Viscous dissipation in steep capillary–gravity waves

1997 ◽  
Vol 344 ◽  
pp. 271-289 ◽  
Author(s):  
MICHAEL S. LONGUET-HIGGINS
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Steady Motion ◽  
Capillary Waves ◽  
Large Wave ◽  
Order Of Magnitude ◽  
Rate Of Decay ◽  
Rates Of Decay ◽  
Work Done ◽  
Viscous Stresses

Some simple but exact general expressions are derived for the viscous stresses required at the surface of irrotational capillary–gravity waves of periodic or solitary type on deep water in order to maintain them in steady motion. These expressions are applied to nonlinear capillary waves, and to capillary–gravity waves of solitary type on deep water. In the case of pure capillary waves some algebraic expressions are found for the work done by the surface stresses, from which it is possible to infer the viscous rate of decay of free, nonlinear capillary waves.Similar calculations are carried out for capillary–gravity waves of solitary type on deep water. It is shown that the limiting rate of decay of a solitary wave at low amplitudes is just twice that for linear, periodic waves. This is due to the spreading out of the wave envelope at low wave steepnesses. At large wave steepnesses the dissipation increases by an order of magnitude, owing to the sharply increased curvature in the wave troughs. The calculated rates of decay are in agreement with recent observations.

A CASCADE MODEL OF WAVE TURBULENCE WITH APPLICATIONS TO SURFACE GRAVITY AND CAPILLARY WAVES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 513-520 ◽  
Author(s):  
ROMAN E. GLAZMAN
Keyword(s):  
Gravity Waves ◽  
Wave Motion ◽  
Power Spectra ◽  
Fractal Dimensions ◽  
Capillary Waves ◽  
External Parameter ◽  
Wave Spectra ◽  
Large Wave ◽  
Mean Wind Speed ◽  
The Mean

A heuristic approach to the derivation of power spectra of wave motion is described and applied to capillary waves. The case of gravity waves studied earlier is briefly reviewed. In contrast to the previous studies, the nonlinearity of the wave motion is not required to be small, and the mean number of resonantly interacting wave harmonics is not limited to a smallest possible number (which is 4 for gravity waves on a deep fluid and 3 for capillary waves). The main external parameter of the problem is the input flux Q of the wave energy related to the mean wind velocity as QαU3. Depending on its value, wave spectra S(ω)αω−qand F(k) α k−p take various forms—from that corresponding to the weak-turbulence limit and to that corresponding to the saturated (Phillips’) wave spectra. Fractal dimensions of the sea surface are related to external factors, specifically to the mean wind speed. The theoretically predicted spectra are in qualitative agreement with the observations on capillary waves conducted in a large wave tank.

scholarly journals Effect of a surface shear layer on gravity and gravity–capillary waves of permanent form

1990 ◽  
Vol 216 ◽  
pp. 93-101 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Thin Sheet ◽  
Capillary Waves ◽  
Wave Crest ◽  
Wave Shape ◽  
Surface Shear ◽  
Wind Drift ◽  
Permanent Form ◽  
Drift Layer

Calculations are carried out of the shape of gravity and gravity–capillary waves on deep water in the presence of a thin sheet of uniform vorticity which models the effect of a wind drift layer. The dependence of the fluid speed at the wave crest is determined and compared for gravity waves with the theory of Banner & Phillips (1974). It is found that this theory underestimates the retardation due to drift and tendency to break. The retardation disappears when capillary forces are significant, but in this case it is found that there can be a significant alteration of the wave shape.

Measurement of high frequency capillary waves on steep gravity waves

1978 ◽  
Vol 86 (3) ◽  
pp. 401-413 ◽  
Author(s):  
John H. Chang ◽  
Richard N. Wagner ◽  
Henry C. Yuen
Keyword(s):  
Surface Tension ◽  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Deep Water ◽  
High Frequency ◽  
Qualitative Agreement ◽  
Capillary Wave ◽  
Capillary Waves ◽  
Good Qualitative Agreement

The properties of high frequency capillary waves generated by steep gravity waves on deep water have been measured with a high resolution laser optical slope gauge. The results have been compared with the steady theory of Longuet-Higgins (1963). Good qualitative agreement is obtained. However, the quantitative predictions of the capillary wave slopes cannot be verified by the data because the theory requires knowledge of an idealized quantity - the crest curvature of the gravity wave in the absence of surface tension - which cannot be measured experimentally.

Unsteady ripple generation on steep gravity–capillary waves

1999 ◽  
Vol 386 ◽  
pp. 281-304 ◽  
Author(s):  
LEI JIANG ◽  
HUAN-JAY LIN ◽  
WILLIAM W. SCHULTZ ◽  
MARC PERLIN
Keyword(s):  
Gravity Waves ◽  
Initial Conditions ◽  
Low Frequency ◽  
Inviscid Flow ◽  
Capillary Waves ◽  
Wave Crest ◽  
Wave Steepness ◽  
Large Wave ◽  
Time Marching ◽  
Characteristic Features

Parasitic ripple generation on short gravity waves (4 cm to 10 cm wavelengths) is examined using fully nonlinear computations and laboratory experiments. Time-marching simulations show sensitivity of the ripple steepness to initial conditions, in particular to the crest asymmetry. Significant crest fore–aft asymmetry and its unsteadiness enhance ripple generation at moderate wave steepness, e.g. ka between 0.15 and 0.20, a mechanism not discussed in previous studies. The maximum ripple steepness (in time) is found to increase monotonically with the underlying (low-frequency bandpass) wave steepness in our simulations. This is different from the sub- or super-critical ripple generation predicted by Longuet-Higgins (1995). Unsteadiness in the underlying gravity–capillary waves is shown to cause ripple modulation and an interesting ‘crest-shifting’ phenomenon – the gravity–capillary wave crest and the first ripple on the forward slope merge to form a new crest. Including boundary layer efects in the free-surface conditions extends some of the simulations at large wave amplitudes. However, the essential process of parasitic ripple generation is nonlinear interaction in an inviscid flow. Mechanically generated gravity–capillary waves demonstrate similar characteristic features of ripple generation and a strong correlation between ripple steepness and crest asymmetry.

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.

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

Steep gravity waves in water of arbitrary uniform depth

1977 ◽  
Vol 286 (1335) ◽  
pp. 183-230 ◽  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Perturbation Parameter ◽  
Intermediate Energy ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Accurate Calculation ◽  
Theoretical Developments ◽  
Deep Water Waves

Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

scholarly journals Emergence of Peregrine solitons in integrable turbulence of deep water gravity waves

2020 ◽  
Vol 5 (8) ◽  
Author(s):  
Guillaume Michel ◽  
Félicien Bonnefoy ◽  
Guillaume Ducrozet ◽  
Gaurav Prabhudesai ◽  
Annette Cazaubiel ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Deep Water

scholarly journals Integration of Rucio in Belle II

2021 ◽  
Vol 251 ◽  
pp. 02057
Author(s):  
Cédric Serfon ◽  
Ruslan Mashinistov ◽  
John Steven De Stefano ◽  
Michel Hernández Villanueva ◽  
Hironori Ito ◽  
...  
Keyword(s):  
Data Management ◽  
Smooth Transition ◽  
Distributed Data ◽  
Simulation Data ◽  
Migration Strategy ◽  
Distributed Data Management ◽  
Order Of Magnitude ◽  
Belle Ii ◽  
Work Done ◽  
Data Management Software

The Belle II experiment, which started taking physics data in April 2019, will multiply the volume of data currently stored on its nearly 30 storage elements worldwide by one order of magnitude to reach about 340 PB of data (raw and Monte Carlo simulation data) by the end of operations. To tackle this massive increase and to manage the data even after the end of the data taking, it was decided to move the Distributed Data Management software from a homegrown piece of software to a widely used Data Management solution in HEP and beyond : Rucio. This contribution describes the work done to integrate Rucio with Belle II distributed computing infrastructure as well as the migration strategy that was successfully performed to ensure a smooth transition.

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