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.

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.

Experiments on the generation of small water waves by wind

1969 ◽  
Vol 35 (4) ◽  
pp. 625-656 ◽  
Author(s):  
E. J. Plate ◽  
P. C. Chang ◽  
G. M. Hidy
Keyword(s):  
Water Waves ◽  
Wind Waves ◽  
Air Flow ◽  
Wave Spectrum ◽  
Direct Interaction ◽  
Turbulence Structure ◽  
Constant Frequency ◽  
Equilibrium Limit ◽  
Small Water ◽  
The Waves

The generation and growth of small water waves by a turbulent wind has been investigated in a laboratory channel. The evolution of these oscillations with fetch was traced from their inception with amplitudes in the micron range under conditions of steady air flow. The experiments revealed that the waves are generated at all air velocities in small bursts consisting of groups of waves of nearly constant frequency. After travelling for some distance downstream, these wavelets attain sufficient amplitude to become visible. For this condition, a wind speed critical to raise waves is well defined. After the first wavelets appear, two new stages of growth are identified at longer fetches if the air speed remains unchanged. In the first of these, the wave component associated with the spectral peak grows faster with fetch than any other part of the wave spectrum of the initial waves until its amplitude attains an upper limit consistent with Phillips's equilibrium range, which appears to be universal for wind waves on any body of water. If the air flow is not changed, then the frequency of this dominant wave remains constant with fetch up to equilibrium. This frequency tends to decrease, however, with increasing wind shear on the water. In the second stage of growth, only the energy of wave components with spectral densities lower than the equilibrium limit tend to increase with fetch so that the wave spectrum is maintained near equilibrium in the high-frequency range of the spectrum.The origin of the first waves and the rate of their subsequent growth was examined in the light of possible generating mechanisms. There was no indication that they were produced by direct interaction of the water surface with the air turbulence. Neither could any significant feedback of the waves into the turbulence structure be detected. The growth of the waves was found to be in better agreement with theoretical predictions. Under the shearing action of the wind, the first waves were found to grow exponentially. The growth rates agreed with the estimates from the viscous shearing mechanism of Miles (1962a) to a fractional error of 61% or less. A slight improvement was obtained with the viscous theory of Drake (1967) in which Miles’ model is extended to include the effect of the drift current induced by the wind in the water. Since the magnitude of the water currents observed in the tunnel is very small, this improvement is not significant.

Stabilizing effect of surrounding gas flow on a plane liquid sheet

2011 ◽  
Vol 672 ◽  
pp. 5-32 ◽  
Author(s):  
OUTI TAMMISOLA ◽  
ATSUSHI SASAKI ◽  
FREDRIK LUNDELL ◽  
MASAHARU MATSUBARA ◽  
L. DANIEL SÖDERBERG
Keyword(s):  
Growth Rate ◽  
Gas Flow ◽  
Liquid Velocity ◽  
Air Flow ◽  
Liquid Sheet ◽  
Mean Velocity ◽  
Order Of Magnitude ◽  
The Stability ◽  
The Waves ◽  
Half Thickness

The stability of a plane liquid sheet is studied experimentally and theoretically, with an emphasis on the effect of the surrounding gas. Co-blowing with a gas velocity of the same order of magnitude as the liquid velocity is studied, in order to quantify its effect on the stability of the sheet. Experimental results are obtained for a water sheet in air at Reynolds number Rel = 3000 and Weber number We = 300, based on the half-thickness of the sheet at the inlet, water mean velocity at the inlet, the surface tension between water and air and water density and viscosity. The sheet is excited with different frequencies at the inlet and the growth of the waves in the streamwise direction is measured. The growth rate curves of the disturbances for all air flow velocities under study are found to be within 20% of the values obtained from a local spatial stability analysis, where water and air viscosities are taken into account, while previous results from literature assuming inviscid air overpredict the most unstable wavelength with a factor 3 and the growth rate with a factor 2. The effect of the air flow on the stability of the sheet is scrutinized numerically and it is concluded that the predicted disturbance growth scales with (i) the absolute velocity difference between water and air (inviscid effect) and (ii) the square root of the shear from air on the water surface (viscous effect).

scholarly journals On Growth Rate of Wind Waves: Impact of Short-Scale Breaking Modulations

2016 ◽  
Vol 46 (1) ◽  
pp. 349-360 ◽  
Author(s):  
Vladimir Kudryavtsev ◽  
Bertrand Chapron
Keyword(s):  
Growth Rate ◽  
Surface Pressure ◽  
Wind Waves ◽  
Breaking Waves ◽  
Generation Model ◽  
Wave Growth ◽  
Short Scale ◽  
Scale Breaking ◽  
Aerodynamic Roughness ◽  
Inner Region

AbstractThe wave generation model based on the rapid distortion concept significantly underestimates empirical values of the wave growth rate. As suggested before, inclusion of the aerodynamic roughness modulations effect on the amplitude of the slope-correlated surface pressure could potentially reconcile this model approach with observations. This study explores the role of short-scale breaking modulations to amplify the growth rate of modulating longer waves. As developed, airflow separations from modulated breaking waves result in strong modulations of the turbulent stress in the inner region of the modulating waves. In turn, this leads to amplifying the slope-correlated surface pressure anomalies. As evaluated, such a mechanism can be very efficient for enhancing the wind-wave growth rate by a factor of 2–3.

A numerical model of the air flow above water waves. Part 2

1977 ◽  
Vol 82 (2) ◽  
pp. 349-369 ◽  
Author(s):  
P. R. Gent
Keyword(s):  
Energy Transfer ◽  
Numerical Model ◽  
Water Waves ◽  
Air Flow ◽  
Field Observations ◽  
Transfer Rates ◽  
Fractional Rate ◽  
Theoretical Predictions ◽  
The Waves ◽  
Nonlinear Numerical Model

Further results from the nonlinear numerical model of the air flow in a deep turbulent boundary layer above water waves described in Gent & Taylor (1976) are presented. The results are calculated with the surface roughness z0 both constant and varying with position along the wave. With the form used when z0 varies, the fractional rate |ζ| of energy transfer per radian advance in phase due to the working of the pressure forces is larger than for z0 constant both when the transfer is from wind to waves and when it is from waves to wind. The latter case occurs when the waves are travelling faster than, or against, the wind. The energy transfer rates are compared with other theoretical predictions and with recent field observations.

On the wind-induced growth of slow water waves of finite steepness

2008 ◽  
Vol 608 ◽  
pp. 243-274 ◽  
Author(s):  
WILLIAM L. PEIRSON ◽  
ANDREW W. GARCIA
Keyword(s):  
Tangential Stress ◽  
Growth Rates ◽  
Water Waves ◽  
Dynamic Range ◽  
Wind Waves ◽  
Laboratory Data ◽  
Quantitative Agreement ◽  
Wave Drag ◽  
Wave Growth ◽  
Wave Range

Determining characteristic growth rates for water waves travelling more slowly than the wind has continued to be a key unresolved problem of air–sea interaction for over half a century. Analysis of previously reported and recently acquired laboratory wave data shows a systematic decline in normalized wave growth with increasing mean wave steepness that has not previously been identified. The normalized growth dynamic range is comparable with previously observed scatter amongst other laboratory data gathered in the slow wave range. Strong normalized growth rates are observed at low wave steepnesses, implying an efficient wave-coherent tangential stress contribution. Data obtained during this study show quantitative agreement with the predictions of others of the interactions between short wind waves and the longer lower-frequency waves. Measured normalized wave growth rates are consistent with numerically predicted growth due to wave drag augmented by significant wave-coherent tangential stress.

Modelling low-Reynolds-number effects in the turbulent air flow over water waves

2000 ◽  
Vol 415 ◽  
pp. 155-174 ◽  
Author(s):  
JAN F. MEIRINK ◽  
VLADIMIR K. MAKIN
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Water Waves ◽  
Air Flow ◽  
Viscous Effects ◽  
Wind Speeds ◽  
Short Waves ◽  
Dimensionless Energy ◽  
Sensing Applications ◽  
Turbulent Air Flow

In studies of the turbulent air flow over water waves it is usually assumed that the effect of viscosity near the water surface is negligible, i.e. the Reynolds number, Re = u∗λ/v, is considered to be high. However, for short waves or low wind speeds this assumption is not valid. Therefore, a second-order turbulence closure that takes into account viscous effects is used to simulate the air flow. The model shows reasonable agreement with laboratory measurements of wave-induced velocity profiles. Next, the dependence of the dimensionless energy flux from wind to waves, or growth rate, on Re is investigated. The growth rate of waves that are slow compared to the wind is found to increase strongly when Re decreases below 104, with a maximum around Re = 800. The numerical model predictions are in good agreement with analytical theories and laboratory observations. Results of the study are useful in field conditions for the short waves in the spectrum, which are particularly important for remote sensing applications.

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.

On weakly turbulent scaling of wind sea in simulations of fetch-limited growth

2011 ◽  
Vol 669 ◽  
pp. 178-213 ◽  
Author(s):  
ELODIE GAGNAIRE-RENOU ◽  
MICHEL BENOIT ◽  
SERGEI I. BADULIN
Keyword(s):  
Numerical Simulations ◽  
Wave Energy ◽  
Water Waves ◽  
Wind Wave ◽  
Wind Waves ◽  
Initial Growth ◽  
Limited Growth ◽  
Wave Growth ◽  
Wide Range ◽  
Wind Sea

Extensive numerical simulations of fetch-limited growth of wind-driven waves are analysed within two approaches: a ‘traditional’ wind-speed scaling first proposed by Kitaigorodskii (Bull. Acad. Sci. USSR, Geophys. Ser., Engl. Transl., vol. N1, 1962, p. 105) in the early 1960s and an alternative weakly turbulent scaling developed recently by Badulin et al. (J. Fluid Mech.591, 2007, 339–378). The latter one uses spectral fluxes of wave energy, momentum and action as physical scales of the problem and allows for advanced qualitative and quantitative analysis of wind-wave growth and features of air–sea interaction. In contrast, the traditional approach is shown to be descriptive rather than proactive. Numerical simulations are conducted on the basis of the Hasselmann kinetic equation for deep-water waves in a wide range of wind speeds from 5 to 30 m s −1 and for the ideal case of fetch-limited growth: permanent wind blowing perpendicularly to a straight coastline. Two different wave input functions, Sin, and two methods for calculating the nonlinear transfer term Snl (Gaussian quadrature method, or GQM, a quasi-exact method based on the use of Gaussian quadratures, and the discrete interaction approximation, or DIA) are used in the simulations. Comparison of the corresponding results firstly shows the relevance of the analysis of wind-wave growth in terms of the proposed weakly turbulent scaling, and secondly, allows us to highlight some critical points in the modelling of wind-generated waves. Three stages of wind-wave development corresponding to qualitatively different balance of the source terms, Sin, Sdiss and Snl, are identified: initial growth, growing sea and fully developed sea. Validity of the asymptotic weakly turbulent approach for the stage of growing wind sea is determined by the dominance of nonlinear transfers, which results in a rigid link between spectral fluxes and wave energy. This stage of self-similar growth is investigated in detail and presented as a consequence of three sub-stages of qualitatively different coupling of air flow and growing wind waves. The key self-similarity parameter of the asymptotic theory is estimated to be αss = 0.68 ± 0.1.Further prospects of wind-wave modelling in the context of the presented weakly turbulent scaling are discussed.

scholarly journals Effect of water flow and depth on fatigue crack growth rate of underwater wet welded low carbon steel SS400

2021 ◽  
Vol 11 (1) ◽  
pp. 329-338 ◽  
Author(s):  
E. Surojo ◽  
J. Anindito ◽  
F. Paundra ◽  
A. R. Prabowo ◽  
E. P. Budiana ◽  
...  
Keyword(s):  
Growth Rate ◽  
Fatigue Crack ◽  
Carbon Steel ◽  
Crack Growth Rate ◽  
Crack Growth ◽  
Water Flow ◽  
Water Depth ◽  
Water Flow Rate ◽  
Low Carbon Steel ◽  
Low Carbon

Abstract Underwater wet welding (UWW) is widely used in repair of offshore constructions and underwater pipelines by the shielded metal arc welding (SMAW) method. They are subjected the dynamic load due to sea water flow. In this condition, they can experience the fatigue failure. This study was aimed to determine the effect of water flow speed (0 m/s, 1 m/s, and 2 m/s) and water depth (2.5 m and 5 m) on the crack growth rate of underwater wet welded low carbon steel SS400. Underwater wet welding processes were conducted using E6013 electrode (RB26) with a diameter of 4 mm, type of negative electrode polarity and constant electric current and welding speed of 90 A and 1.5 mm/s respectively. In air welding process was also conducted for comparison. Compared to in air welded joint, underwater wet welded joints have more weld defects including porosity, incomplete penetration and irregular surface. Fatigue crack growth rate of underwater wet welded joints will decrease as water depth increases and water flow rate decreases. It is represented by Paris's constant, where specimens in air welding, 2.5 m and 5 m water depth have average Paris's constant of 8.16, 7.54 and 5.56 respectively. The increasing water depth will cause the formation of Acicular Ferrite structure which has high fatigue crack resistance. The higher the water flow rate, the higher the welding defects, thereby reducing the fatigue crack resistance.

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