Wind-induced growth of mechanically generated water waves[dagger]

1973 ◽  
Vol 58 (3) ◽  
pp. 435-460 ◽  
Author(s):  
W. Stanley Wilson ◽  
Michael L. Banner ◽  
Ronald J. Flower ◽  
Jeffrey A. Michael ◽  
Donald G. Wilson
Keyword(s):  
Growth Rates ◽  
Water Waves ◽  
Shear Velocity ◽  
Viscous Sublayer ◽  
Outer Edge ◽  
S Wave ◽  
Viscous Effects ◽  
Mean Velocity ◽  
Centre Line ◽  
Wind Velocities

An experimental study was conducted to measure the growth rates of mechanically generated surface water waves when subjected to a fully developed turbulent channel airflow. The study was designed to test the accuracy of the growth rates predicted by Miles's (1962b) theory. For a series of wave frequencies (from 2·04 to 6·04 Hz at 0·50 Hz increments) and centre-line wind velocities (0·20, 1·12 and 1·84 m/s) wave amplitudes were measured at three stations (2–21, 3–43 and 4·65 m) downwind from a wave generator. In addition, for centre-line velocities of 1–12 and 1·84 m/s, U* (the velocity at the outer edge of the viscous sublayer) and U1, (the shear velocity) were obtained from measured mean velocity and Reynolds stress profiles. The wave amplitude measurements at the wind velocity of 0·20 m/s provided attenuation rate estimates which agreed reasonably well with theoretical attenuation rates based on viscous effects both on the walls and in the bulk of the water. The amplitude measurements at the wind velocities of 1·12 and 1·84m/s provided growth rate estimates which were compared with theoretical growth rates (computed using the wave frequency, U1 and U* predicted by Miles's (1962b) theory. At 1·12m/s Miles's growth rateswere two to five times larger than those measured; at 1·84 m/s Miles's growth rates were about two times larger.

Laboratory studies of the velocity field over deep-water waves

1970 ◽  
Vol 42 (4) ◽  
pp. 733-754 ◽  
Author(s):  
Robert H. Stewart
Keyword(s):  
Velocity Field ◽  
Deep Water ◽  
Water Waves ◽  
Numerical Solutions ◽  
Viscous Sublayer ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Measured Velocity ◽  
The Mean ◽  
Deep Water Waves

The mean-velocity field over monochromatic, 1·96 Hz, deep-water waves was measured by means of hot-wire anemometers for a range of wind speeds (relative to wave speed) of 0·4 to 3·0. The mean-velocity profile, over waves 0·64 cm in amplitude, was the same as that over a rough plate; that is, the mean velocity varied as the logarithm of the height above the mean-water level, except very close to the water, where the effect of the viscous sublayer became important. The wave-induced perturbation-velocity field and its associated Reynolds stresses were also measured and compared with numerical solutions of various linear equations governing shearing flow over a wavy boundary. The comparison showed that the measured velocity field was not well predicted by these theories.

Temporal and Spatial Growth of Wind Waves

2007 ◽  
Vol 37 (1) ◽  
pp. 106-114 ◽  
Author(s):  
M. Stiassnie ◽  
Y. Agnon ◽  
P. A. E. M. Janssen
Keyword(s):  
Growth Rates ◽  
Water Waves ◽  
Wind Profile ◽  
Wind Waves ◽  
Shear Velocity ◽  
Spatial Growth ◽  
Wave Celerity ◽  
Temporal And Spatial ◽  
Distinct Maximum ◽  
Logarithmic Wind Profile

Abstract A solution of Rayleigh’s instability equation, which circumvents the apparent critical-layer singularity, is provided. The temporal and spatial growth rates of water waves exposed to a logarithmic wind profile are calculated and discussed. The findings are similar to previously published results, except for shear velocity–to–wave celerity ratios larger than 2, where the newly calculated growth rates start to decrease after having reached a distinct maximum. The ratio of the spatial to temporal growth rates is examined. It is shown to deviate by up to 20% from the leading-order value of 2. The implications of the growth rate to the modal distributions of energy input from wind to waves, for young and mature seas, and in temporal/spatial growth scenarios, are analyzed.

The Stochastic Parametric Mechanism for Growth of Wind-Driven Surface Water Waves

2008 ◽  
Vol 38 (4) ◽  
pp. 862-879 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Surface Water ◽  
Growth Rates ◽  
Atmospheric Pressure ◽  
Water Waves ◽  
Wave Amplitude ◽  
Pressure Fluctuations ◽  
Theoretical Understanding ◽  
Wave Growth ◽  
Atmospheric Pressure Fluctuations ◽  
Surface Water Waves

Abstract Theoretical understanding of the growth of wind-driven surface water waves has been based on two distinct mechanisms: growth due to random atmospheric pressure fluctuations unrelated to wave amplitude and growth due to wave coherent atmospheric pressure fluctuations proportional to wave amplitude. Wave-independent random pressure forcing produces wave growth linear in time, while coherent forcing proportional to wave amplitude produces exponential growth. While observed wave development can be parameterized to fit these functional forms and despite broad agreement on the underlying physical process of momentum transfer from the atmospheric boundary layer shear flow to the water waves by atmospheric pressure fluctuations, quantitative agreement between theory and field observations of wave growth has proved elusive. Notably, wave growth rates are observed to exceed laminar instability predictions under gusty conditions. In this work, a mechanism is described that produces the observed enhancement of growth rates in gusty conditions while reducing to laminar instability growth rates as gustiness vanishes. This stochastic parametric instability mechanism is an example of the universal process of destabilization of nearly all time-dependent flows.

scholarly journals Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

2021 ◽  
Vol 118 (34) ◽  
pp. e2111144118 ◽  
Author(s):  
Kevin Patrick Griffin ◽  
Lin Fu ◽  
Parviz Moin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flows ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
General Transformation ◽  
Law Of The Wall ◽  
Velocity Transformation ◽  
Logarithmic Region ◽  
Logarithmic Layer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

Wind-generated gravity-capillary waves: laboratory measurements of temporal growth rates using microwave backscatter

1975 ◽  
Vol 70 (3) ◽  
pp. 417-436 ◽  
Author(s):  
T. R. Larson ◽  
J. W. Wright
Keyword(s):  
Growth Rates ◽  
Water Waves ◽  
Friction Velocity ◽  
Capillary Waves ◽  
Spectral Amplitude ◽  
Bragg Scattering ◽  
Laboratory Measurements ◽  
Wind Speeds ◽  
Tightly Coupled ◽  
Microwave Backscatter

The growth rates of wind-induced water waves at fixed fetch were measured in a laboratory wave tank using microwave backscatter. The technique strongly filters out all wavenumber component pairs except for a narrow window at the resonant Bragg scattering conditions. For these waves the spectral amplitude was measured as a function of the time after a fixed wind was abruptly started. The radars were aligned to respond to waves travelling in the downwind direction at wavelengths of 0·7-7 cm. Wind speeds ranged from 0·5 to 15 m/s. Fetches of 1·0, 3·0 and 8·4 m were used. In every case, the spectral amplitude initially grew at a single exponential rate β over several orders of magnitude, and then abruptly ceased growing. No dependence of the growth rate on fetch was observed. For all wavelengths and wind speeds the data can be fitted by \[ \beta (k,u_{*},{\rm fetch})=f(k)\,u^n_{*}, \] with n = 1·484 ± 0·027. Here u* is the friction velocity obtained from vertical profiles of mean horizontal velocity. For each wind speed, f(k) had a relative maximum near k = kn ≃ 3·6 cm−1. Rough estimates of β/2ω, where ω is the water wave frequency, and of the wind stress supported by short waves indicate that the observed growth rates are qualitatively very large. These waves are tightly coupled to the wind, and play a significant role in the transfer of momentum from wind to water.

Airside Velocity Measurement Above the Wind-Generated Water Waves

2007 ◽  
Author(s):  
Nasiruddin Shaikh ◽  
Kamran Siddiqui
Keyword(s):  
Water Waves ◽  
Flow Behavior ◽  
Momentum Exchange ◽  
Mean Velocity ◽  
Wind Speeds ◽  
Velocity Magnitude ◽  
Image Velocimetry ◽  
Sweeping Processes ◽  
High Level ◽  
The Waves

An experimental study conducted to investigate the airside flow behavior within the crest-trough region over wind generated water waves is reported. Two-dimensional velocity field in a plane perpendicular to the surface was measured using particle image velocimetry (PIV) at wind speeds ranging from 1.5 m s−1 to 4.4 m s−1. The results show a reduction in the mean velocity magnitude when gravity waves appear on the surface. A sequence of consecutive velocity fields has shown the bursting and sweeping processes and the flow separation above the waves. The results also indicate that the flow dynamics in the crest-trough region are significantly different than that at greater heights. High level of turbulence was observed in this region which could not be predicted from the measurements at greater heights. Thus, it is concluded that the quantitative investigation of the flow in the immediate vicinity of the interface is vital for an improved understanding of the heat, mass and momentum exchange between air and water.

Investigation of Boundary Layer Flows Over a Flat Plate With Different-Size Transverse Square Grooves at s/w = 10

2007 ◽  
Author(s):  
Redha Wahidi ◽  
Walid Chakroun ◽  
Sami Al-Fahad
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Viscous Sublayer ◽  
Velocity Profiles ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Uncertainty Range ◽  
The Mean

Turbulent boundary layer flows over a flat plate with multiple transverse square grooves spaced 10 element widths apart were investigated. Mean velocity profiles, turbulence intensity profiles, and the distributions of the skin-friction coefficients (Cf) and the integral parameters are presented for two grooved walls. The two transverse square groove sizes investigated are 5mm and 2.5mm. Laser-Doppler Anemometer (LDA) was used for the mean velocity and turbulence intensity measurements. The skin-friction coefficient was determined from the gradient of the mean velocity profiles in the viscous sublayer. Distribution of Cf in the first grooved-wall case (5mm) shows that Cf overshoots downstream of the groove and then oscillates within the uncertainty range and never shows the expected undershoot in Cf. The same overshoot is seen in the second grooved-wall case (2.5mm), however, Cf continues to oscillate above the uncertainty range and never returns to the smooth-wall value. The mean velocity profiles clearly represent the behavior of Cf where a downward shift is seen in the Cf overshoot region and no upward shift is seen in these profiles. The results show that the smaller grooves exhibit larger effects on Cf, however, the boundary layer responses to these effects in a slower rate than to those of the larger grooves.

Low-Reynolds-Number Turbulent Boundary Layers

1981 ◽  
Vol 103 (4) ◽  
pp. 624-630 ◽  
Author(s):  
B. R. White
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Reynolds Numbers ◽  
Viscous Sublayer ◽  
Factor H ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Boundary Layer Height ◽  
Wind Tunnel Data ◽  
Logarithmic Velocity Profile

This paper presents experimental wind-tunnel data that show the universal logarithmic velocity profile for zero-pressure-gradient turbulent boundary layer flows is valid for values of momentum-deficit Reynolds numbers Rθ as low as 600. However, for values of Rθ between 425 and 600, the von Ka´rma´n and additive constants vary and are shown to be functions of Rθ and shape factor H. Furthermore, the viscous sublayer in the range 425<Rθ<600 can no longer maintain its characteristically small size. It is forced to grow, due to viscous effects, into a super sublayer (6-9 percent of the boundary layer height) that greatly exceeds conventional predictions of sublayer heights.

Electrohydrodynamic stability: effects of charge relaxation at the interface of a liquid jet

1971 ◽  
Vol 48 (4) ◽  
pp. 815-827 ◽  
Author(s):  
D. A. Saville
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
The Other ◽  
Liquid Jet ◽  
Relaxation Phenomena ◽  
Viscous Effects ◽  
Axisymmetric Mode ◽  
Charge Relaxation ◽  
Small Fields ◽  
Interfacial Charge

The interactions between electrical tractions at the interface of a liquid jet and instability phenomena are studied with emphasis on effects due to interfacial charge relaxation. Charge relaxation causes the oscillatory growth of a perturbation. When viscous effects are small, small fields tend to decrease the growth rate of the axisymmetric mode, up to a point, and precipitate instability of the non-axisymmetric modes. Still larger field strengths increase the growth rates of asymmetric as well as axisymmetric modes. Instabilities characterized by highfrequency oscillations appear to persist even though the charge relaxation phenomena may be quite rapid. When, on the other hand, viscous effects predominate the only unstable disturbance form is the axisymmetric one, although the manner of growth may be oscillatory.

Simplified theory of the near-wall turbulent layer of Newtonian and drag-reducing fluids

1982 ◽  
Vol 119 ◽  
pp. 423-441 ◽  
Author(s):  
M. A. Goldshtik ◽  
V. V. Zametalin ◽  
V. N. Shtern
Keyword(s):  
Velocity Profile ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Outer Boundary ◽  
Viscous Sublayer ◽  
Viscous Layer ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
The Mean ◽  
Near Wall

We propose a simplified theory of a viscous layer in near-wall turbulent flow that determines the mean-velocity profile and integral characteristics of velocity fluctuations. The theory is based on the concepts resulting from the experimental data implying a relatively simple almost-ordered structure of fluctuations in close proximity to the wall. On the basis of data on the greatest contribution to transfer processes made by the part of the spectrum associated with the main size of the observed structures, the turbulent fluctuations are simulated by a three-dimensional running wave whose parameters are found from the problem solution. Mathematically the problem reduces to the solution of linearized Navier-Stokes equations. The no-slip condition is satisfied on the wall, whereas on the outer boundary of a viscous layer the conditions of smooth conjunction with the asymptotic shape of velocity and fluctuation-energy profiles resulting from the dimensional analysis are satisfied. The formulation of the problem is completed by the requirement of maximum curvature of the mean-velocity profile on the outer boundary applied from stability considerations.The solution of the problem does not require any quantitative empirical data, although the conditions of conjunction were formulated according to the well-known concepts obtained experimentally. As a result, the near-wall law for the averaged velocity has been calculated theoretically and is in good agreement with experiment, and the characteristic scales for fluctuations have also been determined. The developed theory is applied to turbulent-flow calculations in Maxwell and Oldroyd media. The elastic properties of fluids are shown to lead to near-wall region reconstruction and its associated drag reduction, as is the case in turbulent flows of dilute polymer solutions. This theory accounts for several features typical of the Toms effect, such as the threshold character of the effect and the decrease in the normal fluctuating velocity. The analysis of the near-wall Oldroyd fluid flow permits us to elucidate several new aspects of the drag-reduction effect. It has been established that the Toms effect does not always result in thickening of the viscous sublayer; on the contrary, the most intense drag reduction takes place without thickening in the viscous sublayer.

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