scholarly journals Long-term wave growth and its linear and nonlinear interactions with wind fluctuations

2008 ◽  
Vol 26 (4) ◽  
pp. 747-758 ◽  
Author(s):  
Z. Ge ◽  
P. C. Liu
Keyword(s):  
Wave Field ◽  
Wind Wave ◽  
Wave Spectrum ◽  
Wave Interactions ◽  
Wave Growth ◽  
Linear And Nonlinear ◽  
Equilibrium Range ◽  
Wave Induced ◽  
The Waves

Abstract. Following Ge and Liu (2007), the simultaneously recorded time series of wave elevation and wind velocity are examined for long-term (on Lavrenov's τ4-scale or 3 to 6 h) linear and nonlinear interactions between the wind fluctuations and the wave field. Over such long times the detected interaction patterns should reveal general characteristics for the wave growth process. The time series are divided into three episodes, each approximately 1.33 h long, to represent three sequential stages of wave growth. The classic Fourier-domain spectral and bispectral analyses are used to identify the linear and quadratic interactions between the waves and the wind fluctuations as well as between different components of the wave field. The results show clearly that as the wave field grows the linear interaction becomes enhanced and covers wider range of frequencies. Two different wave-induced components of the wind fluctuations are identified. These components, one at around 0.4 Hz and the other at around 0.15 to 0.2 Hz, are generated and supported by both linear and quadratic wind-wave interactions probably through the distortions of the waves to the wind field. The fact that the higher-frequency wave-induced component always stays with the equilibrium range of the wave spectrum around 0.4 Hz and the lower-frequency one tends to move with the downshifting of the primary peak of the wave spectrum defines the partition of the primary peak and the equilibrium range of the wave spectrum, a characteristic that could not be revealed by short-time wavelet-based analyses in Ge and Liu (2007). Furthermore, these two wave-induced peaks of the wind spectrum appear to have different patterns of feedback to the wave field. The quadratic wave-wave interactions also are assessed using the auto-bispectrum and are found to be especially active during the first and the third episodes. Such directly detected wind-wave interactions, both linear and nonlinear, may complement the existing theoretical and numerical models, and can be used for future model development and validation.

Wind–wave coupling study using LES of wind and phase-resolved simulation of nonlinear waves

2019 ◽  
Vol 874 ◽  
pp. 391-425 ◽  
Author(s):  
Xuanting Hao ◽  
Lian Shen
Keyword(s):  
Wave Field ◽  
Water Waves ◽  
Wind Wave ◽  
Wave Spectrum ◽  
High Order ◽  
Band Spectrum ◽  
Wave Growth ◽  
Turbulent Wind ◽  
Wind Turbulence ◽  
The Waves

We present a study on the interaction between wind and water waves with a broad-band spectrum using wave-phase-resolved simulation with long-term wave field evolution. The wind turbulence is computed using large-eddy simulation and the wave field is simulated using a high-order spectral method. Numerical experiments are carried out for turbulent wind blowing over a wave field initialised using the Joint North Sea Wave Project spectrum, with various wind speeds considered. The results show that the waves, together with the mean wind flow and large turbulent eddies, have a significant impact on the wavenumber–frequency spectrum of the wind turbulence. It is found that the shear stress contributed by sweep events in turbulent wind is greatly enhanced as a result of the waves. The dependence of the wave growth rate on the wave age is consistent with the results in the literature. The probability density function and high-order statistics of the wave surface elevation deviate from the Gaussian distribution, manifesting the nonlinearity of the wave field. The shape of the change in the spectrum of wind-waves resembles that of the nonlinear wave–wave interactions, indicating the dominant role played by the nonlinear interactions in the evolution of the wave spectrum. The frequency downshift phenomenon is captured in our simulations wherein the wind-forced wave field evolves for $O(3000)$ peak wave periods. Using the numerical result, we compute the universal constant in a wave-growth law proposed in the literature, and substantiate the scaling of wind–wave growth based on intrinsic wave properties.

scholarly journals A time-localized response of wave growth process under turbulent winds

2007 ◽  
Vol 25 (6) ◽  
pp. 1253-1262 ◽  
Author(s):  
Z. Ge ◽  
P. C. Liu
Keyword(s):  
Wind Wave ◽  
Wave Spectrum ◽  
Small Time ◽  
Wave Interactions ◽  
Wave Fields ◽  
Energy Transfers ◽  
Background Turbulence ◽  
Wave Development ◽  
Short Time ◽  
Wave Induced

Abstract. Very short time series (with lengths of approximately 40 s or 5~7 wave periods) of wind velocity fluctuations and wave elevation were recorded simultaneously and investigated using the wavelet bispectral analysis. Rapid changes in the wave and wind spectra were detected, which were found to be intimately related to significant energy transfers through transient quadratic wind-wave and wave-wave interactions. A possible pattern of energy exchange between the wind and wave fields was further deduced. In particular, the generation and variation of the strong wave-induced perturbation velocity in the wind can be explained by the strengthening and diminishing of the associated quadratic interactions, which cannot be unveiled by linear theories. On small time scales, the wave-wave quadratic interactions were as active and effective in transferring energy as the wind-wave interactions. The results also showed that the wind turbulence was occasionally effective in transferring energy between the wind and the wave fields, so that the background turbulence in the wind cannot be completely neglected. Although these effects are all possibly significant over short times, the time-localized growth of the wave spectrum may not considerably affect the long-term process of wave development.

Wave-Coherent Airflow and Critical Layers over Ocean Waves

2013 ◽  
Vol 43 (10) ◽  
pp. 2156-2172 ◽  
Author(s):  
Laurent Grare ◽  
Luc Lenain ◽  
W. Kendall Melville
Keyword(s):  
Momentum Flux ◽  
Wave Spectrum ◽  
Phase Speed ◽  
Ocean Waves ◽  
Naval Research ◽  
Critical Height ◽  
Office Of Naval Research ◽  
Mean Wind Speed ◽  
Wave Induced ◽  
The Waves

Abstract An analysis of coherent measurements of winds and waves from data collected during the Office of Naval Research (ONR) High-Resolution air–sea interaction (HiRes) program, from the Floating Instrument Platform (R/P FLIP), off the coast of northern California in June 2010 is presented. A suite of wind and wave measuring systems was deployed to resolve the modulation of the marine atmospheric boundary layer by waves. Spectral analysis of the data provided the wave-induced components of the wind velocity for various wind–wave conditions. The power spectral density, the amplitude, and the phase (relative to the waves) of these wave-induced components are computed and bin averaged over spectral wave age c/U(z) or c/u*, where c is the linear phase speed of the waves, U(z) is the mean wind speed measured at the height z of the anemometer, and u* is the friction velocity in the air. Results are qualitatively consistent with the critical layer theory of Miles. Across the critical height zc, defined such that U(zc) = c, the wave-induced vertical and horizontal velocities change significantly in both amplitude and phase. The measured wave-induced momentum flux shows that, for growing waves, less than 10% of the momentum flux at z ≈ 10 m is supported by waves longer than approximately 15 m. For older sea states, these waves are able to generate upward wave-induced momentum flux opposed to the overall downward momentum flux. The measured amplitude of this upward wave-induced momentum flux was up to 20% of the value of the total wind stress when Cp/u* > 60, where Cp is the phase speed at the peak of the wave spectrum.

scholarly journals The Effect of Wind–Wave–Current Interaction on Air–Sea Momentum Fluxes and Ocean Response in Tropical Cyclones

2009 ◽  
Vol 39 (4) ◽  
pp. 1019-1034 ◽  
Author(s):  
Yalin Fan ◽  
Isaac Ginis ◽  
Tetsu Hara
Keyword(s):  
Surface Wave ◽  
Wave Field ◽  
Tropical Cyclones ◽  
Momentum Flux ◽  
Wind Wave ◽  
Wave Spectrum ◽  
Peak Frequency ◽  
Current Interaction ◽  
Subsurface Current ◽  
The Right

Abstract In this paper, the wind–wave–current interaction mechanisms in tropical cyclones and their effect on the surface wave and ocean responses are investigated through a set of numerical experiments. The key element of the authors’ modeling approach is the air–sea interface model, which consists of a wave boundary layer model and an air–sea momentum flux budget model. The results show that the time and spatial variations in the surface wave field, as well as the wave–current interaction, significantly reduce momentum flux into the currents in the right rear quadrant of the hurricane. The reduction of the momentum flux into the ocean consequently reduces the magnitude of the subsurface current and sea surface temperature cooling to the right of the hurricane track and the rate of upwelling/downwelling in the thermocline. During wind–wave–current interaction, the momentum flux into the ocean is mainly affected by reducing the wind speed relative to currents, whereas the wave field is mostly affected by refraction due to the spatially varying currents. In the area where the current is strongly and roughly aligned with wave propagation direction, the wave spectrum of longer waves is reduced, the peak frequency is shifted to a higher frequency, and the angular distribution of the wave energy is widened.

scholarly journals A Two-Scale Approximation for Efficient Representation of Nonlinear Energy Transfers in a Wind Wave Spectrum. Part I: Theoretical Development

2008 ◽  
Vol 38 (12) ◽  
pp. 2801-2816 ◽  
Author(s):  
Donald T. Resio ◽  
William Perrie
Keyword(s):  
Wind Wave ◽  
Wave Spectrum ◽  
Estimation Method ◽  
Finite Depth ◽  
Theoretical Development ◽  
Wave Interactions ◽  
Transfer Rates ◽  
Energy Transfers ◽  
Total Integral ◽  
Discrete Interaction

Abstract A new method for estimating the transfer rates in wind wave spectra is derived and tested, based on a two-scale approximation (TSA) to the total integral for quadruplet wave–wave interactions. Comparisons of this new estimation method to the full integral are given for several idealized spectra, including Joint North Sea Wave Project spectra with different peakednesses, a finite depth case, and cases with perturbations added to underlying parametric spectra. In particular, these comparisons show that the TSA is a significant improvement over the discrete interaction approximation (DIA) in deep water and an even greater improvement in shallow water.

scholarly journals Conversion of the wavelength distribution to the energy spectrum of the wave

2021 ◽  
Vol 2131 (5) ◽  
pp. 052055
Author(s):  
V I Sichkarev ◽  
B V Palagushkin
Keyword(s):  
Wave Field ◽  
Wind Wave ◽  
Complete Solution ◽  
Wave Disturbance ◽  
Radar Images ◽  
Available Information ◽  
Wave Induced ◽  
Wavelength Distribution ◽  
Mathematical Connection ◽  
Function Assessment

Abstract When designing a vessel, spectral calculating methods of wave induced oscillation are used, and during vessel operation, available technical means allow us to obtain only the pitch spectrum. For a complete solution of navigational tasks, it is necessary to have a wave disturbance spectrum and pitch amplitude-frequency characteristic as well. The latter function can be received in sailing, if obtaining the actual wave disturbance spectrum is possible. The lack of available and sufficiently accurate methods of actual wave disturbance assessment in modern navigation creates the need to use statistical mathematical models in addition to available information in order to connect various wave elements. Taking into account the possibility of obtaining the wavelength distribution from the wave field radar image, a hypothesis is formulated about the possibility of using a statistical mathematical connection between the wind wave lengths and heights. Within the proposed hypothesis, an algorithm is presented for converting the actual wavelength probability distribution obtained from wave field radar images into the disturbance frequency spectrum. The conclusion is made about possible application of the hypothesis in pitch transfer function assessment.

X-Ray Dynamical Diffraction Process Inside a Distorted Crystal

1982 ◽  
Vol 37 (5) ◽  
pp. 460-464
Author(s):  
S. Takagi
Keyword(s):  
Wave Field ◽  
Perfect Crystal ◽  
Primary Wave ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Exit Surface ◽  
Wave Induced ◽  
The Waves ◽  
Resultant Wave

It is shown that the dynamical diffraction process inside a distorted crystal consists of ordinary dynamical progression inside perfect portions of the crystal and scattering at distortions. The scattered waves proceed as in the perfect crystal and can be multiply scattered. The sum of the primary wave induced at the entrance surface and the waves scattered at distorted parts inside the “inverted Borrmann triangle” gives the resultant wave field at the exit surface.

scholarly journals Wind–Wave Modeling: Where We Are, Where to Go

2020 ◽  
Vol 8 (4) ◽  
pp. 260 ◽  
Author(s):  
Luigi Cavaleri ◽  
Francesco Barbariol ◽  
Alvise Benetazzo
Keyword(s):  
Wind Wave ◽  
Wave Spectrum ◽  
Specific Situation ◽  
Physical Processes ◽  
Wave Modeling ◽  
Wave Heights ◽  
Meteorological Input ◽  
Operational Models

We perform a critical analysis of the present approach in wave modeling and of the related results. While acknowledging the good quality of the best present forecasts, we point out the limitations that appear when we focus on the corresponding spectra. Apart from the meteorological input, these are traced back to the spectral approach at the base of the present operational models, and the consequent approximations involved in properly modeling the various physical processes at work. Future alternatives are discussed. We then focus our attention on how, given the situation, to deal today with the estimate of the maximum wave heights, both in the long term and for a specific situation. For this, and within the above limits, a more precise evaluation of the wave spectrum is shown to be a mandatory condition.

scholarly journals The Role of Nonlinear Momentum Fluxes on the Evolution of Directional Wind-Wave Spectra

2011 ◽  
Vol 41 (4) ◽  
pp. 781-801 ◽  
Author(s):  
Donald T. Resio ◽  
Charles E. Long ◽  
William Perrie
Keyword(s):  
Energy Flux ◽  
Wind Wave ◽  
Stationary Solutions ◽  
Wave Spectra ◽  
Wave Interactions ◽  
Numerical Studies ◽  
Momentum Fluxes ◽  
Directional Distributions ◽  
Equilibrium Range

Abstract It has long been known that nonlinear wave–wave interactions produce stationary solutions related to constant energy flux through the equilibrium range when a deep-water spectrum follows an f−4 form, as has been verified in numerical studies in which spectra follow a constant angular spreading distribution. This paper shows that, although energy fluxes through such spectra remain essentially constant, momentum fluxes do not. On the other hand, if the angular distribution of a spectrum is allowed to behave in a manner consistent with observations, both the energy flux and the momentum flux tend to remain constant through a major portion of the spectrum. Thus, it appears that directional distributions of energy within wind-wave spectra adjust to a form consistent with nondivergent nonlinear fluxes, suggesting that these fluxes likely play a very prominent role in the evolution of directional spectra during wave generation.

Wave Transformation and Soil Response Due to Submerged Permeable Breakwater

2006 ◽  
Author(s):  
Ching-Piao Tsai ◽  
Hong-Bin Chen ◽  
Dong-Sheng Jeng ◽  
Kuan-Hong Chen
Keyword(s):  
Pore Pressure ◽  
Wave Spectrum ◽  
Experimental Results ◽  
Wave Transformation ◽  
Harmonic Mode ◽  
Submerged Breakwater ◽  
Soil Response ◽  
Higher Harmonic ◽  
Wave Induced ◽  
The Waves

This study reports the experimental results of the wave transformation and the wave-induced soil response when the waves pass through the submerged permeable breakwater. The model of the submerged breakwater was built on a horizontal sandy bottom. The experimental results of the spectrum of the wave transformation and the wave-induced pore-pressure are first analyzed in this paper. It is found that the wave spectrum is similar to the condition of the impermeable bottom that the higher harmonic mode appears when the waves pass over the submerged structure. However, the higher harmonic mode is not found in the spectrum of the wave-induced pore pressure, showing that the nonlinearity of the pore pressure is damped by the porous bed. The influences of the geometry of the submerged breakwater to the transformation of the wave height and the pore-pressure are also investigated. Based on the experimental results, the regression formulas for the coefficients of the wave reflection, the wave transmission and the wave energy dissipation are obtained in the paper.

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