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 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.

scholarly journals On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere

2009 ◽  
Vol 27 (11) ◽  
pp. 4105-4124 ◽  
Author(s):  
I. P. Chunchuzov
Keyword(s):  
Wave Field ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Spectrum ◽  
Broad Band ◽  
Internal Gravity Waves ◽  
Wave Number ◽  
Band Spectrum ◽  
Relative Temperature ◽  
Lagrangian Variables

Abstract. The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.

Wind-induced growth of water waves

1982 ◽  
Vol 123 ◽  
pp. 425-442 ◽  
Author(s):  
H. Mitsuyasu ◽  
T. Honda
Keyword(s):  
Growth Rate ◽  
Water Waves ◽  
Friction Velocity ◽  
Wind Wave ◽  
Wind Waves ◽  
Pure Water ◽  
Wave Flume ◽  
Wind Speeds ◽  
Wind Profiles ◽  
The Waves

Spatial growth of mechanically generated water waves under the action of wind has been measured in a laboratory wind-wave flume both for pure water and for water containing a surfactant (sodium lauryl sulphate, concentration 2.6 × 10−2%). I n the latter case, no wind waves develop on the surface of the mechanically generated waves as well as on the still water surface for wind speeds up to U10≈ 15 m/s, where U10 is the wind velocity at the height Z = 10 m. Therefore we can study the wind-induced growth of monochromatic waves without the effects of co-existing short wind waves. The mechanically generated waves grew exponentially under the action of the wind, with fetch in both cases. The measured growth rate β for the pure water can be fitted by β/f = 0.34(U*/C)2 0.1 [lsime ] U*/C [lsime ] 1.0, where f is the frequency of the waves, C is the corresponding phase velocity, and U, is the friction velocity obtained from vertical wind profiles. The effect of the wave steepness H/L on the dimensionless growth rate β/f is not clear, but seems to be small. For water containing the surfactant, the measured growth rate is smaller than that for pure water, but the friction velocity of the wind is also small, and the above relation between β/f and U*/C holds approximately if the measured friction velocity U* is used for the relation.

Nonlinear phase-resolved reconstruction of irregular water waves

2018 ◽  
Vol 838 ◽  
pp. 544-572 ◽  
Author(s):  
Yusheng Qi ◽  
Guangyu Wu ◽  
Yuming Liu ◽  
Moo-Hyun Kim ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Reconstruction Error ◽  
High Order ◽  
Order Effects ◽  
Wave Fields ◽  
Wave Measurements ◽  
Wave Nonlinearity

We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\mathcal{P}}_{NL}$ matches the linear predictable zone ${\mathcal{P}}_{L}$, verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\mathcal{P}}_{NL}$ contains and is generally greater than ${\mathcal{P}}_{L}$. Thus ${\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\mathcal{P}}_{NL}$ when the underlying wave field is not known.

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.

Water waves excited by near-impulsive wind forcing

2017 ◽  
Vol 828 ◽  
pp. 459-495 ◽  
Author(s):  
Andrey Zavadsky ◽  
Lev Shemer
Keyword(s):  
Wave Field ◽  
Water Waves ◽  
Wind Wave ◽  
Wind Forcing ◽  
Wave Parameter ◽  
Small Scale ◽  
Detailed Knowledge ◽  
Limited Information ◽  
Statistical Parameters ◽  
Resonance Model

Only limited information is currently available on the evolution of waves generated by wind that varies in time, and in particular on the initial stages of wind–wave growth from rest under a suddenly applied wind forcing. The emerging wind–wave field varies in time as well as in space. Detailed knowledge of wave parameter distributions under those conditions contributes to a better understanding of the mechanisms of wind wave generation. In the present study, the instantaneous surface elevation and two components of the instantaneous surface slope were recorded at various fetches in a small-scale experimental facility under nearly impulsive wind forcing. Numerous independent realizations have been recorded for each selection of operational conditions. Sufficient data at a number of fetches were accumulated to calculate reliable ensemble-averaged statistical parameters of the evolving random wind–wave field as a function of the time elapsed from activation of wind forcing. Distinct stages in the wave evolution process from appearance of initial ripples to emergence of a quasi-steady wind–wave field were identified. The experimental results during each stage of evolution were analysed in view of the viscous instability theory by Kawai (J. Fluid Mech., vol. 93, 1979, pp. 661–703) and the resonance model by Phillips (J. Fluid Mech., vol. 2, 1957, pp. 417–445).

Statistical Analysis of the Spatial Evolution of the Stationary Wind Wave Field

2013 ◽  
Vol 43 (1) ◽  
pp. 65-79 ◽  
Author(s):  
A. Zavadsky ◽  
D. Liberzon ◽  
L. Shemer
Keyword(s):  
Wave Field ◽  
High Frequency ◽  
Water Waves ◽  
Wind Wave ◽  
Field Measurements ◽  
Quantitative Comparison ◽  
Spatial Evolution ◽  
Frequency Spectra ◽  
Wave Flume ◽  
Laboratory Facilities

Abstract Detailed investigation of wind-generated water waves in a 5-m-long wind wave flume facility is reported. Careful measurements were carried out at a large number of locations along the test section and at numerous airflow rates. The evolution of the wind wave field was investigated using appropriate dimensionless parameters. When possible, quantitative comparison with the results accumulated in field measurements and in larger laboratory facilities was performed. Particular attention was given to the evolution of wave frequency spectra along the tank, distinguishing between the frequency domain around the spectral peak and the high-frequency tail of the spectrum. Notable similarity between the parameters of the evolving wind wave field in the present facility and in field measurements was observed.

scholarly journals A New Inversion Method to Obtain Upper-Ocean Current-Depth Profiles Using X-Band Observations of Deep-Water Waves

2017 ◽  
Vol 34 (5) ◽  
pp. 957-970 ◽  
Author(s):  
Jeffrey Campana ◽  
Eric J. Terrill ◽  
Tony de Paolo
Keyword(s):  
Wave Field ◽  
Water Waves ◽  
Wave Spectrum ◽  
Field Measurements ◽  
New Method ◽  
Ocean Current ◽  
Inversion Method ◽  
Depth Profiles ◽  
X Band ◽  
Rms Error

AbstractA new method for estimating current-depth profiles from observations of wavenumber-dependent Doppler shifts of the overlying ocean wave field is presented. Consecutive scans of marine X-band backscatter provide wave field measurements in the time–space domain that transform into the directional wavenumber–frequency domain via a 3D fast Fourier transform (FFT). Subtracting the linear dispersion shell yields Doppler shift observations in the form of (kx, ky, Δω) triplets. A constrained linear regression technique is used to extract the wavenumber-dependent effective velocities, which represent a weighted depth average of the Eulerian currents (Stewart and Joy). This new method estimates these Eulerian currents from the effective velocities via the inversion of the integral relationship, which was first derived by Stewart and Joy. To test the effectiveness of the method, the inverted current profiles are compared to concurrent ADCP measurements. The inversion method is found to successfully predict current behavior, with a depth-average root-mean-square (RMS) error less than 0.1 m s−1 for wind speeds greater than 5 m s−1 and a broad wave spectrum. The ability of the inversion process to capture the vertical structure of the currents is assessed using a time-average RMS error during these favorable conditions. The time-averaged RMS error is found to be less than 0.1 m s−1 for depths shallower than 20 m, approximately twice the depth of existing methods of estimating current shear from wave field measurements.

Linear dynamics of wind waves in coupled turbulent air—water flow. Part 1. Theory

1994 ◽  
Vol 271 ◽  
pp. 119-151 ◽  
Author(s):  
S. E. Belcher ◽  
J. A. Harris ◽  
R. L. Street
Keyword(s):  
Growth Rate ◽  
Water Flow ◽  
Water Waves ◽  
Wind Waves ◽  
Air Flow ◽  
Local Equilibrium ◽  
Outer Region ◽  
Wave Growth ◽  
Drift Current ◽  
The Waves

When air blows over water the wind exerts a stress at the interface thereby inducing in the water a sheared turbulent drift current. We present scaling arguments showing that, if a wind suddenly starts blowing, then the sheared drift current grows in depth on a timescale that is larger than the wave period, but smaller than a timescale for wave growth. This argument suggests that the drift current can influence growth of waves of wavelength λ that travel parallel to the wind at speed c.In narrow ‘inner’ regions either side of the interface, turbulence in the air and water flows is close to local equilibrium; whereas above and below, in ‘outer’ regions, the wave alters the turbulence through rapid distortion. The depth scale, la, of the inner region in the air flow increases with c/u*a (u*a is the unperturbed friction velocity in the wind). And so we classify the flow into different regimes according to the ratio la/λ. We show that different turbulence models are appropriate for the different flow regimes.When (u*a + c)/UB(λ) [Lt ] 1 (UB(z) is the unperturbed wind speed) la is much smaller than λ. In this limit, asymptotic solutions are constructed for the fully coupled turbulent flows in the air and water, thereby extending previous analyses of flow over irrotational water waves. The solutions show that, as in calculations of flow over irrotational waves, the air flow is asymmetrically displaced around the wave by a non-separated sheltering effect, which tends to make the waves grow. But coupling the air flow perturbations to the turbulent flow in the water reduces the growth rate of the waves by a factor of about two. This reduction is caused by two distinct mechanisms. Firstly, wave growth is inhibited because the turbulent water flow is also asymmetrically displaced around the wave by non-separated sheltering. According to our model, this first effect is numerically small, but much larger erroneous values can be obtained if the rapid-distortion mechanism is not accounted for in the outer region of the water flow. (For example, we show that if the mixing-length model is used in the outer region all waves decay!) Secondly, non-separated sheltering in the air flow (and hence the wave growth rate) is reduced by the additional perturbations needed to satisfy the boundary condition that shear stress is continuous across the interface.

Higher Order Resonant Interaction of Surface Waves by Undulatory Bottom Topography

2009 ◽  
Author(s):  
Mohammad-Reza Alam ◽  
Yuming Liu ◽  
Dick K. P. Yue
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Wave Generation ◽  
Higher Order ◽  
Class I ◽  
Band Spectrum ◽  
Alternative Mechanism ◽  
Bragg Resonance

Higher order (quartet) Bragg resonance of water waves by bottom undulations and its effect on the evolution of ocean wave spectrum, particularly over continental shelves and littoral zones, are considered. Higher order Bragg resonance can provide a viable mechanism for distribution of (initially confined) energy across the spectrum. Contrary to classical Bragg resonances (Class I and II) where the resonant wave has to have the same frequency as the incident wave, Class III (quartet) Bragg resonance of three free waves and a bottom topography component allow participant waves to have different frequencies. Of particular interest here are higher-order resonances that lead to infragravity wave generation as a result of interaction of regular sea waves with bottom undulations (of the same order of wavelength as the primary waves), and, long/medium surface wave generation by nonlinear interaction between short surface waves and medium wavelength bottom undulations. These mechanisms can accelerate the rate by which energy is damped by the bottom friction. The second mechanism also provides a potential alternative mechanism for explaining microseismic noise observed in shallow waters. We further consider the oblique higher order Bragg resonance. Although for Class I, oblique resonance is less important than normal incidence, it is shown here via illustrative examples and direct simulations that there are strong oblique Class II and III Bragg cases. Inclusion of higher order interactions paves a path for the energy transfer to higher and lower frequencies of an initially narrow band spectrum. Ensuing multiple (exact/near) such resonant interactions can result in the generation of multiple new transmitted/reflected waves that fill a broad wavenumber band eventually leading to loss of order and chaotic motion of water surface.

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