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.

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 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 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.

scholarly journals Observation of resonant interactions among surface gravity waves

2016 ◽  
Vol 805 ◽  
Author(s):  
F. Bonnefoy ◽  
F. Haudin ◽  
G. Michel ◽  
B. Semin ◽  
T. Humbert ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Phase Locking ◽  
Wave Interaction ◽  
Quantitative Agreement ◽  
Acute Angle ◽  
Experimental Results ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
Resonant Wave ◽  
Resonant Interactions

We experimentally study resonant interactions of oblique surface gravity waves in a large basin. Our results strongly extend previous experimental results performed mainly for perpendicular or collinear wave trains. We generate two oblique waves crossing at an acute angle, while we control their frequency ratio, steepnesses and directions. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory with no fitting parameter. Off-resonance experiments are also reported and the relevant theoretical analysis is conducted and validated.

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