Preliminary results of measurements of atmospheric turbulence over the sea

We perform the experimental verification of the applicability of the theory of similarity to the wave boundary layer and the assessment of wave-induced perturbations of the air flow depending on various conditions of stratification of the atmosphere and the state of the sea. The measurements were carried out from a stationary platform located in the coastal part of the Black Sea. The experimental procedure is based on the simultaneous measurements of the profile and fluctuations of the wind speed at 5–6 levels in the 1.3–21-m layer, the elevations of the sea surface, the directions of waves and winds, and the mean gradients of temperature and humidity of air. The structure of the boundary layer in the region of measurements depends on the direction of the wind. For weak and moderate onshore winds (< 9 m/sec), the approximate balance is preserved between the production and dissipation of turbulent energy in the cases of unstable and neutral stratification. On the average, the estimates of friction velocity according to the profiles are higher than the dissipative estimates by 10% mainly due to the deficiency of dissipation near the surface. For the offshore wind, the structure of the boundary layer abruptly changes and is determined not by the local parameters but by strong turbulent eddies formed over the dry land. The intensity of low-frequency turbulent fluctuations and the gradient of wind velocity near the surface in the coastal zone are 1.5–2 times higher than for the open sea. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 42–61, May–June, 2007.     

Experimental study of turbulent oscillatory boundary layers in an oscillating water tunnel

A high-quality experimental study including a large number of tests which correspond to full-scale coastal boundary layer flows is conducted using an oscillating water tunnel for flow generations and a Particle Image Velocimetry system for velocity measurements. Tests are performed for sinusoidal, Stokes and forward-leaning waves over three fixed bottom roughness configurations, i.e. smooth, “sandpaper” and ceramic-marble bottoms. The experimental results suggest that the logarithmic profile can accurately represent the boundary layer flows in the very near-bottom region, so the log-profile fitting analysis can give highly accurate determinations of the theoretical bottom location and the bottom roughness. The first-harmonic velocities of both sinusoidal and nonlinear waves, as well as the second-harmonic velocities of nonlinear waves, exhibit similar patterns of vertical variation. Two dimensionless characteristic boundary layer thicknesses, the elevation of 1% velocity deficit and the elevation of maximum amplitude, are found to have power-law dependencies on the relative roughness for rough bottom tests. A weak boundary layer streaming embedded in nonlinear waves and a small but meaningful third-harmonic velocity embedded in sinusoidal waves are observed. They can be only explained by the effect of a time-varying turbulent eddy viscosity. The measured period-averaged vertical velocities suggest the presence of Prandtl's secondary flows of the second kind in the test channel. Among the three methods to infer bottom shear stress from velocity measurements, the Reynolds stress method underestimates shear stress due to missed turbulent eddies, and the momentum integral method also significantly underestimates bottom shear stress for rough bottom tests due to secondary flows, so only the log-profile fitting method is considered to yield the correct estimate. The obtained bottom shear stresses are analyzed to give the maximum and the first three harmonics, and the results are used to validate some existing theoretical models.     

Study of the Neutral Ekman Flow Using an Algebraic Reynolds Stress Model

A recently developed fully explicit algebraic model of Reynolds stress and turbulent heat flux in a thermally stratified planetary atmospheric boundary layer without stratification has been used for a numerical study of the Ekman turbulent boundary layer over a homogeneous rough surface for different dimensionless surface Rossby numbers. A comparative analysis has been conducted for a closure model of the transport term in the prognostic equation of turbulent kinetic energy dissipation including third-order moments. Dependences of the total wind rotation angle on the Rossby number have been obtained. The calculated vertical profiles of mean velocity, turbulent stress, turbulent kinetic energy, surface-friction velocity, and boundary-layer height agree satisfactorily with observational and earlier obtained LES data.     

Fine structure of the turbulent atmospheric boundary layer over the water surface

In this paper, the results of a laboratory experiment on investigating the wind-velocity field over a water surface using the PIV method are described. The use of a rapid CCD-camera made it possible to perform a detailed study of the eddy structure of airflow. We have measured the velocity fields over a flat plate by wind waves and waves induced by a wave generator. The model of a turbulent boundary layer over a rough surface was directly verified. It has been shown that the wind-velocity profiles over waves obtained by averaging the instantaneous fields over the ensemble of samples and horizontal coordinate are satisfactorily consistent with the profiles calculated within the frameworks of the model of wind flow over rough water surface.     

A note on a critical wind speed for air–sea boundary processes

Wind and wind-generated waves were measured in a wind-wave tank. A clear transition was found in the relation between the wind speed U ₁₀ and the wind friction velocity u _* near u _* = 0.2 m/s, where U ₁₀ is the wind speed at 10 m height extrapolated from the measured wind profile in a logarithmic layer, and u _* = 0.2 m/s corresponds roughly to U ₁₀ = 8 m/s in the present measurement. Quite a similar transition was found in the relation between the spectral density of high frequency wind waves and u _*. These results suggest the existence of the critical wind speed for air–sea boundary processes, which was proposed by Munk (J Marine Res 6:203–218, 1947) more than half a century ago. His original idea of the critical wind speed was based on the discontinuities in such phenomena as white caps, wind stress, and evaporation, which commonly appear at a wind speed near 7 m/s. On the basis of the results of our present study and those of earlier studies, we discuss the phenomena which are relevant to the critical wind speed for the air–sea boundary processes. The conclusion is that the critical wind speed exists and it is attributed to the start of wave breaking rather than the Kelvin–Helmholtz instability, but the air–sea boundary processes are not discontinuous at a particular wind speed; because of the stochastic nature of breaking waves, the changes occur over a range of wind speeds. Detailed discussions are presented on the dynamical processes associated with the critical wind speed such as wind-induced change of sea surface roughness and high frequency wave spectrum. Future studies are required, however, to clarify the dynamical processes quantitatively. In particular, there is a need to further examine the gradual change of breaking patterns of wind waves with the increase of wind speed, and the associated change of the structure of the wind over wind waves, such as separation of the airflow at the crest of wind waves, the turbulent stress, and wave-induced stress. Studies on the dynamical structure of the high frequency wave spectrum are also needed.     

The wind field over wind-waves

The velocity fluctuations of wind over wind-waves in a wind tunnel are measured with a X-type hot-wire anemometer at some heights over the water surface.The observed vertical profiles of the wave-induced velocity fluctuations and the wave-induced Reynolds stress at the wave spectral peak frequency are different from those expected from the inviscid quasi-laminar model;i.e., the observed vertical profiles of the power spectral density of the wave-induced horizontal or vertical velocity fluctuations of wind have the minimum value at the height much heigher than the critical layer, and the value of the wave-induced Reynolds stress is negative at several heights over the water surface. From the comparison between the experimental results and the numerical solutions of a linear model of the turbulent shear flow over the wavy boundary, it is shown that the discrepancy described above can be attributed to the atmospheric turbulence.     

Measurements of the atmospheric turbulence in the coastal zone of the sea during weak wind from a mountainous coast

Results of measurements of the atmospheric turbulence in the layer between 1.5 and 21 m above sea level and the drag coefficient of the sea surface as the wind blows from a 4-km-long mountainous slope with a mean inclination of 11° are presented. The measurements of wind-speed profiles and its fluctuations at several levels, waves, and the main meteorological parameters were carried out in autumn 2005 and 2008 from a stationary platform located in the Black Sea at a distance of approximately 1 km from the southern coast of Crimea. It is shown that during weak synoptic wind a low-level wind jet develops at night over the sea with a maximum velocity up to 5–6 m/s at a level of approximately 6 m over the sea induced by the katabatic wind over the coastal slope. According to the approximate estimates, the horizontal scale of the low-level jet can reach a few tens of kilometers. This flow is characterized by the dissipation rate of the turbulence energy independent of height and low-frequency velocity fluctuations related to the gravity waves and advection of turbulence from the coast. It is shown that the lower part of the boundary layer (up to a height of 3 m) is adjusted to the sea-surface roughness. The dependencies of the drag coefficient on the wind speed or wave age are steadier than in the data for the open sea. However, the age of the waves is not a universal parameter at long and short fetches.     

Turbulent structure in water under laboratory wind waves

The structure of the turbulent boundary layer underneath laboratory wind waves was studied by using a combination of a high-sensitivity thermometer array with a two-component sonic flowmeter. The temperature fluctuations are used to detect movements of water parcels, with temperature as a passive quantity. The turbulence energy was dominant in the frequency range (0.01 0.1 Hz), which was much smaller than the wind-wave frequency (2 5 Hz), and in which the turbulence was anisotropic. There was a frequency range (0.2 2 Hz for velocity, 0.2 5 Hz for temperature fluctuation) where the turbulence was isotropic and had a –5/3 slope in the energy spectrum. These points are the same as those in previous works. However, by analyses of the time series by using a variable-interval time-averaging technique (VITA), it has been found that conspicuous events in this main turbulence energy band are the downward bursting from the vicinity of the water surface. Thus the structure of the water layer underneath the wind waves has characters which are similar to the familiar turbulent boundary layer over a rough solid wall, as already conceived. It has been found that, at the same time, the turbulence energy can be related to quantities of the wind waves (the root mean squared water level fluctuation and the wave peak frequency), for different wind and wave conditions. That is, the turbulence underneath the wind waves develops under a close coupling with the wind waves.     

Wind-wave coupled downward-bursting boundary layer (DBBL) beneath the sea surface

By synthesizing data of the turbulent structure beneath wind waves in laboratory tanks, with some re-analyses, we propose the existence of a particular turbulent boundary layer which is directly coupled with wind waves, a downward-bursting boundary layer (DBBL) in water beneath wind waves. The data set indicates that the depth of this layer is from 3 to 7, or about 5 times the significant wave height of wind waves. The data observed in laboratory tanks agree with data of acoustic observations of bubble clouds under breaking wind waves in the sea made by Thorpe (1986, 1992). It is inferred that DBBL is formed in equilibrium with the local wind waves, as a common feature from initially generated wind waves, young laboratory wind waves to mature wind waves in the sea.     

The “slip law” of the free surface

A “slip law” connects the excess velocity or “slip” of a wind-blown water surface, relative to the motion in the middle of the mixed layer, to the wind stress, the wind-wave field, and buoyancy flux. An inner layer-outer layer model of the turbulent shear flow in the mixed layer is appropriate, as for a turbulent boundary layer or Ekman layer over a solid surface, allowing, however, for turbulent kinetic energy transfer from the air-side via breaking waves, and for Stokes drift. Asymptotic matching of the velocity distributions in inner and outer portions of the mixed layer yields a slip law of logarithmic form, akin to the drag law of a turbulent boundary layer. The dominant independent variable is the ratio of water-side roughness length to mixed layer depth or turbulent Ekman depth. Convection due to surface cooling is also an important influence, reducing surface slip. Water-side roughness length is a wind-wave property, varying with wind speed similarly to air-side roughness. Slip velocity is typically 20 times water-side friction velocity or 3% of wind speed, varying within a range of about 2 to 4.5%. A linearized model of turbulent kinetic energy distribution shows much higher values near the surface than in a wall layer. Nondimensional dissipation peaks at a value of about eight, a short distance below the surface.     

Laboratory observation of boundary layer flow under spilling breakers in surf zone using particle image velocimetry

A boundary layer flow under spilling breakers in a laboratory surf zone with a smooth bottom is investigated using a high resolution particle image velocimetry (PIV) technique. By cross-correlating the images, oscillatory velocity profiles within a viscous boundary layer of O(1) mm in thickness are resolved over ten points. Using PIV measurements taken for an earlier study and the present study, flow properties in the wave bottom boundary layer (WBBL) over the laboratory surf zone are obtained, including the mean velocities, turbulence intensity, Reynolds stresses, and intermittency of coherent events. The data are then used to estimate the boundary layer thickness, phase variation, and bottom shear stress. It is found that while the time averaged mass transport inside the WBBL is onshore in the outer surf zone, it changes to offshore in the inner surf zone. The zero Eulerian mass transport occurs at h/h_b ≈ 0.92 in the outer surf zone. The maximum overshoot of the streamwise velocity and boundary layer thickness are not constant across the surf zone. The bottom shear stress is mainly contributed by the viscous stress through mean velocity gradient while the Reynolds stress is small and negligible. The turbulence level is higher in the inner surf zone than that in the outer surf zone, although only a slight increase of turbulent intensity is observed inside the WBBL from the outer surf zone to the inner surf zone. The variation of phase inside and outside the WBBL was examined through the spatial velocity distribution. It is found the phase lead is not constant and its value is significantly smaller than previous thought. By analyzing instantaneous velocity and vorticity fields, a remarkable number of intermittent turbulent eddies are observed to penetrate into the WBBL in the inner surf zone. The size of the observed large eddies is about 0.11 to 0.16 times the local water depth. Its energy spectra follow the − 5/3 slope in the inertial subrange and decay exponentially in the dissipation subrange.     

Internal flow structure of short wind waves

The minimum value of wind stress under which the flow velocity in short wind waves exceeds the phase speed is estimated by calculating the laminar boundary layer flow induced by the surface tangential stress with a dominant peak at the wave crest as observed in previous experiments. The minimum value of the wind stress is found to depend strongly on, the ratio of the flow velocity just below the boundary layer and the phase speed, but weakly onL, the wavelength. For wind waves previously studied (=0.5,L=10 cm), the excess flow appears when the air friction velocityu _* is larger than about 30 cm sec^–1. The present results confirm that the excess flow found in my previous experiments is associated with the local growth of a laminar boundary layer flow near the wave crest.     

Spatial spectra and characteristic horizontal scales of temperature and velocity fluctuations in the convective boundary layer of the atmosphere

Using a high-resolution LES numerical model, we calculated the turbulent thermal convection for high ratios of horizontal and vertical sizes of the computational domain (26: 26: 1). The natural analog of the simulated process is a planetary boundary layer (PBL) of the atmosphere growing with height in the background of stably stratified overlying air layers over a horizontally homogeneous heated surface under a weak average wind. We obtained the spectral distributions of variances of fluctuations in potential temperature and velocity components in ranges corresponding to scales from a few tens of meters to a few tens of kilometers. We found energetically significant segments of the spectrum of large-scale fluctuations in the potential temperature for which the power dependences S ～ k ^?1/3 and S ～ k ^?4/3 are satisfied with good accuracy. We calculated the characteristic spatial scales of horizontal fluctuations in velocity and temperature. We obtained a dependence of these scales on the height of the growing convective PBL. We discuss the characteristic features of large-scale distributions in terms of the self-similarity of the growing boundary layer behavior.     

Characteristics of radiative heat transfer in the atmospheric surface layer from the results of direct measurements

Results of direct measurements of the long-wavelength (LW) radiative heat influx (RHI) in the atmospheric surface layer (ASL) are presented. These measurements were performed in August 2003 at the IAP RAS base in Tsimlyansk under the conditions of unstable and stable stratification during a weak wind and a cloudless sky and under nonsteady conditions during cumulus cloudiness in the daytime. The underlying surface was dry steppe with spars grass. The in situ RHI measurements were performed with an original optoacoustic receiver having a quasi-spherical angle of view at heights from 0.15 to 4 m. It is shown that the radiative heating in the ASL was many times the actual heating, especially during near-noon hours. In the daytime, the radiative heating attained its maximum at the heights of measurements 0.15–1 m and decreased with height. The radiative heating at these heights in the near-noon hours was on average about 20 K/h, attaining 60 K/h under a cloudless sky and a weak wind. Under inversion stratification, the radiative cooling usually exceeded the actual cooling, amounting on average from 0 to ?8 K/h and changing with height only slightly. Periods with close (in phase) fluctuations of the radiative and actual cooling, sometimes changing to heating, were observed during the night. Regression equations, showing a high correlation between the RHI values at the heights of measurements 0.5 and 1 m and the soil-air temperature differences at the height of measurements, are obtained for different heights. The diurnal mean RHI profiles are characterized by a heating on the order of several K/h in the lower part of the layer of measurements, which decreases with height and changes to cooling at heights of up to 4 m. A change in the effective radiation with height in the layer of measurements, which was obtained through the summation of RHI values at several heights, was significant, attaining on average ?25 W/m² in the near-noon hours and +10 W/m² in the evening hours. The nonradiative (turbulent) heat influx, obtained as the difference between the rates of actual and radiative temperature variations measured in situ, decreased the radiative heating in the daytime many times. The main sources of error in direct RHI measurements are estimated.     

Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part II: Cnoidal waves

Vortex generation and evolution due to flow separation around a submerged rectangular obstacle under incoming cnoidal waves is investigated both experimentally and numerically. The Particle Image Velocimetry (PIV) technique is used in the measurement. Based on the PIV data, a characteristic velocity, phrased in terms of incoming wave height, phase speed, dimension of the obstacle, and a local Reynolds number are proposed to describe the intensity of vortex. The numerical model, which solves the two dimensional Reynolds Averaged Navier Stokes (RANS) equations, is used to further study the effects of wave period on the vortex intensity. Measurements for the mean and turbulent velocity fields further indicate that the time history of the intensity of fluid turbulence is closely related to that of the vortex intensity.     

The wind-field structure in a stably stratified atmospheric boundary layer over a rough surface

Both wind turning with height and ageostrophic flow in a stably stratified atmospheric boundary layer are analyzed using a three-parameter turbulence model. For a quasi-steady state of the boundary layer, the cross-isobaric flow is determined only by turbulent stress at the surface in the direction of geostrophic wind. The “operative” prediction models, in which the first-order turbulence closure schemes are used, tend to overestimate the boundary-layer depth and underestimate the angle between the surface and geostrophic winds when compared to “research” models (schemes of high-level turbulence closure). The true value of the angle between the surface and geostrophic winds is significant for the presentation of a large-scale flow. A nocturnal low-level jet is a mesoscale phenomenon reflected in data obtained from measurements in a stably stratified atmospheric boundary layer. It is found that such jets are of great importance in transporting humidity, momentum, and air pollution. In this study, the difference between jet flows over a homogeneous underlying surface and over a spatially localized large-scale aerodynamic roughness is shown.     

风浪和海洋飞沫对海表面拖曳系数和风廓线的影响

基于埃克曼理论,本文将波致应力和飞沫应力引入到海-气边界层的界面应力中,来研究海表面风浪和海洋飞沫对海-气边界层动量交换的影响,并得到修改后的埃克曼模型的理论解。波致应力是由风浪谱和波增长函数估计,并得到在中低风速下,波致应力、飞沫应力与湍流应力相比,对海表面拖曳系数和风廓线的影响非常小。当风速高于25米/秒时,海洋飞沫通过飞沫应力对海-气界面应力的作用远高于波致应力,以至于波致应力可以忽略。海表面拖曳系数在高风速下,随着风速的增大而减小。通过采用风浪谱的不同波龄,得到海洋飞沫的产生会导致海-气边界层风速的增加。最后,理论解与现场的观察数据进行了对比。对比后的数据表明,在中高风速下,飞沫对海-气边界层的影响远大于表面风浪。     

Detailed observation of the wind-exerted surface flow by use of flow visualization methods

Detailed observations were performed of the wind-exerted surface flow, before and after the generation of wind waves. As flow visualization techniques, 6 classes of polystyrene beads of from 0.33 mm to 1.93 mm in diameter, with a specific gravity of 0.99, and also, hydrogen bubble lines, were used. Experiments were carried out at three ranges of the wind speed: 4.0, 6.2 and 8.6ms^–1 in the mean in the wind-wave tunnel section, and the observations were made at 2.85 m in fetch. In the case of 6.2 m s^–1, when the initial surface skin flow attains 0.22 cm in the scale thickness and 16 cm s^–1 in the surface velocity in about 3 second from the onset of the wind, regular waves of about 1.7 cm in wave length appear on the water surface. In one second after that, the downward thrust of the surface flow and the consequent forced convection commences, and the transition of the surface layer to a turbulent state occurs. Ordinary wind waves begin to develop from this state. In developed wind waves the viscous skin flow grows on the windward side of the crests, frequently producing macroscopic skin flows, and these skin flows converge to make a downward thrust at the lee side, and the viscous skin layer disappears there. The velocity of the downward flow has a maximum at the phase of about 30, and the value is of the order of 10 cm s^–1 at 4-mm depth after the orbital velocity of the sinusoidal wave is subtracted. As the process through which the wind stress acts on the water surface, it is considered that the following particular one may be real: the skin friction concentrated at the windward side of the crest produces skin flows, which thrust into the inner region to make the forced convection, carrying the acquired momentum. The viscous shearing stress just before the generation of the surface undurations was about 1/4 of the total shearing stress under the existence of wind waves. It is considered that the increase of the wind stress by wind waves is caused by this mechanism.     

Features of wind field over the sea surface in the coastal area

In this paper we analyze SAR wind field features, in particular the effects of wind shadowing. These effects represent the dynamics of the internal atmospheric boundary layer, which is formed due to the transition of the air flow arriving from the rough land surface to the “smooth” water surface. In the wind-shadowed area, the flow accelerates, and a surface wind stress increases with fetch. The width of the shadow depends not only on the wind speed and atmospheric boundary layer stratification, but also on geographic features such as windflow multiple transformations over the complex surface land–Lake Chudskoe–land–Gulf of Finland. Measurements showed that, in the area of wind acceleration, the surface stress normalized by an equilibrium value (far from the coast) is a universal function of dimensionless fetch Xf/G. Surface wind stress reaches an equilibrium value at Xf/G ≈ 0.4, which is the scale of the planetary-boundary-layer relaxation.