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.

Experimental study of the initial stages of wind waves' spatial evolution

2011 ◽  
Vol 681 ◽  
pp. 462-498 ◽  
Author(s):  
DAN LIBERZON ◽  
LEV SHEMER
Keyword(s):  
Energy Transfer ◽  
Growth Rates ◽  
Water Surface ◽  
Wind Waves ◽  
Pressure Fluctuations ◽  
Theoretical Models ◽  
Small Scale ◽  
Wave Flume ◽  
Spatial Growth ◽  
The Mean

Despite a significant progress and numerous publications over the last few decades a comprehensive understanding of the process of waves' excitation by wind still has not been achieved. The main goal of the present work was to provide as comprehensive as possible set of experimental data that can be quantitatively compared with theoretical models. Measurements at various air flow rates and at numerous fetches were carried out in a small scale, closed-loop, 5 m long wind wave flume. Mean airflow velocity and fluctuations of the static pressure were measured at 38 vertical locations above the mean water surface simultaneously with determination of instantaneous water surface elevations by wave gauges. Instantaneous fluctuations of two velocity components were recorded for all vertical locations at a single fetch. The water surface drift velocity was determined by the particle tracking velocimetry (PTV) method. Evaluation of spatial growth rates of waves at various frequencies was performed using wave gauge records at various fetches. Phase relations between various signals were established by cross-spectral analysis. Waves' celerities and pressure fluctuation phase lags relative to the surface elevation were determined. Pressure values at the water surface were determined by extrapolating the measured vertical profile of pressure fluctuations to the mean water level and used to calculate the form drag and consequently the energy transfer rates from wind to waves. Directly obtained spatial growth rates were compared with those obtained from energy transfer calculations, as well as with previously available data.

On the wind-induced growth of slow water waves of finite steepness

2008 ◽  
Vol 608 ◽  
pp. 243-274 ◽  
Author(s):  
WILLIAM L. PEIRSON ◽  
ANDREW W. GARCIA
Keyword(s):  
Tangential Stress ◽  
Growth Rates ◽  
Water Waves ◽  
Dynamic Range ◽  
Wind Waves ◽  
Laboratory Data ◽  
Quantitative Agreement ◽  
Wave Drag ◽  
Wave Growth ◽  
Wave Range

Determining characteristic growth rates for water waves travelling more slowly than the wind has continued to be a key unresolved problem of air–sea interaction for over half a century. Analysis of previously reported and recently acquired laboratory wave data shows a systematic decline in normalized wave growth with increasing mean wave steepness that has not previously been identified. The normalized growth dynamic range is comparable with previously observed scatter amongst other laboratory data gathered in the slow wave range. Strong normalized growth rates are observed at low wave steepnesses, implying an efficient wave-coherent tangential stress contribution. Data obtained during this study show quantitative agreement with the predictions of others of the interactions between short wind waves and the longer lower-frequency waves. Measured normalized wave growth rates are consistent with numerically predicted growth due to wave drag augmented by significant wave-coherent tangential stress.

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.

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.

Some Characteristics of High Waves in Closed Channels Approaching Kelvin-Helmholtz Instability

1977 ◽  
Vol 99 (2) ◽  
pp. 339-346 ◽  
Author(s):  
E. Kordyban
Keyword(s):  
Surface Pressure ◽  
Water Waves ◽  
Internal Flow ◽  
Flow Patterns ◽  
Pressure Variation ◽  
Helmholtz Instability ◽  
Wave Celerity ◽  
Theoretical Considerations ◽  
Wave Shapes

The characteristics of water waves produced by flowing air in closed channels were studied to uncover the effects of surface pressure variation. From theoretical considerations, it is proposed that the point of onset of the Kelvin-Helmholtz instability for such waves may be found from 1.35ρaρwVc2ghc=1 Photographs of internal flow patterns and wave shapes confirm the occurrence of this instability, but the theoretically predicted reduction in wave celerity does not occur. The wave celerity for high waves was found to be predictable by the formula C=0.191gLtanh2πhwL1/2 The measured height to length ratios for the highest observed waves are of the order of 0.1.

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.

scholarly journals Two-dimensional modulation instability of wind waves

2019 ◽  
Vol 5 (4) ◽  
pp. 413-417 ◽  
Author(s):  
Roger Grimshaw
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Water Waves ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Wind Waves ◽  
Nonlinear Schrodinger Equation ◽  
Wind Forcing ◽  
Nonlinear Schrödinger ◽  
Peregrine Breather

Abstract It is widely known that deep-water waves are modulationally unstable and that this can be modelled by a nonlinear Schrödinger equation. In this paper, we extend the previous studies of the effect of wind forcing on this instability to water waves in finite depth and in two horizontal space dimensions. The principal finding is that the instability is enhanced and becomes super-exponential and that the domain of instability in the modulation wavenumber space is enlarged. Since the outcome of modulation instability is expected to be the generation of rogue waves, represented within the framework of the nonlinear Schrödinger equation as a Peregrine breather, we also examine the effect of wind forcing on a Peregrine breather. We find that the breather amplitude will grow at twice the rate of a linear instability.

Experimental study of the stability of boundary-layer flow along a heated, inclined plate

1998 ◽  
Vol 367 ◽  
pp. 1-25 ◽  
Author(s):  
E. J. ZUERCHER ◽  
J. W. JACOBS ◽  
C. F. CHEN
Keyword(s):  
Boundary Layer ◽  
Growth Rates ◽  
Growth Curves ◽  
Leading Edge ◽  
Heated Plate ◽  
Inclined Plate ◽  
Double Pass ◽  
Longitudinal Vortices ◽  
Spatial Growth ◽  
Layer Flow

Experiments are conducted to study the longitudinal vortices that develop in the boundary layer on the upper surface of an inclined, heated plate. An isothermal plate in water is inclined at angles ranging from 20 to 60 degrees (from the vertical) while the temperature difference is varied from 2 to 23°C. A double-pass Schlieren system is used to visualize the vortices and particle image velocimetry (PIV) is used to measure velocities. In addition, a unique method is developed such that both the Schlieren visualization and PIV can be performed simultaneously. The wavelengths of the vortices and the critical modified Reynolds numbers (R˜) for the onset, merging, and breakup of the vortices are determined from Schlieren images for Pr=5.8. The critical values for R˜ and the critical wavelengths are compared to results of previous experiments and stability analyses. The spatial growth rates of vortices are determined by using the PIV measurements to determine how the circulation in the vortices grows with distance from the leading edge. This is the first time that the growth rate of the vortices have been found using velocity measurements. These spatial growth rates are compared to the results of Iyer & Kelly (1974) and found to be in general agreement. By defining a suitable circulation threshold, the critical R˜ for the onset of the vortices can be found from the growth curves.

scholarly journals Generation of Gravity-Capillary Wind Waves by Instability of a Coupled Shear-Flow

2022 ◽  
Vol 10 (1) ◽  
pp. 46
Author(s):  
Malek Abid ◽  
Christian Kharif ◽  
Hung-Chu Hsu ◽  
Yang-Yih Chen
Keyword(s):  
Velocity Profile ◽  
Unstable Mode ◽  
Wind Waves ◽  
Surface Current ◽  
Viscous Flows ◽  
Shear Velocity ◽  
Threshold Value ◽  
Surface Velocity ◽  
Mixing Length ◽  
Flow Turbulence

The theory of surface wave generation, in viscous flows, is modified by replacing the linear-logarithmic shear velocity profile, in the air, with a model which links smoothly the linear and logarithmic layers through the buffer layer. This profile includes the effects of air flow turbulence using a damped mixing-length model. In the water, an exponential shear velocity profile is used. It is shown that this modified and coupled shear-velocity profile gives a better agreement with experimental data than the coupled linear-logarithmic, non smooth profile, (in the air)–exponential profile (in the water), widely used in the literature. We also give new insights on retrograde modes that are Doppler shifted by the surface velocity at the air-sea interface, namely on the threshold value of the surface current for the occurrence of a second unstable mode.

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