On the generation of sea waves by a turbulent wind

Miles' (1957) theory of wave generation is modified to include the effects of air turbulence. It is shown that the fluctuating wave-induced Reynolds stresses are important only within a critical layer surrounding the critical height where the mean wind speed matches the wave phase speed. When the critical height is such that the critical layer extends to the air-sea interface, the energy transfer from the wind to the wave is affected greatly by the turbulence.     

Particle dispersion and mixing induced by breaking internal gravity waves

The purpose of this paper is to analyze diapycnal mixing induced by the breaking of an internal gravity wave — the primary wave — either standing or propagating. To achieve this aim we apply two different methods. The first method consists of a direct estimate of vertical eddy diffusion from particle dispersion while the second method relies upon potential energy budgets [Winters, K.B., Lombard, P.N., Riley, J.J., D’Asaro, E.A., 1995. J. Fluid Mech. 289, 115–128; Winters, K.B., D’Asaro, E.A., 1996. J. Fluid Mech. 317, 179–193]. The primary wave we consider is of small amplitude and is statically stable, a case for which the breaking process involves two-dimensional instabilities. The dynamics of the waves have been previously analyzed by means of two-dimensional direct numerical simulations [Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1995. J. Fluid Mech. 285, 265–301; Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1996. Dyn. Atmos. Oceans 29, 41–63; Koudella, C., Staquet, C., 1998. In: Davis, P. (Ed.), Proceedings of the IMA Conference on Mixing and Dispersion on Stably-stratified Flows, Dundee, September 1996. IMA Publication]. High resolution three-dimensional calculations of the same wave are also reported here [Koudella, C., 1999].A local estimate of mixing is first inferred from the time evolution of sets of particles released in the flow during the breaking regime. We show that, after an early evolution dominated by shear effects, a diffusion law is reached and the dispersion coefficient is fairly independent of the initial seeding location of the particles in the flow.The eddy diffusion coefficient, K, is then estimated from the diapycnal diffusive flux. A good agreement with the value inferred from particle dispersion is obtained. This finding is of particular interest regarding the interpretation of in situ estimates of K inferred either from tracer dispersion or from microstructure measurements. Computation of the Cox number, equal to the ratio of eddy diffusivity to molecular diffusivity, shows that the Cox number varies within the interval [9, 262], which corresponds to the range of vertical eddy diffusivity measured in the interior of the ocean. The Cox number is found to depend on the turbulent Froude number squared.We show eventually that mixing results in a weak distortion of the initial density profile and we relate this result to observations made at small scale in the ocean.Comparisons between the analysis of the two-dimensional and high resolution (256³) three-dimensional direct numerical simulations of the primary wave were also conducted. We show that the energetics and the amount of mixing are very close when the primary wave is of small amplitude. This results from the fact that, for a statically stable wave, the dynamics of the initially two-dimensional primary wave remains mostly two-dimensional even after the onset of wavebreaking.     

The roughness of wind waves

In this paper, a new dynamic roughness equation for airflow over wind waves is proposed, based on relationships of dimensionless parameters and the 1986 HEXMAX field data. The equation can be considered as a modification of the Charnock formula. The data are also compared with the parameterizations of Toba and Koga, and of Hsu, and the consequences of the new equation for aerodynamic drag are discussed. In the new equation, the drag coefficient is expressed as a function of both wind speed and wave age c _p/u_*. This testifies to the strong wave-age dependence of the drag, found in several experimental studies. It is also in good agreement with results of a theoretical model of the airflow-seawave interaction, proposed by Janssen (1989).Also: Dept. of Applied Physics, Techn. Univ. Delft, the Netherlands.     

Numerical simulation of air flow over breaking waves

The air flow above breaking monochromatic Stokes waves is studied using a numerical nonlinear model of the turbulent air flow above waves of finite amplitude. The breaking event (spilling breaker) is parameterized by increasing the local roughness at the downwind slope of the wave, just beyond the crest. Both moderate slope waves and steep waves are considered. Above steep breaking waves, a large increase (typically 100%) in the total wind stress — averaged over the wave profile — is found compared to nonbreaking moderate slope waves. This is due to the drastic increase of the form drag, which arises from the asymmetrical surface pressure pattern above breaking waves. Both increase of wave slope (sharpening of the crest) and increase of local roughness in the spilling breaker area cause this asymmetrical surface pressure pattern. A comparison of the numerical results with the recent experimental measurements of Banner (1990) is carried out and a good agreement is found for the structure of the pressure pattern above breaking waves and for the magnitude of enhanced momentum transfer. Also: Dept. of Applied Physics, Techn. Univ. Delft, Netherlands.     

Influence of vertical wind on stratospheric aerosol transport

The main goals of this work are climatological analysis of characteristics of vertical wind in the stratosphere and estimation of potential opportunities of its influence on stratospheric aerosol particles. High-altitude, temporal, and latitude dependences of zonal mean vertical wind velocity for the period of 1992?C2006 from the UKMO atmospheric general circulation model are analyzed. It is shown that monthly averaged amplitudes of the vertical wind are approximately ±5?mm/s, while annual averaged ones are ±1?mm/s. The upward wind can provide the vertical lifting against gravity for sufficiently large (up to 3?C5???m) aerosol particles with a density up to 1.0?C1.5?g/cm³ at stratospheric and mesospheric altitudes. The vertical wind, probably, is a substantial factor for particle motion up to altitudes of 30?C40?km and can change essentially the sedimentation velocities and the residence times of stratospheric aerosols. The structure of the averaged fields of vertical wind supposes the opportunity of formation of dynamically stable aerosol layers in the middle stratosphere. With the problem regarding the action of a permanent source of monodisperse particles near the stratopause taken as an example, it is shown that if the action of the averaged vertical component is taken into account along with the gravitational sedimentation and turbulent diffusion, the standard vertical profiles of the relative concentration of particles change cardinally. Estimations for the levitation heights for particles of different densities and sizes in the stratosphere under action of gravity and vertical wind pressure are presented.     

Surface film effect on short wind waves

The results are presented of experiments with artificial slicks carried out at different wind velocities and with different films in natural conditions. In particular, variations of the wave number and frequency spectra of the short wind waves at wavelengths of 4 cm-1 m and frequencies of 2–20 Hz in slicks are analysed. It is shown that ripple flattening at gentle (up to 1–1.5 m s⁻¹) and moderate (>5–6 s⁻¹) winds can be described in the framework of the theoretical model of the variability of centimetre-waves taking into account their anomalous attenuation due to the elastic film. The measurements of the natural film elasticity are taken and its considerable growth in natural slicks is registered; the estimate of the elasticity sufficient for the formation of film slicks is given. The influence of ripple flattening on the transformation of the wind velocity field above the film slicks and the amplification of decimeter-waves caused by this are discussed; correct estimates of the effects observed are made.     

On the deep‐water fetch laws for wind‐generated surface gravity waves

Abstract

With the object of providing an accurate set of open‐sea wave spectra in a variety of conditions, we deployed, in conjunction with CASP, an array of 9 wave buoys (3 directional, 6 non‐directional) along a 30‐km line offshore from Martinique Beach, N.S. A large set of high‐quality wave spectra was collected in conjunction with extensive meteorological information. The data set is unique in the sense that a large onshore swell component was normally present.

Offshore‐wind cases for three windows: ±5°, ±15° and ±30° with respect to the shore normal, have been considered. Wind speed was found to be a strong function of fetch, and attempts were made to allow for this in the analysis. Power‐law regressions have been produced of dimensionless sea energy, peak frequency and high‐frequency spectral level (the Kitaigorodskii “alpha” parameter) vs dimensionless fetch and wind speed (inverse wave age). The regressions are compared with earlier work: the Joint North Sea Waves Project (Jonswap) and the Canada Centre for Inland Waters (CCIW) Lake Ontario study.

The comparisons indicate that dimensionless wave energies, peak frequencies and alpha values in this experiment are comparable with those from earlier experiments; in spite of different wind analysis methods, the CASP and CCIW fetch‐limited growth laws are consistent within the contexts of the two experiments. Differences among the estimated parameters are as large within the analyses of the three windows as they are among the three experiments we compare.     

Vertical mixing of passive scalars owing to breaking gravity waves

In this paper, some aspects of dispersion of air pollutants as emitted from aircraft in the lower stratosphere have been investigated. As this part of the atmosphere is always stably stratified, mixing as a result of small-scale turbulence is very slow. Instead, effective vertical mixing can be provided by breaking gravity waves. We have examined the mixing properties of those events by means of a numerical model, which simulates the wave development as well as the dispersion of passive trace substances. From these simulations, an effective diffusion coefficient for the entire event of a breaking gravity wave of about 0.7 m² s⁻¹ was calculated.     

The observed generation and breaking of atmospheric internal gravity waves over the ocean

Observations are presented for internal gravity waves and their breaking at a height of 23.5 m over the ocean in surface-based inversions which are formed because of the advection of warm air over cold water. The spectral and cospectral analyses of velocity and temperature fluctuations were made to establish the characteristic features of the waves. Flow visualization photographs of smoke released during the breaking of a wave are also presented. Comparison between the turbulent energies present during and after breaking of a wave indicates enormous mixing and dispersion occurring during breaking.This research was performed under Contract No. EY-76-C-02-0016 with the United States Energy Research and Development Administration.     

A study of internal waves in a wind tunnel

The combined use of a stratified flow wind tunnel and of periodic sampling methods in low Reynolds number flows allows the recovery of the instantaneous dynamics of internal waves. Several detailed examples are given of the thermal structure of large propagating and breaking internal waves and Kelvin-Hemholtz waves. Preliminary measurements of the stability of finite waves as a function of Richardson number are also reported.     

The influence of sea waves on the wind profile

From wind profile and wave measurements performed during the JONSWAP II experiment, relations between the dimensionless profile slope and the significant wave height are derived. It is shown that the wind profile is distorted by the waves especially in the vicinity of the water surface. The wave influence on the profile seems to be restricted to heights below about three wave heights. Above this level, the dimensionless profile slope is an approximately constant value corresponding to a drag coefficient of about 1.15 × 10^–3.     

A note on ‘separation’ over short wind waves

Whether or not separation occurs in the airflow over wind-generated water waves is partly a question of semantics but also has an important bearing on the wave generation process. In the present paper we use a rather formal and perhaps narrow definition of separation and show that it does not occur where the shear stress is zero but only in conjunction with wave breaking. This is unlikely to happen except in the presence of quite strong surface drift velocities in the water. A similar connection between separation, surface drift and wave breaking has recently been established by Banner and Melville (1976).The effects of increasing wave amplitude or steepness are investigated with a numerical model of the airflow over water waves. Variations in the depth of the closed streamline region are predicted. The model is also used to investigate the possible importance of surface drift velocities.On leave 1976, Atmospheric Environment Service, Downsview, Ont., Canada.     

Low level wind shear and baroclinic growth of monsoon depression scale waves

Summary A quasi-geostrophic, linear stability analysis was carried out to find the effect of low level wind shear on the baroclinic growth of monsoon depression scale waves. The low level wind shear of the mean monsoon flow is altered by varying the surface wind, the position and the magnitude of the westerly maximum. The growth rate and phase velocity of the short unstable waves for all the cases of wind profiles are obtained. It is noticed that the growth rate and phase velocity of the depression scale waves (L2000 to 2500 km) are not influenced by small variations in the position or magnitude of the westerly maximum. But the growth rate of depression scale waves does depend on the average wind shear between 850–500 mb region.

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Zusammenfassung Die Scherung des Windes in den unteren Schichten und das barokline Wachstum von kurzen Wellen der MonsundepressionEs wurde eine quasigeostrophische, lineare Stabilitäts-analyse durchgeführt, um die Auswirkung der Windscherung in den unteren Luftschichten auf das barokline Wachstum von kurzen Wellen der Monsundepression zu studieren. Die Windscherung der mittleren Monsunströmung wird durch wechselnden Wind am Boden sowie die Lage und die Stärke des Westwindmaximums verändert. Für alle Fälle von Windprofilen wurde die Wachstumsrate und die Phasengeschwindigkeit der kurzen labilen Wellen (L2000 bis 2500 km) bestimmt. Man erkennt, daß beide von kleineren Änderungen in Lage und Stärke des Westwindmaximums nicht beeinflußt werden. Dagegen hängt die Wachstumsrate der kurzen Wellen der Monsundepression wohl von der mittleren Windscherung im Niveau zwischen 850 und 500 mb ab.

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With 5 Figures     

Observation of wind shear during evening transition and an estimation of submicron aerosol concentrations in Beijing using a Doppler wind lidar

The wind speed and direction measured over six months by a Doppler wind lidar (Windcube-8) were compared with wind cup anemometers mounted on the 325-m Beijing meteorological tower (BMT). Five mountain–plain wind cases characterized by wind direction shear were selected based on the high-frequency (1.1 s) wind profile of the Windcube-8 and analyzed with 1-h mesoscale surface weather charts. Also analyzed was the relationship between in-situ PM₁ (aerodynamic diameter ≤ 1 μm) concentrations measured at 260 m on BMT and the carrier-to-noise ratio (CNR) of the co-located Windcube-8. The results showed that the 10-min averaged wind speed and direction were highly correlated (R = 0.96–0.99) at three matched levels (80, 140, and 200 m). The evening transition duration was 1–3 h, with an average wind speed of 1 m s^–1 at 80 m above the ground. In addition, there was a zero horizontal-wind-speed zone along the wind direction shear line, and in one case, the wind speed was characterized by a Kelvin–Helmholtz gravity wave. The variability of the PM₁ concentrations was captured by the CNR of the Windcube-8 in a fair weather period without the long-range transport of dust.     

2016年4—10月我国主要暴雨天气过程简述

利用杭瑞高速洞庭湖大桥测风塔上的三维超声风速仪观测资料以及岳阳气象站逐小时降水资料,分析了2016年7月3—5日湖南岳阳一次大暴雨过程的三个不同时段近地层湍流特征。结果表明：(1)强降水来临前180—230 min和结束前10—50 min的近地层物理量场出现异常,且强降水来临前的物理量场异常出现时间较结束前早。风速、湍流强度、湍流动能在大暴雨过程中出现异常偏大,强降水来临前230 min,风速出现最大值4.875 m·s^-1;强降水结束前50 min,湍流强度出现最大值,水平纵向、水平横向、垂直向的湍流强度分别为1.255、1.173、0.195。(2)强降水来临前与结束前,湍流功率谱密度出现异常偏大。大暴雨过程中的湍流功率谱密度减小,湍流功率谱密度最大值的频率左移。(3)强降水来临前的湍涡尺度最大,强降水期间的湍涡尺度次之,强降水结束后的湍涡尺度在三者中最小,低频大涡为大暴雨过程中的湍流活动提供了能量。

     

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air–water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate Γ, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer.For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as ∝ 1/Γ), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.