Wind velocity distribution over wind-generated water waves
TL;DR: The results of laboratory investigations conducted to study the wind dynamics above wind-generated water waves are presented in this article, and available field measurements strongly suggest a logarithmic law for the wind-velocity distribution in the region close to the perturbed water surface.
About: This article is published in Coastal Engineering.The article was published on 1977-01-01. It has received 3 citations till now. The article focuses on the topics: Wind wave & Wind stress.
Citations
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TL;DR: In this paper, the authors investigated the similarities and dissimilarities of the airflow structure over water and solid surfaces for smooth and wavy conditions, and found that the level of enhancement of normalized Reynolds stress, rates of energy production, and dissipation from the free-stream region toward the surface is higher over the water surface especially in the presence of waves as compared to that over the solid surface.
Abstract: Results from an experimental study, investigating the similarities and dissimilarities of the airflow structure over water and solid surfaces for smooth and wavy conditions, are reported. The experiments were conducted at the same location, under identical flow conditions. The two-dimensional velocity fields were measured using particle image velocimetry technique over a wind speed range from 1.5 to 4.4 m s−1. The mean velocity profiles for all surface configurations showed the logarithmic behavior. The profiles of different turbulent properties followed similar trend over water and solid surfaces, however, their magnitudes varied over different surface types. The results show that the level of enhancement of normalized Reynolds stress, rates of energy production, and dissipation from the free-stream region toward the surface is higher over the water surface especially in the presence of waves as compared to that over the solid surface. It is also observed that the normalized magnitudes of turbulent prope...
13 citations
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01 Jun 2013
TL;DR: ................................................................................................................. xii CHAPTER ONE ................................................................................................................
Abstract: ................................................................................................................. xii CHAPTER ONE .................................................................................................................
9 citations
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01 Jan 2008
TL;DR: In this paper, a series of laboratory experiments were conducted over a wind speed range of 1.5 m s -1 to 4.4 m s-1 and at a fetch of 2.1 m. The results showed a reduction in the mean velocity magnitudes and the tangential stresses when gravity waves appeared on the water surface.
Abstract: The study of airside flow structure and its interaction with water at the air-water interface is important in order to understand the exchange of momentum, heat and mass fluxes between the two mediums. The present dissertation deals with the quantitative investigation of the near-surface flow above wind-sheared water surface through a series of laboratory experiments conducted over a wind speed range of 1.5 m s -1 to 4.4 m s-1 and at a fetch of 2.1 m. The two-dimensional velocity fields were measured using particle image velocimetry (PIV). To compare the airflow structure over the water surface with that over solid wall, the measurements were also made over the smooth and wavy walls at the same location, under identical conditions. The results show a reduction in the mean velocity magnitudes and the tangential stresses when gravity waves appear on the water surface. An enhanced vorticity layer was observed immediately above the water surface that extended to a height of approximately two times of the significant wave height. A novel approach is used to separate the wave-induced component from the instantaneous velocity fields. The flow structure was analyzed as a function of wave phase. The phase-averaged profiles of wave-induced velocity, vorticity and Reynolds stress showed different behaviour on the windward and leeward sides of the wave in the near-surface region. The results also show that the turbulent Reynolds stress mainly supports downward momentum transfer whereas the wave-induced Reynolds stress is responsible for the upward momentum transfer from wave to wind. This dissertation also provides first quantitative comparison of the mean, wave-induced and turbulent properties for the separated and non-separated flows over wind generated water waves. The maximum difference between the flow characteristics of the separated and non-separated flows is observed on the leeward side, within core of the separation region, where, higher magnitudes of the vorticity and turbulent properties were observed, indicating that the turbulence is significantly enhanced within the separation region. The comparison of the flow over smooth and wavy water and solid surfaces showed that although the trends in profiles over water and solid surfaces are mostly similar, the relative magnitudes of turbulent properties and their level of enhancement towards the surface are different over water and solid surfaces. Thus, the models for the flow over solid surfaces may not accurately predict the flow properties over the water surface especially in the near-surface region.
2 citations
References
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01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.
17,321 citations
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TL;DR: In this paper, the vertical distribution of horizontal mean wind in the lowest 8 metres over a reservoir (1·6 km × 1 km) has been measured using sensitive anemometers freely exposed from a fixed mast in water 16 m deep, the fetch being more than 1 km.
Abstract: The vertical distribution of horizontal mean wind in the lowest 8 metres over a reservoir (1·6 km × 1 km) has been measured using sensitive anemometers freely exposed from a fixed mast in water 16 m deep, the fetch being more than 1 km. The resulting profiles are closely logarithmic, the small differences being systematic and possibly due to the thermal instability which existed when the measurements were made.
The usual law for wind profiles in neutral stability is
where u is the wind speed at height z, k is von Karman's constant, log z (0) the intercept on the log z axis, and u* the so-called friction velocity defined by τ0 = pu, τ0 being the surface drag and rH the density of the air.
To characterize the profiles u*/k, their slope, was plotted in relation to z (0), their intercept; this allowed a direct comparison with other profiles, in particular those recently measured in a laboratory channel by Sibul. The agreement was better than expected and indicated that z (0) was comparatively independent of fetch and stability but was largely determined by u*. The relation between u* and z (0) agreed roughly with the simplest non-dimensional relation between them, gz (0)/u = constant, so that one is led to a generalized wind profile for flow over a water surface
which specifies the drag, given the wind at one known height. An approximate value of the constant is 12·5.
This expression can be compared with earlier work. The better wind-profile observations show rough agreement; the experimental scatter is necessarily large since a water surface is aerodynamically much smoother than most land surfaces, precision anemometry in difficult circumstances being required to provide sufficiently precise values. Oceanographic measurements of the tilt of water surfaces are in fair agreement at high wind speeds but at low wind speeds the data are conflicting. The early results which imply that the drag-coefficient (u/u2) increases with decreasing wind speed in light winds are thought to be in error; some support for this belief comes from recent estimates of drag using a modified ageostrophic technique, which agree roughly among themselves and with the general expression.
1,792 citations
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TL;DR: In this paper, an approximate solution to the boundary value problem is developed for a logarithmic profile and the corresponding spectral distribution of the energy transfer coefficient calculated as a function of wave speed.
Abstract: A mechanism for the generation of surface waves by a parallel shear flow U(y) is developed on the basis of the inviscid Orr-Sommerfeld equation. It is found that the rate at which energy is transferred to a wave of speed c is proportional to the profile curvature -U"(y) at that elevation where U = c. The result is applied to the generation of deep-water gravity waves by wind. An approximate solution to the boundary value problem is developed for a logarithmic profile and the corresponding spectral distribution of the energy transfer coefficient calculated as a function of wave speed. The minimum wind speed for the initiation of gravity waves against laminar dissipation in water having negligible mean motion is found to be roughly 100cm/sec. A spectral mean value of the sheltering coefficient, as defined by Munk, is found to be in order-of-magnitude agreement with total wave drag measurements of Van Dorn. It is concluded that the model yields results in qualitative agreement with observation, but truly quantitative comparisons would require a more accurate solution of the boundary value problem and more precise data on wind profiles than are presently available. The results also may have application to the flutter of membranes and panels.
1,399 citations
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TL;DR: In this paper, a theoretical study is made of shearing flows bounded by a simple-harmonic wavy surface, the main object being to calculate the normal and tangential stresses on the boundary.
Abstract: A theoretical study is made of shearing flows bounded by a simple-harmonic wavy surface, the main object being to calculate the normal and tangential stresses on the boundary. The type of flow considered is approximately parallel in the absence of the waves, being exemplified by two-dimensional boundary layers over a plane. Account is taken of viscosity; but, as the Reynolds number is assumed to be large, its effects are seen to be confined within narrow ‘friction layers’, one of which adjoins the wave and another surrounds the ‘critical point’ where the velocity of flow equals the wave velocity. The boundary conditions are made as general as possible by including the three cases where respectively the boundary is rigid, flexible yet still solid, or completely mobile as if it were the interface with a second fluid.The theory is developed on the model of stable laminar flow, although it is proposed that the same theory may usefully be applied also to examples of turbulent flow considered as ‘pseudo-laminar’ with velocity profiles corresponding to the mean-velocity distribution. Use is made of curvilinear co-ordinates which follow the contour of the wave-train. This admits a linearized form of the problem whose validity requires only that the wave amplitude be small in comparison with the wavelength, even when large velocity gradients exist close to the boundary. The analysis is made largely without restriction to particular forms of the velocity profile; but eventually consideration is given to the example of a linear profile and the example of a boundary-layer profile approximated by a quarter-period sinusoid. In § 7 some general methods are set out for the treatment of disturbed boundary-layer proses: these apply with greatest precision to thin boundary layers, but are also useful for the initially very steep but on the whole fairly diffuse profiles which occur in most practical instances of turbulent flow over waves.The phase relationships found between the stresses and the wave elevation are discussed for several examples, and their interest in connexion with problems of wave generation by wind is pointed out. It is shown that in most circumstances the stresses are distributed in much the same way as if the leeward slopes of the waves were sheltered. For instance, the pressure distribution often has a substantial component in phase with the wave slope, just as if a wake were formed behind each wave crest—although of course actual separation effects are outside the scope of the present theory. In this aspect, the analysis amplifies the work of Miles (1957).
484 citations
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TL;DR: In this article, the Stokes mass transport, related to wave characteristics, is only a small component of the surface drift in laboratory tanks and the fraction of the wind stress supported by the wave drag seems to vary with the wind and wave conditions.
Abstract: Systematic measurements of drift currents below and of airflows above an air-water interface have been made under various wind conditions. The current near but not immediately below the water surface is found to follow a Karman-Prandtl (logarithmic) velocity distribution. The current immediately below the water surface varies linearly with depth. The transitions of the current boundary layer to various regimes appear to lag behind, or to occur a t a higher wind velocity than, those of the airflow. The fraction of the wind stress supported by the wave drag seems to vary with the wind and wave conditions: a large fraction is obtained at low wind velocities with shorter waves and a small fraction is obtained a t high wind velocities with longer waves. At the air-water interface, the wind-induced current is found to be proportional to the friction velocity of the wind. The Stokes mass transport, related to wave characteristics, is only a small component of the surface drift in laboratory tanks. However, in terms of the fraction of the wind velocity, the mass transport increases, while the wind drift decreases, as the fetch increases. The ratio between the total surface drift and the wind velocity decreases gradually as the fetch increases and approaches a constant value of about 3·5% at very long fetches.
344 citations