Parametric subharmonic instability in a narrow-band wave spectrum

2019 ◽  
Vol 865 ◽  
pp. 247-280
Author(s):  
Yohei Onuki ◽  
Toshiyuki Hibiya
Keyword(s):  
Narrow Band ◽  
Wave Train ◽  
Wave Spectrum ◽  
Random Wave ◽  
Weakly Nonlinear ◽  
Statistical Equation ◽  
Random Wave Field ◽  
Background Wave ◽  
Parametric Subharmonic Instability ◽  
New Criterion

Parametric subharmonic instability arising in a narrow-band wave spectrum is investigated. Using a statistical equation that describes weakly nonlinear interactions in a random wave field, we perform analytical and numerical stability analyses for a modulating wave train. The analytically obtained growth rate $\unicode[STIX]{x1D706}=(-\unicode[STIX]{x1D707}+\sqrt{\unicode[STIX]{x1D707}^{2}+4CE_{B}})/2$ agrees favourably with the results from direct numerical experiments, where $\unicode[STIX]{x1D707}$ is the half-value width of the background wave frequency spectrum, $E_{B}$ is the background wave energy density, and $C$ is a constant. This expression has two asymptotic limits: $\unicode[STIX]{x1D706}\sim \sqrt{CE_{B}}$ for $\unicode[STIX]{x1D707}\ll \sqrt{CE_{B}}$ and $\unicode[STIX]{x1D706}\sim CE_{B}/\unicode[STIX]{x1D707}$ for $\unicode[STIX]{x1D707}\gg \sqrt{CE_{B}}$. In the terms of weak turbulence, these two growth rates correspond to the ones occurring in the dynamic and kinetic time scales. In this way, our formulation successfully unifies the two conventional types of parametric subharmonic instability and offers a new criterion to determine the applicability of the classical kinetic equation in three-wave systems.

Large-time evolution of statistical moments of wind–wave fields

2013 ◽  
Vol 726 ◽  
pp. 517-546 ◽  
Author(s):  
Sergei Y. Annenkov ◽  
Victor I. Shrira
Keyword(s):  
Wave Field ◽  
Large Time ◽  
Random Wave ◽  
Wave Spectra ◽  
Large Time Asymptotics ◽  
Wave Fields ◽  
Weakly Nonlinear ◽  
Time Asymptotics ◽  
Random Wave Field ◽  
Skewness And Kurtosis

AbstractWe study the long-term evolution of weakly nonlinear random gravity water wave fields developing with and without wind forcing. The focus of the work is on deriving, from first principles, the evolution of the departure of the field statistics from Gaussianity. Higher-order statistical moments of elevation (skewness and kurtosis) are used as a measure of this departure. Non-Gaussianity of a weakly nonlinear random wave field has two components. The first is due to nonlinear wave–wave interactions. We refer to this component as ‘dynamic’, since it is linked to wave field evolution. The other component is due to bound harmonics. It is non-zero for every wave field with finite amplitude, contributes both to skewness and kurtosis of gravity water waves and can be determined entirely from the instantaneous spectrum of surface elevation. The key result of the work, supported both by direct numerical simulation (DNS) and by the analysis of simulated and experimental (JONSWAP) spectra, is that in generic situations of a broadband random wave field the dynamic contribution to kurtosis is small in absolute value, and negligibly small compared with the bound harmonics component. Therefore, the latter dominates, and both skewness and kurtosis can be obtained directly from the instantaneous wave spectra. Thus, the departure of evolving wave fields from Gaussianity can be obtained from evolving wave spectra, complementing the capability of forecasting spectra and capitalizing on the existing methodology. We find that both skewness and kurtosis are significant for typical oceanic waves; the non-zero positive kurtosis implies a tangible increase of freak wave probability. For random wave fields generated by steady or slowly varying wind and for swell the derived large-time asymptotics of skewness and kurtosis predict power law decay of the moments. The exponents of these laws are determined by the degree of homogeneity of the interaction coefficients. For all self-similar regimes the kurtosis decays twice as fast as the skewness. These formulae complement the known large-time asymptotics for spectral evolution prescribed by the Hasselmann equation. The results are verified by the DNS of random wave fields based on the Zakharov equation. The predicted asymptotic behaviour is shown to be very robust: it holds both for steady and gusty winds.

scholarly journals Discussion and answer to "on the statistic of narrow band random wave with weak nonlinearity".

1999 ◽  
pp. 195-202
Author(s):  
Toshikazu KITANO ◽  
Hajime MASE ◽  
Nobuhito MORI ◽  
Takashi YASUDA
Keyword(s):  
Narrow Band ◽  
Random Wave ◽  
Weak Nonlinearity

Transformation of Random Wave Spectrum on Beaches

1979 ◽  
Vol 105 (4) ◽  
pp. 711-717
Author(s):  
Cheng Y. Yang ◽  
Yun Hai Chen
Keyword(s):  
Wave Spectrum ◽  
Random Wave

scholarly journals Random wave-driven drag forces on near-bed vegetation in shallow water based on deepwater wind conditions

2019 ◽  
Vol 233 (4) ◽  
pp. 1287-1290
Author(s):  
Dag Myrhaug
Keyword(s):  
Shallow Water ◽  
Drag Force ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Random Wave ◽  
Random Waves ◽  
Coastal Zones ◽  
Drag Forces ◽  
Mean Wind Speed ◽  
Wave Induced

This article provides a simple analytical method for giving estimates of random wave-driven drag forces on near-bed vegetation in shallow water from deepwater wind conditions. Results are exemplified using a Pierson–Moskowitz model wave spectrum for wind waves with the mean wind speed at the 10 m elevation above the sea surface as the parameter. The significant value of the drag force within a sea state of random waves is given, and an example typical for field conditions is presented. This method should serve as a useful tool for assessing random wave-induced drag force on vegetation in coastal zones and estuaries based on input from deepwater wind conditions.

scholarly journals Weakly nonlinear transient waves on a shear current: ring waves and skewed Langmuir rolls

2019 ◽  
Vol 863 ◽  
pp. 114-149 ◽  
Author(s):  
Andreas H. Akselsen ◽  
Simen Å. Ellingsen
Keyword(s):  
Mode Coupling ◽  
Continuous Wave ◽  
Wave Spectrum ◽  
Vortex Structures ◽  
Second Order ◽  
Ocean Current ◽  
Initial Surface ◽  
Weakly Nonlinear ◽  
Special Cases ◽  
Shear Current

We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. The shear field makes this problem three-dimensional and rotational in nature, but an analytical solution is permitted via integration of the Euler equations. Although similar problems were investigated in the 1960s and 70s for special cases of resonance, this is to our knowledge the first general wave interaction (mode coupling) solution derived to second order with a shear current present. Wave interactions are integrable in a spectral convolution to yield the second-order dynamics of initial value problems. To second order, irrotational wave dynamics interacts with the background vorticity field in a way that creates new vortex structures. A notable example is the large parallel vortices which drive Langmuir circulation as oblique plane waves interact with an ocean current. We also investigate the effect on wave pairs which are misaligned with the shear current to find that similar, but skewed, vortex structures are generated in every case except when the mean wave direction is precisely perpendicular to the direction of the current. This is in contrast to a conjecture by Leibovich (Annu. Rev. Fluid Mech., vol. 15, 1983, pp. 391–427). Similar nonlinear wave–shear interactions are found to also generate near-field vortex structures in the Cauchy–Poisson problem with an initial surface elevation. These interactions create further groups of dispersive ring waves in addition to those present in linear theory. The second-order solution is derived in a general manner which accommodates any initial condition through mode coupling over a continuous wave spectrum. It is therefore applicable to a range of problems including special cases of resonance. As a by-product of the general theory, a simple expression for the Stokes drift due to a monochromatic wave propagating at oblique angle with a current of uniform vorticity is derived, for the first time to our knowledge.

Nonlinear and Dissipative Characteristics of a Combined Random-Cnoidal Wave Field

2017 ◽  
Author(s):  
James M. Kaihatu ◽  
John T. Goertz ◽  
Samira Ardani ◽  
Alex Sheremet
Keyword(s):  
Wave Spectrum ◽  
Leading Edge ◽  
Dissipation Function ◽  
Indian Ocean Tsunami ◽  
Random Wave ◽  
Cnoidal Wave ◽  
State University ◽  
Large Wave ◽  
Wave Flume ◽  
Wave Trains

Images of the 2004 Indian Ocean tsunami at landfall shows a leading edge marked by short waves (“fission” waves). These waves appear to be cnoidal in shape and of a temporal and spatial scale in line with the longest swell present in the region, and may interact with the longer waves in the background random wave spectrum. As part of a comprehensive series of experiments, the Large Wave Flume at Oregon State University (USA) was used to generate and measure the properties of cnoidal, random, and combined cnoidal-random wave trains. Both the nonlinear energy transfer characteristics (via bispectral analysis) and dissipation characteristics (via a proxy dissipation function) are studied for all generated wave conditions. It is generally determined that the characteristics of the cnoidal wave dominate the combined cnoidal-random wave signals if the energy of the cnoidal wave is at least equal to that of the random wave.

scholarly journals Space–Time Wave Extremes: The Role of Metocean Forcings

2015 ◽  
Vol 45 (7) ◽  
pp. 1897-1916 ◽  
Author(s):  
Francesco Barbariol ◽  
Alvise Benetazzo ◽  
Sandro Carniel ◽  
Mauro Sclavo
Keyword(s):  
Wind Speed ◽  
Wave Spectrum ◽  
Domain Size ◽  
Space Time ◽  
Statistical Prediction ◽  
Random Wave ◽  
Spectral Parameters ◽  
Frequency Spectra ◽  
Space Domain ◽  
Time Dynamics

AbstractWave observations and modeling have recently demonstrated that wave extremes of short-crested seas are poorly predicted by statistics of time records. Indeed, the highest waves pertain to wave groups at focusing that have space–time dynamics. Therefore, the statistical prediction of extremes of short-crested sea states should rely on the multidimensional random wave fields’ assumption. To adapt wave extreme statistics to the space–time domain, theoretical models using parameters of the directional wave spectrum have been recently developed. In this paper, the influence of metocean forcings (wind conditions, ambient current, and bottom depth) on these parameters and hence on wave extremes is studied with a twofold strategy. First, parametric spectral formulations [Pierson–Moskowitz and Joint North Sea Wave Project (JONSWAP) frequency spectra with cos2 directional distribution function] are considered to represent the dependence of wave extremes upon wind speed, fetch, and space domain size. Afterward, arbitrary conditions are simulated by using the SWAN numerical model adapted to store the spectral parameters, and the effects on extremes of current- and depth-induced shoaling are investigated. Preliminarily, the space–time extremes prediction model adopted is assessed by means of numerical simulations of Gaussian random seas. Compared to the significant wave height of the sea state and for a given space domain size, results show that space–time extremes are enhanced by opposite currents, whereas they are weakened by increasing wind conditions (wind speed and fetch) and by depth-induced shoaling. In this respect, the remarkable contribution to wave extremes of the size of the space domain is substantiated.

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