scholarly journals On Growth Rate of Wind Waves: Impact of Short-Scale Breaking Modulations

2016 ◽  
Vol 46 (1) ◽  
pp. 349-360 ◽  
Author(s):  
Vladimir Kudryavtsev ◽  
Bertrand Chapron
Keyword(s):  
Growth Rate ◽  
Surface Pressure ◽  
Wind Waves ◽  
Breaking Waves ◽  
Generation Model ◽  
Wave Growth ◽  
Short Scale ◽  
Scale Breaking ◽  
Aerodynamic Roughness ◽  
Inner Region

AbstractThe wave generation model based on the rapid distortion concept significantly underestimates empirical values of the wave growth rate. As suggested before, inclusion of the aerodynamic roughness modulations effect on the amplitude of the slope-correlated surface pressure could potentially reconcile this model approach with observations. This study explores the role of short-scale breaking modulations to amplify the growth rate of modulating longer waves. As developed, airflow separations from modulated breaking waves result in strong modulations of the turbulent stress in the inner region of the modulating waves. In turn, this leads to amplifying the slope-correlated surface pressure anomalies. As evaluated, such a mechanism can be very efficient for enhancing the wind-wave growth rate by a factor of 2–3.

scholarly journals The Dynamical Coupling of Wind-Waves and Atmospheric Turbulence: A Review of Theoretical and Phenomenological Models

2021 ◽  
Author(s):  
Alex Ayet ◽  
Bertrand Chapron
Keyword(s):  
Phenomenological Models ◽  
Wind Wave ◽  
Numerical Models ◽  
Wind Waves ◽  
Breaking Waves ◽  
Multiple Time ◽  
Wave Growth ◽  
Breaking Wind Waves ◽  
Turbulent Coherent Structures ◽  
Dynamical Coupling

AbstractWhen wind blows over the ocean, short wind-waves (of wavelength smaller than 10 m) are generated, rapidly reaching an equilibrium with the overlying turbulence (at heights lower than 10 m). Understanding this equilibrium is key to many applications since it determines (i) air–sea fluxes of heat, momentum and gas, essential for numerical models; (ii) energy loss from wind to waves, which regulates how swell is generated and how energy is transferred to the ocean mixed layer and; (iii) the ocean surface roughness, visible from remote sensing measurements. Here we review phenomenological models describing this equilibrium: these models couple a turbulence kinetic energy and wave action budget through several wave-growth processes, including airflow separation events induced by breaking waves. Even though the models aim at reproducing measurements of air–sea fluxes and wave growth, some of the observed variability is still unexplained. Hence, after reviewing several state-of-the-art phenomenological models, we discuss recent numerical experiments in order to provide hints about future improvements. We suggest three main directions, which should be addressed both through dedicated experiments and theory: (i) a better quantification of the variability wind-wave growth and of the role played by the modulation of short and breaking wind-waves by long wind-waves; (ii) an improved understanding of the imprint of wind-waves on turbulent coherent structures and; (iii) a quantification of the interscale interactions for a realistic wind-wave sea, where wind-and-wave coupling processes coexist at multiple time and space scales.

The influence of wave breaking on the surface pressure distribution in wind—wave interactions

1990 ◽  
Vol 211 ◽  
pp. 463-495 ◽  
Author(s):  
Michael L. Banner
Keyword(s):  
Pressure Distribution ◽  
Surface Pressure ◽  
Wave Breaking ◽  
Wind Wave ◽  
Wind Waves ◽  
Breaking Waves ◽  
Wind Forcing ◽  
Wave Interactions ◽  
Form Drag ◽  
Surface Pressure Distribution

In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress.Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves.In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.

Linear dynamics of wind waves in coupled turbulent air—water flow. Part 1. Theory

1994 ◽  
Vol 271 ◽  
pp. 119-151 ◽  
Author(s):  
S. E. Belcher ◽  
J. A. Harris ◽  
R. L. Street
Keyword(s):  
Growth Rate ◽  
Water Flow ◽  
Water Waves ◽  
Wind Waves ◽  
Air Flow ◽  
Local Equilibrium ◽  
Outer Region ◽  
Wave Growth ◽  
Drift Current ◽  
The Waves

When air blows over water the wind exerts a stress at the interface thereby inducing in the water a sheared turbulent drift current. We present scaling arguments showing that, if a wind suddenly starts blowing, then the sheared drift current grows in depth on a timescale that is larger than the wave period, but smaller than a timescale for wave growth. This argument suggests that the drift current can influence growth of waves of wavelength λ that travel parallel to the wind at speed c.In narrow ‘inner’ regions either side of the interface, turbulence in the air and water flows is close to local equilibrium; whereas above and below, in ‘outer’ regions, the wave alters the turbulence through rapid distortion. The depth scale, la, of the inner region in the air flow increases with c/u*a (u*a is the unperturbed friction velocity in the wind). And so we classify the flow into different regimes according to the ratio la/λ. We show that different turbulence models are appropriate for the different flow regimes.When (u*a + c)/UB(λ) [Lt ] 1 (UB(z) is the unperturbed wind speed) la is much smaller than λ. In this limit, asymptotic solutions are constructed for the fully coupled turbulent flows in the air and water, thereby extending previous analyses of flow over irrotational water waves. The solutions show that, as in calculations of flow over irrotational waves, the air flow is asymmetrically displaced around the wave by a non-separated sheltering effect, which tends to make the waves grow. But coupling the air flow perturbations to the turbulent flow in the water reduces the growth rate of the waves by a factor of about two. This reduction is caused by two distinct mechanisms. Firstly, wave growth is inhibited because the turbulent water flow is also asymmetrically displaced around the wave by non-separated sheltering. According to our model, this first effect is numerically small, but much larger erroneous values can be obtained if the rapid-distortion mechanism is not accounted for in the outer region of the water flow. (For example, we show that if the mixing-length model is used in the outer region all waves decay!) Secondly, non-separated sheltering in the air flow (and hence the wave growth rate) is reduced by the additional perturbations needed to satisfy the boundary condition that shear stress is continuous across the interface.

scholarly journals Taxation of Land and Economic Growth

Economies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 61
Author(s):  
Shulu Che ◽  
Ronald Ravinesh Kumar ◽  
Peter J. Stauvermann
Keyword(s):  
Economic Growth ◽  
Growth Rate ◽  
Generation Model ◽  
Young Generation ◽  
Overlapping Generation ◽  
Land Rents ◽  
Stamp Duty

In this paper, we theoretically analyze the effects of three types of land taxes on economic growth using an overlapping generation model in which land can be used for production or consumption (housing) purposes. Based on the analyses in which land is used as a factor of production, we can confirm that the taxation of land will lead to an increase in the growth rate of the economy. Particularly, we show that the introduction of a tax on land rents, a tax on the value of land or a stamp duty will cause the net price of land to decline. Further, we show that the nationalization of land and the redistribution of the land rents to the young generation will maximize the growth rate of the economy.

scholarly journals Suppression of Wind Ripples and Microwave Backscattering Due to Turbulence Generated by Breaking Surface Waves

2020 ◽  
Vol 12 (21) ◽  
pp. 3618
Author(s):  
Stanislav Ermakov ◽  
Vladimir Dobrokhotov ◽  
Irina Sergievskaya ◽  
Ivan Kapustin
Keyword(s):  
Remote Sensing ◽  
Surface Waves ◽  
Wave Breaking ◽  
Wave Train ◽  
Wind Waves ◽  
Breaking Waves ◽  
Doppler Spectrum ◽  
Strong Wave ◽  
Wave Maker ◽  
Radar Backscattering

The role of wave breaking in microwave backscattering from the sea surface is a problem of great importance for the development of theories and methods on ocean remote sensing, in particular for oil spill remote sensing. Recently it has been shown that microwave radar return is determined by both Bragg and non-Bragg (non-polarized) scattering mechanisms and some evidence has been given that the latter is associated with wave breaking, in particular, with strong breaking such as spilling or plunging. However, our understanding of mechanisms of the action of strong wave breaking on small-scale wind waves (ripples) and thus on the radar return is still insufficient. In this paper an effect of suppression of radar backscattering after strong wave breaking has been revealed experimentally and has been attributed to the wind ripple suppression due to turbulence generated by strong wave breaking. The experiments were carried out in a wind wave tank where a frequency modulated wave train of intense meter-decimeter-scale surface waves was generated by a mechanical wave maker. The wave train was compressed according to the gravity wave dispersion relation (“dispersive focusing”) into a short-wave packet at a given distance from the wave maker. Strong wave breaking with wave crest overturning (spilling) occurred for one or two highest waves in the packet. Short decimeter-centimeter-scale wind waves were generated at gentle winds, simultaneously with the long breaking waves. A Ka-band scatterometer was used to study microwave backscattering from the surface waves in the tank. The scatterometer looking at the area of wave breaking was mounted over the tank at a height of about 1 m above the mean water level, the incidence angle of the microwave radiation was about 50 degrees. It has been obtained that the radar return in the presence of short wind waves is characterized by the radar Doppler spectrum with a peak roughly centered in the vicinity of Bragg wave frequencies. The radar return was strongly enhanced in a wide frequency range of the radar Doppler spectrum when a packet of long breaking waves arrived at the area irradiated by the radar. After the passage of breaking waves, the radar return strongly dropped and then slowly recovered to the initial level. Measurements of velocities in the upper water layer have confirmed that the attenuation of radar backscattering after wave breaking is due to suppression of short wind waves by turbulence generated in the breaking zone. A physical analysis of the effect has been presented.

Harbour oscillations generated by shear flow

1995 ◽  
Vol 282 ◽  
pp. 203-217 ◽  
Author(s):  
A. L. Fabrikant
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Wave Reflection ◽  
Wind Waves ◽  
Vortex Sheet ◽  
Flow Speed ◽  
Natural Mode ◽  
Exciting Forces ◽  
Wavenumber Spectrum ◽  
Harbour Oscillations

A new mechanism that could be responsible for excitation of long-period oscillations in partially enclosed harbours is discussed. This mechanism is based on the interaction between a shear flow and the harbour-basin natural mode and does not suppose any external exciting forces caused by wind waves, tsunami, etc. The growth rate of harbour oscillations is found in terms of a plane-wave reflection coefficient integrated on the wavenumber spectrum of the oscillating outflow field near the harbour entrance. Analytical considerations for simple shear flows (vortex sheet and jet) show that the growth rate changes its sign depending on the ratio of oscillation frequency to flow speed.

scholarly journals Miles Theory Revisited with Constant Vorticity in Water of Infinite Depth

2020 ◽  
Vol 8 (8) ◽  
pp. 623
Author(s):  
Christian Kharif ◽  
Malek Abid
Keyword(s):  
Growth Rate ◽  
Wave Energy ◽  
Wind Wave ◽  
Wind Waves ◽  
Infinite Depth ◽  
Energy Growth ◽  
Constant Vorticity ◽  
Generation Of Wind Waves ◽  
Amplitude Growth

The generation of wind waves at the surface of a pre-existing underlying vertically sheared water flow of constant vorticity is considered. Emphasis is put on the role of the vorticity in water on wind-wave generation. The amplitude growth rate increases with the vorticity except for quite old waves. A limit to the wave energy growth is found in the case of negative vorticity, corresponding to the vanishing of the growth rate.

Comparison of quasi-linear predictions with a computer simulation of whistler waves in unstable plasmas

1974 ◽  
Vol 11 (3) ◽  
pp. 397-401 ◽  
Author(s):  
S. Cuperman ◽  
L. R. Lyons
Keyword(s):  
Growth Rate ◽  
Computer Simulation ◽  
Distribution Function ◽  
Mode Coupling ◽  
Simulation Experiment ◽  
Electron Distribution Function ◽  
Linear Wave ◽  
Wave Growth ◽  
Whistler Mode Waves ◽  
Computer Simulation Experiment

The quasi-linear concept of plateau formation along resonant diffusion surfaces is compared with the time evolution of the electron distribution function during a computer simulation experiment of whistler-mode waves in unstable plasmas. It is found that, as the wave intensities grow, plateau formation does indeed occur, with the distribution function becoming constant along diffusion surfaces at the time when wave intensities maximize. Following the formation of the plateaus, both the wave intensities and the slope of the distribution function along diffusion surfaces oscillate in a manner suggesting msh;mode coupling. Tbe slope of the distribution function along diffusion surfaces, which controls the linear wave growth rate, also gives good predictions of the sign of the actual wave growth rate during the experiment.

scholarly journals Effects of current on wind waves in strong winds

Ocean Science ◽  
2020 ◽  
Vol 16 (5) ◽  
pp. 1033-1045
Author(s):  
Naohisa Takagaki ◽  
Naoya Suzuki ◽  
Yuliya Troitskaya ◽  
Chiaki Tanaka ◽  
Alexander Kandaurov ◽  
...  
Keyword(s):  
Phase Velocity ◽  
Doppler Shift ◽  
Wind Waves ◽  
Surface Current ◽  
Breaking Waves ◽  
Wave Frequency ◽  
High Wind ◽  
Adequate Model ◽  
Wind Speeds ◽  
Waves And Currents

Abstract. It is important to investigate the effects of current on wind waves, called the Doppler shift, at both normal and extremely high wind speeds. Three different types of wind-wave tanks along with a fan and pump are used to demonstrate wind waves and currents in laboratories at Kyoto University, Japan, Kindai University, Japan, and the Institute of Applied Physics, Russian Academy of Sciences, Russia. Profiles of the wind and current velocities and the water-level fluctuation are measured. The wave frequency, wavelength, and phase velocity of the significant waves are calculated, and the water velocities at the water surface and in the bulk of the water are also estimated by the current distribution. The study investigated 27 cases with measurements of winds, waves, and currents at wind speeds ranging from 7 to 67 m s−1. At normal wind speeds under 30 m s−1, wave frequency, wavelength, and phase velocity depend on wind speed and fetch. The effect of the Doppler shift is confirmed at normal wind speeds; i.e., the significant waves are accelerated by the surface current. The phase velocity can be represented as the sum of the surface current and artificial phase velocity, which is estimated by the dispersion relation of the deepwater waves. At extremely high wind speeds over 30 m s−1, a similar Doppler shift is observed as under the conditions of normal wind speeds. This suggests that the Doppler shift is an adequate model for representing the acceleration of wind waves by current, not only for wind waves at normal wind speeds but also for those with intensive breaking at extremely high wind speeds. A weakly nonlinear model of surface waves at a shear flow is developed. It is shown that it describes dispersion properties well not only for small-amplitude waves but also strongly nonlinear and even breaking waves, which are typical for extreme wind conditions (over 30 m s−1).

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