic Components ◽  
North And South

In contrast to surface gravity waves, planetary waves can interact resonantly at the second order. Hence triplets of planetary waves may occur which are in resonance with each other. For simplicity the situation is studied first on a β plane. The geometrical conditions for two waves to form a triplet with a given third wave are determined, and so also is the rate of energy transfer. Some conservation theorems are proved. The analysis allows for a non-zero horizontal divergence of the motion. For waves which cover a complete sphere it is shown that the resonant interactions between three different harmonic components take place, if at all, in the neighbourhoods of two latitude circles, situated symmetrically north and south of the equator.

Statistical Properties of a Directional Wave Field: Direct Simulations of the Euler Equations and Second-Order Theory

2008 ◽  
Author(s):  
A. Toffoli ◽  
E. M. Bitner-Gregersen ◽  
M. Onorato
Keyword(s):  
Wave Field ◽  
Euler Equations ◽  
Gravity Waves ◽  
Modulational Instability ◽  
Order Theory ◽  
Second Order ◽  
Statistical Properties ◽  
Directional Wave ◽  
Low Probability ◽  
Wind Sea

It is well established that the modulational instability enhances the probability of occurrence for extreme events if waves are long crested. Recent studies, however, have shown that the coexistence of directional wave components can substantially reduce its effects. Here, direct numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. Results will show that the distribution proposed by Forristall [1] provides a good estimate of the simulated crest height also at low probability levels.

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>

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