Procedia IUTAM最新文献

Rational models of wind-wave growth were proposed in the 1950s (Miles 1957, Phillips 1957), theories of wave-wave interactions (Phillips 1960, Hasselmann 1962, Zakharov 1968) and wave-action conservation for waves in fluids (Whitham 1965, Bretherton and Garrett 1969) in the 1960s, but it was not until the 1980s that laboratory experiments (Duncan 1981, Melville and Rapp 1985) and a seminal paper by Owen Phillips in 1985 on a model of the equilibrium range in wind-wave spectra, and a formulation of breaking, began a rational program of research into the role of breaking in surface wave kinematics and dynamics. Two important features of Phillips’ 1985 paper were the introduction of Λ(c)dc, the average total length of breaking fronts per unit area of ocean moving with velocities in the range (c, c + dc) and the statement that the average rate of energy loss per unit area by breakers in the same velocity range was given by

${\varepsilon }_b\left(c\right)dc=b\left(c\right)\rho g^{-1}{c}^5\Lambda \left(c\right)dc$

where b is a dimensionless breaking strength and g is gravity. The energy loss per unit length of breaker, bρg^-1c⁵, was based on Duncan’s work, but anticipated in part by Lighthill (1978). Lower order moments of Λ(c) describe kinematical features of breaking up to the third moment, with the fourth moment describing the momentum flux from waves to currents. The structure of the dissipation equation imposes a combination of different approaches to quantifying it. Estimates of b have depended on arguments based on Taylor’s (1935) inertial scaling of turbulence dissipation, supported by laboratory experiments and recent DNS and LES numerical experiments, while Λ(c) over any significant dynamical range can only be measured in the field. The success of the early attempts to follow this approach has led to recent work on air entrainment for gas transfer, and theoretical uses of fundamental vortex dynamics to develop our knowledge of the role of breaking in air-sea interaction. In this paper I will review the material from the laboratory, through scaling arguments, modeling and field measurements.

A mechanistic theory of wind-wave interaction must rely on verifiable assumptions and offer reproducible observable predictions. For decades, the limited mechanistic grasp on the problem has motivated RANS and LES modeling and has driven a vast empirical effort to describe the interaction in terms of wave-induced modifications of standard statistical characteristics of the wind, such as wind profile, kinetic energy balance or exchange coefficients. Because the mechanistic, empirical and numerical approaches are all concerned with the same phenomenon occurring in the same media, consistency here requires that the assumptions on which the approaches rest and the predictions they generate are compatible with each other and supported by measurements. Recent findings from theoretical analysis and field experiments advanced the understanding of the statistical and dynamic patterns of the wave-coherent flow, which is at the core of the mechanistic description of the wind-wave exchange. The progress prompts reexamining of earlier concepts, efforts and findings to evaluate their suitability, validity and usefulness. For the purpose, this survey traces the development of ideas, methods and results in the study of the wind wave generation.

It is important to develop a wave generation method for extending the fetch in laboratory experiments, because current laboratory studies are limited to fetch shorter than 100 m. Two wave generation methods are proposed for generating wind waves under long-fetch conditions in a wind-wave tank using a programmable irregular-wave generator. The first method is the spectral-model-based wave-generation method (SBWGM), which is appropriate at normal wind speeds for extending the fetch. The SBWGM also can be used at extremely high wind speeds if we know the spectral shape. In SBWGM, a conventional model of the wind-wave spectrum is used for the movement of the programmable irregular-wave generator. The second method is the loop-type wave-generation method (LTWGM), which can be used at wide range of wind speeds and is especially appropriate to be used at extremely high wind speeds, where the spectral shape is unknown. In LTWGM, the waves whose characteristics are most similar to the wind waves measured at the end of the tank are reproduced at the entrance of the tank by the programmable irregular-wave generator to extend the fetch. Water-level fluctuations are measured at both normal and extremely high wind speeds using resistance-type wave gauges. The results show that SBWGM can produces wind waves with a fetch over 500 m, but only at normal wind speeds. However, LTWGM can produce wind waves with long fetches exceeding the length of the wind-wave tank across a broad range of wind speeds, but considerable time is required to produce wind waves at long-fetch conditions, i.e. fetch over 500 m. It is observed that the wind-wave spectrum with a long fetch reproduced by SBWGM is consistent with that of the modelled wind-wave spectrum, although the generated wind waves are different from those in the open ocean because of the finite width of the tank. In addition, the fetch laws with significant wave height and period are confirmed for wind waves under long-fetch conditions. This implies that the ideal wind waves under long-fetch conditions can be reproduced using SBWGM with the programmable irregular-wave generator.

This study describes an approximate quasi-linear model for the description of the turbulent boundary layer over steep surface waves. The model assumes that wave-induced disturbances of the atmospheric turbulent boundary layer could be reasonably described in a linear approximation with the momentum flux from wind to waves retained as the only nonlinear effect in the model. For the case of periodic long-crested waves, the model has been verified with a set of the original laboratory and numerical experiments. The laboratory experimental study of the airflow over the steep waves was performed by means of the PIV technique. The numerical study was performed with direct numerical simulation (DNS) of the turbulent airflow over waved surface at Re=15,000 for quasi-homogeneous waves, wave trains and parasitic capillaries riding on the crest of a steep waves. Examples are given of the application of the quasi-linear approximation to describe the turbulent boundary layer over waves with the continuous spectrum under the assumption of random phases of harmonics. In the latter case the quasi-linear model provides the growth rate of surface waves in the inertial interval of the surface wave spectrum proportional to w7/3 in agreement with predictions in [1].

The well-known linear stability theory of wind-wave generation is revisited with a focus on the generation of wave groups. As well as recovering the usual temporal instability, the analysis has the outcome that the wave group must move with a real-valued group velocity. This has the consequence that both the wave frequency and the wavenumber should be complex-valued. In the frame of reference moving with the group velocity, the growth rate is enhanced above that for just a temporally growing monochromatic sinusoidal wave. The analysis is extended to the weakly nonlinear regime where a nonlinear SchrÖdinger equation with a linear growth term is discussed.

Turbulent flow over steep steady and unsteady wave trains with varying height h(x, t) and propagation speed c is simulated using large-eddy simulation (LES) in a wind-wave channel [17]. The imposed waveshape with steady wave trains is based on measurements of incipient and active breaking waves collected in a wind-wave tank, while a numerical wave code is used to generate an unsteady evolving wave train (or group) [3]. For the adopted waveshapes, process studies are carried out varying the wave age c/u_* from ~ 1 to 10: the airflow friction velocity is u_*. Under strong wind forcing or low wave age c/u_* ~ 1, highly intermittent airflow separation is found in all simulations and the results suggest separation near a wave crest occurs prior to the onset of wave breaking. As wave age increases flow separation is delayed or erased for both steady and unsteady wave trains. Flow visualization shows that near the wave surface vertical velocity w and waveslope ∂h/∂x are positively correlated at c/u_* ~ 1 but are negatively correlated at c/u_* = 10. The vertical speed of the underlying wave oscillations depends on the local waveslope, increases with phase speed, and is a maximum on the leeward side of the wave. Vigorous boundary movement [8] appears to alter the unsteady flow separation patterns which leads to a reduction in form (pressure) drag as wave age increases. For example, the pressure contribution to the total drag of the active breaker wave train decreases from 74% at c/u_* = 1.23 to less than 20% at c/u_* = 10. Critical layer dynamics appears to play a secondary role in the air-wave coupling over steep waves, but requires further investigation. For all simulations, the form drag is found to be strongly dependent on both waveslope ∂h/∂x and wave age c/w_*. The simulations are in good agreement with experimental results for turbulent flow over steep waves under strong wind forcing.

A high-Reynolds-number second-order stress closure model is used to perform numerical simulations of the wind flow above different groups of waves. It is shown that the group profiles can change as the individual waves grow within its envelop due to the energy transfer between the wind and the group. The focus of this study is the behaviour of the critical-layer and the associated with "cat’s-eye" structures which are centred around the critical height, where the real part of the complex wave speed is equal to the mean flow velocity. It is also shown that the position and size of these structures depend on the wave age and the wave steepness. It is demonstrated that the larger these structures become, the greater disturbance of the wind flow above the wave groups appear. Also, the results obtained here demonstrate how the critical layer structures are asymmetrical over the waves within a group because of the shear driven sheltering effect on the downwind side of the group. The results here complement the general review of wind-wave dynamics by Hunt & Sajjadi [1].

Multiperiodic Fourier series solutions of integrable nonlinear wave equations are applied to the study of ocean waves for scientific and engineering purposes. These series can be used to compute analytical formulae for the stochastic properties of nonlinear equations, in analogy to the standard approach for linear equations. Here I emphasize analytically computable results for the correlation functions, power spectra and coherence functions of a nonlinear random process associated with an integrable nonlinear wave equation. The multiperiodic Fourier series have the advantage that the coherent structures of soliton physics are encoded in the formulation, so that solitons, breathers, vortices, etc. are contained in the temporal evolution of the nonlinear power spectrum and phases. I illustrate the method for the Korteweg-deVries and nonlinear SchrÖdinger equations. Applications of the method to the analysis of data are discussed.

We use a suite of advanced numerical tools developed in house to investigate the physical processes in three canonical wind-wave interaction problems. First, we use DNS to investigate the sheltering effect of a long wave on a short wave. It is found that in the presence of the long wave the form drag of the short wave decreases, with the magnitude of the reduction depending on the wave age of the long wave. We also observe that the surface friction is highly correlated to the streamwise vorticity upstream. Next, we study the effect of wave breaking on the wind turbulence. We focus on analyzing small-scale flow physics near the wave surface and the influence of wave breaking on turbulence statistics. It is found that plunging breakers induce acceleration of the air flow near the wave surface. During wave plunging, a large spanwise vortex is generated, which enhances the turbulence mixing around it, and induces large magnitude of turbulent kinetic energy. In the final part, results are presented for wind over broad-band waves in realistic ocean settings. By examining the full wavenumber-frequency spectrum of the turbulent wind, we have identified distinct wave signatures in the space-time correlation of wind turbulence. In the evolution of the wave field, its inner physical process known as the four-wave interaction dominates over wind input, as shown in the frequency downshift phenomenon of the wave field throughout the numerical experiments.

This paper reviews (in qualitative and order of magnitude terms) the main mechanisms determining wind driven waves and their quantitative modelling for the different stages as the wind speed and the Reynolds number both increase, initially through coupling the instability ‘waves’ in the laminar boundary layers above and below the water surface, secondarily through initiation of eddy structures in turbulent boundary flow over flat water surface (’cats paws’) and thirdly as distorted airflow passes over the undulating water surface with different kinds of dynamics, wave shapes (ranging from sinusoidal to pointed forms), amplitude H, wavelength L, travelling at speed c_r and growth rate c_i/U_*, coupled with the flow below the water surface. Significant flow features are the turbulent thin shear layers on the surface and detached ‘critical’ layers above the surface, which are also affected by the variation of surface roughness near the crests of the waves, by recirculating, separated flows near the surface and by high gradients of turbulence structure in the detached critical layers. Two phase flows in the recirculation zones on the lee side of waves leads to spray in the air above the water surface which also amplifies the boundary layer turbulence. Two phase bubbly flows below the surface generate near surface bubbles and may increases the surface drag downstream of the wave crests. The topology of node and saddle singular points in these mean recirculating flows provides a kinematic description of these flows. Idealised dynamical studies are presented of the variation of the wave amplitude through wind forces on waves moving in groups of waves, and thence physical models are proposed for the transfer of wave energy between large and small frequencies and length scales of wave spectra.