Wind Friction Velocity Research Articles

Modeling the atmospheric dust cycle: 1. Design of a soil‐derived dust emission scheme

A soil‐derived dust emission scheme has been designed to provide an explicit representation of the desert dust sources for the atmospheric transport models dealing with the simulation of the desert dust cycle. Two major factors characterizing the erodible surface are considered: (1) the size distribution of the erodible loose particles of the soil which controls the erosion threshold and the emission strength and (2) the surface roughness which imposes the efficient wind friction velocity acting on the erodible surface. These two parameters are included in a formulation of the threshold wind friction velocity by adapting a size‐dependent parameterization proposed by Iversen and White (1982) and by applying to the rough erodible surfaces a drag partition scheme derived from Arya (1975). This parameterization of the threshold friction velocity has been included in an horizontal flux equation proposed by White (1979). This allows to attribute a specific production rate to each soil size range for each type of surface. The dust flux F is then considered as a fraction of the total horizontal flux G, the value of the ratio F/G being imposed, at this time, by the soil clay content. In summary, the computed mass fluxes depend on the soil size distribution, the roughness lengths, and the wind friction velocity. The different steps of this scheme have been independently validated by comparison with relevant experimental data. Globally, the agreement is satisfying, so that the dust fluxes could be retrieved with less uncertainties than those observed in previous simulations of the desert dust cycle.

An assessment of veering wind effects on scatterometry from the sea surface

To characterize scatterometer returns from the sea surface near meteorological fronts, we investigated microwave scattering from seas in which long waves are at oblique angles to short waves. We simulate the effects of veering winds on C- and K-u-band scatterometers by using models in which the short waves align with the wind friction velocity u*, but the long waves are at oblique angles to the u* direction. The analysis reveals two main effects due to the rotation of the long wave slope probability density distribution. Azimuthally averaged normalized radar cross-section a(0) decreases as the oblique angle increases. Additionally, two regimes exist. In the small angle regime, azimuthal scans of normalized radar cross-section sigma degrees exhibit features similar to the classic double-maxima pattern for non-veering wind conditions, but the axis of sigma degrees maxima is rotated toward the long-wave axis. In the large angle regime, more than two maxima are apparent in azimuthal scans. Therefore it may be inappropriate to use standard three term Fourier cosine models for some veering wind conditions.

Wind Stress from Wave Slopes Using Phillips Equilibrium Theory

An open ocean, deep water air–sea interaction experiment was conducted in the Gulf of Alaska. Wave amplitude and slope data were measured using a WAVEC heave, pitch, and roll buoy that was let drift in the Alaska gyre. Wind stress estimates were obtained from a fast-sample anemometer using the dissipation technique and from synoptic measurements through a boundary-layer model. The fundamental correlation and predictive relationships between wind friction velocity and wave spectral properties were established. A comparison of the slope spectrum to simultaneous wind stresses allowed us to estimate the Phillips proposed universal constant β. Reintroducing this constant β into the Phillips slope spectrum and using measured slope spectral characteristics, an inferred wind stress was calculated that was shown to agree well with both the dissipation and model stresses thereby validating both Phillips theory and the boundary-layer model. Any discrepancies with the model stresses were attributed to second-order wave age effects. The roughness length z0, nondimensionalized by the sea rms wave height, was shown to decrease with wave age in a manner consistent with Kitaigorodskii's functional form. A general expression for Cd as a function of wind speed or friction velocity and wave age was proposed and verified with independent data.

Uptake of small particles by tree canopies

A study was undertaken to determine experimentally the deposition of particles on components of different trees and to extrapolate the experimental data so obtained to large-scale canopies by means of a model. The experiments were performed in a wind tunnel allowing canopy components to be exposed to a flow of suspended fluorescent particles of almost uniform size. Emphasis was put on particles in the 0.3- to 1.2-μm subrange, since most of the radioactive particles sampled at long distance from sources are in this size interval. The leaf deposition rates were determined for leaf-bearing twigs of several evergreen species, as a function of wind speed and particle size. The rates obtained were used as input to a model that describes the uptake of particles by a large-scale canopy under specified conditions of weather and canopy structure. Simulations carried out for a typical spruce canopy indicate that the deposition is limited by the strong decrease in wind speed with height in the canopy. The deposition rate to a forested horizontal surface (canopy deposition rate) is between 10 −4 and 10 −3 m·s −1 depending on wind friction velocity. This rate is practically independent of particle size in the size subrange of interest.

Effects of the bottom friction formulation on the energy balance for gravity waves in shallow water

The energy transfer equation for wind‐generated ocean waves is solved numerically for fetch‐limited conditions in waters of limited depth. The resulting growth curves for the total energy and the peak frequency are obtained for five different bottom friction dissipation formulations: an empirical Joint North Sea Wave Project (JONSWAP) expression (Hasselmann et al., 1973), three expressions based on the drag law friction model (Hasselmann and Collins, 1968; Collins, 1972; Madsen et al., 1988a) and a form based on the eddy viscosity friction model (Weber, 1991a). The effects of different bottom friction dissipation formulations on the energy balance are intercompared and evaluated. The results are also compared with the Coastal Engineering Research Center growth curves. Numerical simulation and mathematical analysis show that only the drag law formulations with a fixed drag coefficient scale in terms of the air friction velocity. The empirical JONSWAP, the drag law formulation with dynamically changing drag coefficient, and the eddy viscosity model do not scale. It is possible to tune the dissipation coefficients for one particular wind friction velocity but different water depths so that all five formulations give almost the same growth curves for the total energy and the peak frequency. This can be explained by the fact that the five tuned bottom friction dissipation models have the same effect on the energy balance when integrated over the frequency and angle space.

Modulation of the growth rate of short surface capillary–gravity wind waves by a long wave

Modulation of the growth rate of short capillary–gravity surface wind waves in the presence of a long wave with steepness much smaller than the maximum is studied theoretically. The Miles (1962) mechanism taking into account the viscous wave stresses in the air flow is considered to be the main process of short-wave generation. The short-wave growth rate is defined by the wind velocity gradient in the viscous sublayer of the logarithmic boundary layer. The long wave propagating on the wave surface induces an additional component of the wind velocity gradient oscillating with the length and time periods of the long wave, which results in modulation, with the same period, of the growth rate of the short wave riding on the long one. The growthrate modulation amplitude depends on the parameter M being of the order of the relation between the oscillating and the mean wind velocity gradients in the viscous sublayer \[M=\frac{2kac}{u^2_*}(ckv_{\alpha})^{1/2} \] (where c, k, a are the phase velocity, the wavenumber and the elevation amplitude of the long wave; va is the viscosity coefficient in the air; u* is the wind friction velocity). When M = O(1) (weak winds and long waves) the oscillating component of the shortwave growth rate is of the same order as the mean one. If M is much smaller than unity, then the relative amplitude of the growth rate is of the same order as the steepness of the long wave.

Radiative transfer equation with surface scattering for ocean and atmospheric parameters retrieval from radiometric measurements

Microwave radiometers have been used with success in the past for the retrieval of ocean surface and atmospheric parameters. However, for the most effective use of the measurements provided by these instruments, it is necessary that performant inversion algorithms be available. Existing algorithms have already proved their usefulness but are often based on statistical regressions on the measurements from some particular experiment or on artifical data sets. Progress towards better performances still remains possible. We have developed an iterative retrieval procedure based on a physical scattering and propagation model for observing the ocean surface and the intervening atmosphere. A correction for scattering by the roughened sea surface is proposed and introduced in a previously developed contracted form of the radiative transfer equation. This correction is modelled for a range of frequencies from 5 to 40 GHz, and represented, in the form of a polynomial expansion depending on two parameters only: the total atmospheric attenuation, and the wind friction velocity. Results of inversions on simulated measurements obtained with this approximate model are presented and discussed.

Fully and nonfully developed sea models for microwave remote sensing applications

A new statistical description of the ocean surface is proposed and described. Classically it is assumed that the spectrum of the surface vertical displacements depends only on one external, or forcing parameter-the wind speed (or the wind friction velocity); this is, however, true for fully developed sea states only. In the more general case of nonfully developed sea states, the spectrum should depend as well on internal parameters describing the characteristic features of the surface. Such a representation is discussed in this article for applications to active and passive microwave remote sensing of the oceans.

Spatial measurements of short wind waves using a scanning slope sensor

The spatial structures of short wind-generated waves from 0.6 to 12 cm were measured with a scanning optical slope sensor and the wavenumber-frequency spectra of surface slope and curvature under various wind velocities were computed. The results show that the energy densities of both the frequency and wavenumber spectra increase with the wind-friction velocity. The rate of increase with wind-friction velocity is linear in the gravity and short capillary regions and between square to cubic in the gravity-capillary (centimeter waves) region. The drop-off of the wavenumber ( k) spectrum varies from k −4 in the gravity region to k −8 in the capillary region, with a sharp break between the two regions occurring at the dividing wavelength from 0.8 cm at low winds to 1.6 cm at high winds. The magnitudes of the mean-square slope and mean-square curvature at various wind velocities are also presented. The fractional contribution to the mean-square slope from short waves of 0.6–12 cm in length is more than 50%, and the ratio shows an increase with with velocity

A generation‐dispersion model of ambient and transient bubbles in the close vicinity of breaking waves

Bubble models are necessary to ascertain bubble contribution to ocean‐atmosphere fluxes of gas, aerosols, humidity, and latent heat. Previous theories flatten the wave breaking layer to a theoretical boundary from which bubbles are dispersed by turbulence working against buoyancy lift. As a consequence, bubble population characteristics next to the surface are not derived from these models but depend on empirical or semiempirical assumptions made at this boundary. By considering bubble injection with puffs of intense turbulence, specifying how bubbles are first created by a small‐scale similarity reasoning, and using a wavy interface, the present bubble theory expands this layer to a more physical breaking layer. Bubble concentration density as a function of bubble diameter, depth, and sea state parameters is obtained through explicit integrals. The model is found to be consistent with the previous bubble theories: the back flattening of the model breaking layer indeed results in equations compatible with these theories. The model variations in bubble concentration density with different parameters is coherent with experimental laws: the dominant bubble concentration is found to vary as about d−4 with bubble diameter and u*3 with wind friction velocity, but because of breaking patches, a d−2 bubble distribution is obtained very close to the surface. The concordance of the model with experimental data in the recent and classic bubble literature is quite good.

An analysis of scatterometer returns from a water surface agitated by artificial rain: evidence that ring-waves are the main feature

Both wind and rain roughen the sea surface, but whereas wind generates waves, rain generates craters, stalks and ring-waves. Average backscattered power for scatterometer returns from water surfaces is closely related to small scale features on the water surface, so we use backscattered power from short wind-waves as a basis to evaluate the importance of ring-waves. Experiments were conducted with a 13.5 GHz scatterometer (30-degrees incidence angle, vertical polarization) in a wind-wave tank that is enhanced by a rain simulator. Rain intensities ranged from 3-30 mm h-1 and wind friction velocities were between 10 and 50 cm s-1. The variance of sur-face elevation for small scale features xi(sm)2, i.e., ring-waves and short wind-waves, was computed for each case using data from a capacitance probe. Comparison of the data sets shows that the range of xi(sm)2 for the rain cases is comparable to that from light to moderate wind cases-so ring-wave amplitudes are not negligible. Analysis of the radar data provides evidence that ring-waves are the dominant feature contributing to the backscattered power. Thus ring-waves need to be included in scatterometer numerical models that contain rain effects.

A laboratory study of friction-velocity estimates from scatterometry: low and high regimes

Measurements from scatterometers pointing at wind-waves in three large wave tanks are examined to study fetch effects and the correlation with wind friction velocity. Time-series measurements were made at 13, 35, and 95 m with a Ka-band scatterometer aimed upwind at 30 deg incidence angle and vertical polarization. Average normalized radar cross-section (sigma-0) values from all fetches follow a common trend for sigma-0 as a function of wind friction velocity, so the fetch dependence is negligible. An empirical power-law model yields a high correlation between sigma-0 and wind friction velocity, but, because systematic anomalies arise, we reexamine a turbulence approach that delineates low and high regimes with a transition at a wind friction velocity of approximately 25 cm/s. Using this criteria, the data are well represented by a two-section power-law relationship between sigma-0 and wind friction velocity.

One-dimensional aeolian suspension above beds of loose particles—A new concentration-profile equation

The theoretical solution for concentration profiles of particles in aeolian suspension above large beds of loose particles is re-examined. It is argued that the solution generally found in the literature is based of an erroneous boundary condition at the surface of the particle bed. A revised boundary condition is suggested and this leads to a new equation for particle concentration profiles in the one-dimensional zone. The profiles are a two-parameter family. The parameters are the ratio of particle settling velocity to wind friction velocity and a concentration ratio. Crude estimates of the latter parameter are available from a formula derived in the paper. The new profile equation is supported by experimental data. Also, unlike the old equation, it gives the expected logarithmic concentration profiles in the limiting case of very fine particles.

Radar Sea Returns—Ocean-Ripple Spectrum and Breaking-Wave Influence

Radar cross sections reported by Guinard et al. are normalized with respect to their mean value obtained with different bands but at the same wind velocity. The results confirm that there are significant differences between returns with VV and HH polarizations. The VV-polarized returns, being associated more closely with distributed ocean ripples, support the equilibrium spectrum of ocean waves k−3.5 with the wavenumber k < 0.5 rad cm−1, and the saturated spectrum k−4 at higher wavenumbers. The HH-polarized returns at low wavenumbers have the same trend as those of the VV-returns, but are smaller in magnitude. At high wavenumbers (k > 0.5 rad cm−1), the HH-returns retain the trend of increasing continuously with the Bragg wavenumber; this is believed to be caused by the surface roughness produced by individual breaking waves. Contributions of returns produced by each mechanism are then discussed for radars having various bands. Functional, power-law type, dependence of returns on the wind-friction velocity is also found to vary systematically with the Bragg wavenumber; the exponent of power law increases with the Bragg wavenumber, following k⅓.

Wave Dependence of Sea-Surface Wind Stress

Abstract Distribution of the wind stress over the oceans is usually estimated by using a bulk formula. It contains the squared 10-m wind speed multiplied by the drag coefficient, which has been assumed in many cases to be a weak function of the 10-m wind speed. Over land the important role of thermal stratification has been clearly recognized, but over the sea the influence of wind waves is less well documented. This paper presents evidence showing the likelihood that the influence of the wind waves can also be large. Charnock proposed an expression for the marine atmospheric boundary layer roughness parameter, z0, which depended only on the wind friction velocity, u☆ and the acceleration of gravity, g. Toba and Koga have recently proposed an alternative expression for flow over growing wind waves, which are in local equilibrium with the wind, given by a form including the wind-wave spectral peak frequency explicity. The criterion for local equilibrium of the wave field with the wind is its consistency wi...

Dependence of microwave sea returns on wind-friction velocity under varied atmospheric stability conditions

Microwave sea returns under varied atmospheric conditions and sea states were measured by W.C. Keller et al. (1985). The author has examined quantitative variations of these returns with the wind-friction velocity, incorporating modifications of the atmospheric stability, and has also compared features of sea returns and wind-stress coefficients varying with the stability length. Implications for the inception of fine sea-surface structures by wind and their probable saturation and corrections of stability effects of the wind-stress coefficient are discussed. It is shown that trends based on radar returns at low and high winds can be resolved only with simultaneous measurements of fine sea-surface structures. >

Wavenumber spectra of short gravity waves

The spectral balances involved in shaping the short gravity wave region of the ocean wave-height spectrum have been the subject of recent physical models. In terms of the wind friction velocity u*, gravitational acceleration g and local wavenumber k, these models predict a wavenumber dependence of , where k = |k|, and a linear dependence on u* for the equilibrium range of gravity waves above the spectral peak. In this paper we present the results of an experimental determination of the wavenumber spectrum for the wavelength range of 0.2−1.6 m, based on stereophotogrammetric determinations from an oil platform under open ocean conditions.From our observations, for this wavenumber range, the one-dimensional equilibrium wavenumber spectrum was determined as \[ \phi (k_i) \sim \left(\frac{u^2_*k}{g}\right)^{\gamma} k^{-3}_{i}\;\;\;\;\;\;\;(i=1,2 \;\;\; K = (k_1,k_2)) \] where γ = 0.09±0.09 at the 95% confidence level. These limits embrace wind-independent approximations to the observed one-dimensional and two-dimensional wavenumber spectra of the form \[ \phi (k_i) \sim B k^{-3}_i \;\;\; (i = 1,2), \] and \[ \psi(k_i) \sim A k^{-4}, \] respectively, with B ∼ 10−4 and A ∼ 0.3 × 10−4 for and k = |k| is expressed in cycles/metre.The present findings do not support the wavenumber dependence predicted by the recent models in this wavenumber range and are at variance with their predicted dependence on the friction velocity. However, our observations are generally consistent with the radar reflectivity dependence on wind direction and wind speed under Bragg scattering conditions within our wavenumber range. The experimental observations also point out the potentially important role of wave-breaking of longer wave components in influencing the spectral levels of short gravity wave components.

Variations of Whitecap Coverage with Wind Stress and Water Temperature

Abstract Results of whitecap coverages from five previously reported oceanic experiments by Monahan and coinvestigators have been analyzed; the fractional coverage of the sea surface(W) was shown to follow a power law, W = 2U3.7510, where U10 is the wind velocity at 10 m above the mean sea surface. Attempts were then made to associate the coverage with the wind-friction velocity (u*) deduced from the wind velocity and air–sea temperature differences as W = 0.2u3*. Finally, we discuss effects of the water temperature on the coverage.

On nondimensional correlation between roughness length and wind-friction velocity

Physical bases for nondimensional parameters,z0/(u2*/g) andz0/(u*/σ), characterizing wind-wave interaction are discussed; data selected to support the latter are critically reviewed. Both parameters are herewith unified, with the former describing the primary growth of roughness length with wind and the latter the secondary effects due to waves.

The bursting sequence in the turbulent boundary layer over progressive, mechanically generated water waves

The structure of the pressure and velocity field in the air above progressive, mechanically generated water waves was investigated in order to evaluate the influence of a mobile and deformable boundary on turbulence production and the related bursting phenomena. The Reynolds stress fluctuations were measured in a transformed Eulerian wave-following frame of reference, in a wind-wave research facility at Stanford University.The structure of the wave-coherent velocity field was found to be very sensitive to the height of the critical layer below which the waves travel faster than the wind. Because the critical-layer height changes rapidly with the ratio (c / u*) of the wave speed to the wind friction velocity, the structure of the wave-coherent velocities depends strongly on the parameter c/Uδ0, where Uδ0 is the mean free-stream wind velocity. When the critical height is large enough that most of the flow in the turbulent boundary layer is below the critical height, the structure of the wave-coherent velocities is strongly affected by the Stokes layer (in the air), which under the influence of turbulence can have thickness comparable with the wave amplitude. In contrast, when the critical height is small enough that most of the flow in the boundary layer is above the critical height, the structure of the wave-coherent velocities is strongly affected by the critical layer. The latter was found to be nonlinear and turbulently diffusive.The dependence of the structural behaviour of the wave-coherent velocity field upon the critical and Stokes layers results in considerable modifications of the turbulence-generating mechanism during the bursting-cycle, as the dimensionless wave speed c/Uδ0 changes. Such modifications are manifested by an enhancement of the contributions to the mean Reynolds stress of the bursting events (relative to their solid-wall counterparts), and their dependence on the dimensionless wave speed. For c/Uδ0 [ges ] 0.68 (or c/u* &gt; 20), the nonlinear critical-layer thickness is large compared to the wave amplitude (except when c/Uδ0 = 0.68), and the diffused Stokes layer stimulates the wave-associated stress production. In the water proximity, the bursting contributions remain nearly constant with dimensionless wave speed; ejections account for 90% of the mean Reynolds stress, whereas sweeps provide 77%, the excess over 100% being balanced by the outward and inward interactions. For c/Uδ0 &lt; 0.68, the critical-layer thickness is smaller than the wave amplitude and all contributions increase gradually with c/Uao. However, the ratio of ejection to sweep contributions remains unaltered and ≈ 1.15, indicating that sweeps are nearly as energetic as ejections a t all dimensionless wave speeds. The value of c/Uδ0 ≈ 0.68 appears to separate the flow regimes of high and low critical level, respectively, where significant and weak production of the wave-associated stresses have been found. Near the water surface the height distribution of the fractional contributions of the bursting events is also sensitive to the ratio c/UJO. In the equilibrium region of the boundary layer it remains uniform and in the free stream rises sharply, independent of dimensionless wave speed.The mean time period between ejections or sweeps depends on both the wave and wind field characteristics and does not scale with either the inner or the outer flow variables. The former can be determined from the time between the first two largest consecutive peaks of the phase-averaged Reynolds stress distribution.In the water proximity, the height distribution of the normalized energy production is sensitive to c/Uδ0; only when c/Uδ0 [ges ] 0.68 does it show a peak of increasing magnitude with increasing dimensionless wave speed.