Laboratory measurements of modulation of short-wave slopes by long surface waves

1991 ◽  
Vol 233 ◽  
pp. 389-404 ◽  
Author(s):  
Sarah J. Miller ◽  
Omar H. Shemdin ◽  
Michael S. Longuet-Higgins
Keyword(s):  
Surface Waves ◽  
Gravity Waves ◽  
Wind Waves ◽  
Short Wave ◽  
Wave Interactions ◽  
Wind Speeds ◽  
Short Waves ◽  
Hydrodynamic Modulation ◽  
Work Done ◽  
Good Agreement

Hydrodynamic modulation of wind waves by long surface waves in a wave tank is investigated, at wind speeds ranging from 1.5 to 10 m s−1. The results are compared with the linear, non-dissipative, theory of Longuet-Higgins & Stewart (1960), which describes the modulation of a group of short gravity waves due to straining of the surface by currents produced by the orbital motions of the long wave, and work done against the radiation stresses of the short waves. In most cases the theory is in good agreement with the experimental results when the short waves are not too steep, and the rate of growth due to the wind is relatively small. At the higher wind speeds, the effects of wind-wave growth, dissipation and wave-wave interactions are dominant.

Radiation of short waves from the resonantly excited capillary–gravity waves

2016 ◽  
Vol 810 ◽  
pp. 5-24 ◽  
Author(s):  
M. Hirata ◽  
S. Okino ◽  
H. Hanazaki
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Wave Pattern ◽  
Short Wave ◽  
Bond Number ◽  
Linear Wave ◽  
Cnoidal Wave ◽  
Short Waves ◽  
Long Wave

Capillary–gravity waves resonantly excited by an obstacle (Froude number: $Fr=1$) are investigated by the numerical solution of the Euler equations. The radiation of short waves from the long nonlinear waves is observed when the capillary effects are weak (Bond number: $Bo<1/3$). The upstream-advancing solitary wave radiates a short linear wave whose phase velocity is equal to the solitary waves and group velocity is faster than the solitary wave (soliton radiation). Therefore, the short wave is observed upstream of the foremost solitary wave. The downstream cnoidal wave also radiates a short wave which propagates upstream in the depression region between the obstacle and the cnoidal wave. The short wave interacts with the long wave above the obstacle, and generates a second short wave which propagates downstream. These generation processes will be repeated, and the number of wavenumber components in the depression region increases with time to generate a complicated wave pattern. The upstream soliton radiation can be predicted qualitatively by the fifth-order forced Korteweg–de Vries equation, but the equation overestimates the wavelength since it is based on a long-wave approximation. At a large Bond number of $Bo=2/3$, the wave pattern has the rotation symmetry against the pattern at $Bo=0$, and the depression solitary waves propagate downstream.

Can swell increase the number of freak waves in a wind sea?

2010 ◽  
Vol 650 ◽  
pp. 57-79 ◽  
Author(s):  
ODIN GRAMSTAD ◽  
KARSTEN TRULSEN
Keyword(s):  
Nonlinear Evolution ◽  
Wind Waves ◽  
Short Wave ◽  
Freak Waves ◽  
Freak Wave ◽  
Short Waves ◽  
Term Evolution ◽  
Wind Sea ◽  
Modified Equation

The effect of a swell on the statistical distribution of a directional short-wave field is investigated. Starting from Zakharov's spectral formulation, we derive a new modified nonlinear Schrödinger equation appropriate for the nonlinear evolution of a narrow-banded spectrum of short waves influenced by a swell. The swell-modified equation is solved analytically to yield an extended version of the result of Longuet-Higgins & Stewart (J. Fluid Mech., vol. 8, no. 4, 1960, pp. 565–583) for the modulation of a short wave riding on a longer wave. Numerical Monte Carlo simulations of the long-term evolution of a spectrum of short waves in the presence of a monochromatic swell are employed to extract statistical distributions of freak waves among the short waves. We find evidence that a realistic short-crested wind sea can on average experience a small increase in freak wave probability because of a swell provided the swell is not orthogonal to the wind waves. For orthogonal swell and wind waves we find evidence that there is almost no significant change in the probability of freak waves in the wind sea. If the short waves are unrealistically long crested, such that the Benjamin–Feir index serves as indicator for freak waves (Gramstad & Trulsen, J. Fluid Mech., vol. 582, 2007, pp. 463–472), it appears that the swell has much smaller relative influence on the probability of freak waves than in the short-crested case.

Capillary–gravity and capillary waves generated in a wind wave tank: observations and theories

1995 ◽  
Vol 289 ◽  
pp. 51-82 ◽  
Author(s):  
Xin Zhang
Keyword(s):  
Power Law ◽  
Gravity Waves ◽  
Water Surface ◽  
Wind Wave ◽  
Wind Waves ◽  
Capillary Waves ◽  
Fourth Power ◽  
Two Dimensional ◽  
Short Waves ◽  
Surface Gradient

Short water surface waves generated by wind in a water tunnel have been measured by an optical technique that provides a synoptic picture of the water surface gradient over an area of water surface (Zhang & Cox 1994). These images of the surface gradient can be integrated to recover the shape of the water surface and find the two-dimensional wavenumber spectrum. Waveforms and two-dimensional structures of short wind waves have many interesting features: short and steep waves featuring sharp troughs and flat crests are very commonly seen and most of the short waves are far less steep than the limiting wave forms; waveforms that resemble capillary–gravity solitons are observed with a close match to the form theoretically predicted for potential flows (Longuet-Higgins 1989); capillaries are mainly found as parasitics on the downwind faces of gravity waves, and the longest wavelengths of those parasitic capillaries found are less than 1 cm; the phenomenon of capillary blockage (Phillips 1981) on dispersive freely travelling short waves is also observed. The spectra of short waves generated by low winds show a characteristic dip at the transition wavenumber between the gravity and capillary regimes, and the dip becomes filled in as the wind increases. The spectral cut-off at high wavenumbers shows a power law behaviour with an exponent of about minus four. The wavenumber of the transition from the dip to the cut-off is not sensitive to the change of wind speed. The minus fourth power law of the extreme capillary wind wave spectrum can be explained through a model of energy balances. The concept of an equilibrium spectrum is still useful. It is shown that the dip in the spectrum of capillary–gravity waves is a result of blockage of both capillary–gravity wind waves and parasitic capillary waves.

scholarly journals Interction of a short-wave field with a dominant long wave in deep water: derivation form Zakharov's spectral formulation

1988 ◽  
Vol 29 (4) ◽  
pp. 430-439 ◽  
Author(s):  
A. D. D. Craik
Keyword(s):  
Wave Packet ◽  
Wave Field ◽  
Gravity Waves ◽  
Deep Water ◽  
Short Wave ◽  
Wave Action ◽  
Leading Order ◽  
Order Interaction ◽  
Short Waves ◽  
Long Wave

AbstractThe leading-order interaction of short gravity waves with a dominant long-wave swell is calculated by means of Zakharov's [7] spectral formulation. Results are obtained both for a discrete train of short waves and for a localised wave packet comprising a spectrum of short waves.The results for a discrete wavetrain agree with previous work of Longuet-Higgins & Stewart [5], and general agreement is found with parallel work of Grimshaw [4] which employed a very different wave-action approach.

Oblique wind waves generated by the instability of wind blowing over water

1996 ◽  
Vol 316 ◽  
pp. 163-172 ◽  
Author(s):  
L. C. Morland
Keyword(s):  
Gravity Waves ◽  
Wind Waves ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Mean Flow ◽  
Oblique Angle ◽  
Wind Speeds ◽  
The Mean ◽  
Directional Distributions ◽  
The Waves

The growth rates of gravity waves are computed from linear, inviscid stability theory for wind velocity profiles that are representative of the mean flow in a turbulent boundary layer. The energy transfer to the waves is largely concentrated in an angle (to the wind) interval that broadens with increasing wind speed and narrows with increasing wavelength. At sufficiently high wind speeds and sufficiently short wavelengths, the waves of maximum growth rate propagate at an oblique angle to the wind. The connection with bimodal directional distributions of observed spectra is discussed.

On the kinematics of short waves in the presence of surface flows of larger scales

1995 ◽  
Vol 298 ◽  
pp. 249-269 ◽  
Author(s):  
A. Ramamonjiarisoa
Keyword(s):  
Surface Waves ◽  
Resonance Condition ◽  
Mathieu Equation ◽  
Short Wave ◽  
Surface Flow ◽  
Numerical Resolution ◽  
Short Waves ◽  
Physical Context ◽  
Long Wave ◽  
General Physical

When the resonance condition is satisfied, i.e. that the local group velocity of short surface waves matches the local velocity associated with a larger-scale surface flow, it is known that the short waves are reflected or trapped by the flow. A typical example is the case of short surface waves propagating on long surface waves. By direct numerical resolution of the kinematic equations, some aspects of the reflection or trapping are first examined. Next, the effects of a second long wave on the trajectory of the short waves are considered. It is found that the trajectory is strongly distorted in general. Reflection still occurs, having a larger effect on the variation of the shortwave wavenumber than when only a single long wave is present. The entrapment becomes more sporadic. At short time intervals, a forced Mathieu equation is found to govern the short-wave development. This leads to a discussion on a more general physical context.

An instability of internal gravity waves

1972 ◽  
Vol 52 (2) ◽  
pp. 393-399 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Long Waves ◽  
Wave Number ◽  
Short Waves

When water is slightly stratified, internal gravity waves are considerably shorter than surface waves of comparable frequency. Here, this fact is exploited in demonstrating that an internal wave is unstable when it forms part of a resonant triad with a surface wave and another internal wave whose wave number is approximately equal to that of the original internal wave. It is suggested that in a system where there are two classes of waves of comparable frequencies but greatly differing wavelengths the short waves may be expected to generate long waves by this mechanism.

Laboratory investigation of the effect of sea foam on the scattering of microwave radiation

2020 ◽  
Author(s):  
Georgy Baydakov ◽  
Ermakova Olga ◽  
Vdovin Maxim ◽  
Sergeev Daniil ◽  
Troitskaya Yuliya
Keyword(s):  
Wind Speed ◽  
Surface Waves ◽  
Water Surface ◽  
Wind Waves ◽  
Short Wave ◽  
Doppler Spectrum ◽  
Momentum Exchange ◽  
High Frequency Region ◽  
Wave Flume ◽  
The Impact

&lt;p&gt;This paper models the impact of the presence of foam on the short-wave component of surface waves and momentum exchange in the atmospheric boundary layer at high winds. First, physical experiments were carried out in a wind-wave flume in which foam can be artificially produced at the water surface. Tests were conducted under high wind-speed conditions where equivalent 10-m wind speed, U10, ranged 12&amp;#8211;38 m/s, with measurements made of the airflow parameters, the frequency-wavenumber spectra of the surface waves, the foam coverage of the water surface, and the distribution of the foam bubbles.&lt;/p&gt;&lt;p&gt;Microwave measurements were performed using a coherent Doppler X-band scatterometer with a wavelength of 3.2 cm and a sequential reception of linearly polarized radiation. It was shown that the presence of foam reduces the NRCS of the agitated water surface. Foam formations are concentrated mainly on the ridges and front slopes of wind waves, which make the main contribution to the scattering of radio waves. This may explain the effect of reducing the total NRCS: foam, which has less reflective properties, masks the main diffusers on the water surface. The second mechanism is associated with the effect of foam on short waves, by analogy with surfactant films.&lt;/p&gt;&lt;p&gt;The effect of foam on the shape of the Doppler spectrum of a microwave signal scattered by the water surface was investigated. In the case of weak wind, the presence of foam on the surface leads to a decrease in the short-wave part of the spectrum of surface waves and, as a result, to a decrease in the scattered signal. In addition, a mirror component appears in the Doppler spectrum corresponding to the fundamental frequency of the wave. In the case of a stronger wind, the grouping of additional scatterers (foam) on the crests of the waves leads to a shift of the Doppler spectra to the high-frequency region.&lt;/p&gt;&lt;p&gt;The work was supported by the RFBR (grants 18-35-20068, 19-05-00366, 19-05-00249) and the&amp;#160;RF&amp;#160;President&amp;#8217;s Grant for Young Scientists (MK-144.2019.5).&lt;/p&gt;

scholarly journals Five-Wave Resonances in Deep Water Gravity Waves: Integrability, Numerical Simulations and Experiments

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 205
Author(s):  
Dan Lucas ◽  
Marc Perlin ◽  
Dian-Yong Liu ◽  
Shane Walsh ◽  
Rossen Ivanov ◽  
...  
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Deep Water ◽  
Plane Waves ◽  
Surface Elevation ◽  
Wave Interactions ◽  
Frequency Space ◽  
Target Mode ◽  
The Hilbert Transform

In this work we consider the problem of finding the simplest arrangement of resonant deep-water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wavevectors K1+K2=K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wavepackets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction in a symmetric configuration. Numerical simulations of the governing equations in natural variables using pseudospectral methods require the inclusion of up to 6-wave interactions, which imposes a strong dealiasing cut-off in order to properly resolve the evolving waves. We study the resonance numerically by looking at a target mode in the base triad and showing that the energy transfer to this mode is more efficient when the system is close to satisfying the resonant conditions. We first look at encountering plane waves with base frequencies in the range 1.32–2.35 Hz and steepnesses below 0.1, and show that the time evolution of the target mode’s energy is dramatically changed at the resonance. We then look at a scenario that is closer to experiments: Encountering wavepackets in a 400-m long numerical tank, where the interaction time is reduced with respect to the plane-wave case but the resonance is still observed; by mimicking a probe measurement of surface elevation we obtain efficiencies of up to 10% in frequency space after including near-resonant contributions. Finally, we perform preliminary experiments of encountering wavepackets in a 35-m long tank, which seem to show that the resonance exists physically. The measured efficiencies via probe measurements of surface elevation are relatively small, indicating that a finer search is needed along with longer wave flumes with much larger amplitudes and lower frequency waves. A further analysis of phases generated from probe data via the analytic signal approach (using the Hilbert transform) shows a strong triad phase synchronisation at the resonance, thus providing independent experimental evidence of the resonance.

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