Radiation-Pressure-Induced Capillary Waves
Capillary waves are often observed on the surface of acoustically levitated drops, bubbles and shells.
parameter dependences acoustic energy into wave mo↗
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Laser probe for measuring 2-D wave slope spectra of ocean capillary waves
A laser-optical instrument for use in determining the two-dimensional wave-slope spectrum of ocean capillary waves is described. The instrument measures up to a 35-deg tip angle of the surface normal by measuring the position of a refracted laser beam directed vertically upward through a water surface. A telescope, a continuous two-dimensional Schottky barrier photodiode, and a pair of analog dividers render the signals independent of water height and insensitive to laser-beam intensity fluctuations. Calibration is performed entirely in the laboratory before field use. Sample records and wave-slope spectra are shown for one-dimensional wave-tank tests and for two-dimensional ocean tests. These are presented along with comparison spectra for calm and choppy water conditions. A mechanical wave follower was used to adjust the instrument position in the presence of large ocean swell and tides.
Palm, C. S.↗
A Cascade Model of Wave Turbulence with Applications to Surface Gravity and Capillary Waves
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 contract 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. Depending on its value, wave spectra take various forms---from that corresponding to the weak-turbulence limit to that corresponding to the saturated (Phillips') wave spectra...
Glazman, Roman E.↗
Finite Amplitude Capillary Waves in a Liquid Drop
A theoretical study of finite amplitude waves in an approximately spherical liquid drop subject to surface tension forces is presented.
finite amplitude waves Capillary Waves Nonlinear I↗
Effect of capillary waves on surface tension
The present study is concerned with the effect which a cutting off of the capillary waves has on surface tension, taking into account a calculation based on capillary-wave theory. For simplicity, three-dimensional systems are considered, and capillary-wave theory is used to calculate sigma-k, the surface tension of an interface where only those modes with at least one wave-vector component greater than k are allowed. Attention is given to a review of capillary-wave theory, the calculation of surface tensions, a determination of the range of validity of capillary-wave theory, and some numerical examples. The quantitative behavior of sigma-k and its relation to the surface tension of a finite-size system are considered. The most surprising result is that sigma-k can be significantly larger than the unconstrained surface tension.
Kayser, R. F.↗
Square patterns and secondary instabilities in driven capillary waves
Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from traveling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.
Milner, S. T.↗
Water Surface Currents, Short Gravity-Capillary Waves and Radar Backscatter
Despite their importance for air-sea interaction and microwave remote sensing of the ocean surface, intrinsic properties of short gravity-capillary waves are not well established. This is largely due to water surface currents and their effects on the direct measurements of wave parameters conducted at a fixed point. Frequencies of small scale waves propagating on a surface which itself is in motion, are subject to Doppler shifts. Hence, the high frequency tail of the wave spectra obtained from such temporal observations is smeared. Conversion of this smeared measured-frequency spectra to intrinsic-frequency (or wavenumber) spectra requires corrections for the Doppler shifts. Such attempts in the past have not been very successful in particular when field data were used. This becomes evident if the amplitude modulation of short waves by underlying long waves is considered. Microwave radar studies show that the amplitude of a short wave component attains its maximum value near the crests and its minimum in the troughs of the long waves. Doppler-shifted wave data yield similar results but much larger in modulation magnitude, as expected. In general, Doppler shift corrections reduce the modulation magnitude. Overcorrection may result in a negligible modulation or even in a strong modulation with the maximum amplitude in the wave troughs. The latter situation is clearly contradictory to our visual observations as well as the radar results and imply that the advection by currents is overestimated. In this study, a differential-advection approach is used in which small scale waves are advected by the currents evaluated not at the free surface, but at a depth proportional to their wavelengths. Applicability of this approach is verified by the excellent agreement in phase and magnitude of short-wave modulation between results based on radar and on wave-gauge measurements conducted on a lake.
Atakturk, Serhad S.↗
An air/sea flux model including the effects of capillary waves
An improved model of the air/sea interface is developed. The improvements consist in including the effect of capillary (surface tension) waves on the tropical surface fluxes and the consideration of the sea state, both of which increase the magnitude of tropical surface fluxes. Changes in surface stress are most significant in the low wind-speed regions, which include the areas where westerly bursts occur. It is shown that the changes, from the regular wind conditions to those of a westerly burst or El-Nino, can double when the effects of capillary waves are considered. This implies a much stronger coupling between the ocean and the atmosphere than is predicted by other boundary layer models.
Bourassa, Mark A.↗
Magnetohydrodynamic gravity - Capillary waves in a liquid film.
Magnetic field effect on Kapitza capillary traveling wave on falling conducting liquid film surface
Lu, P.-C.↗
Acoustically Induced Capillary Waves on Bubbles and Shells: Pattern for Motion and Turbulence
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Capillary waves Faraday instability turbulence gra↗
Intrinsic frequency spectra of short gravity-capillary waves obtained from temporal measurements of wave height on a lake
Intrinsic frequency spectra of water waves in the range of 6-17 Hz were obtained as a function of both wind speed and wind stress from point measurements of wave height. In a lake with a limited fetch, there are two types of surface motions causing Doppler shift in the frequencies of short waves: orbital velocity of long waves and surface wind drift. The former was estimated from long-wave amplitude by using a linear wave theory. The error in this estimate is of the order of the long-wave slope, and for this work it is typically 10 percent. The latter was approximated by the friction velocity. The friction velocity could be either taken as 3 percent of the mean wind speed measured at a height of 10 m or obtained from direct measurements of the wind stress. The surface drift velocities obtained by these two approaches were found to be in close agreement. Doppler frequency shift can be corrected in either the frequency or the equivalent spatial domain. The two techniques were found to produce comparable results. Experimental results showed that the spectral energy of short waves rapidly increased in response to increasing winds and jumped up by an order of magnitude when wave breaking occurred.
Atakturk, S. S.↗
Unstable capillary waves on surface of separation of two viscous fluids
The study of the breakup of a liquid jet moving in another medium, for example, a jet of fuel from a nozzle, shows that for sufficiently large outflow velocities the jet breaks up into a certain number of drops of different diameters. At still larger outflow velocities, the continuous part of the jet practically vanishes and the jet immediately breaks up at the nozzle into a large number of droplets of varying diameters (the case of "atomization"). The breakup mechanism in this case has a very complicated character and is quite irregular, with the droplets near the nozzle forming a divergent cone.
JETS - ATOMIZATION↗
A Simple Theory of Capillary-Gravity Wave Turbulence
Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.
Glazman, Roman E.↗
A Simple Theory of Capillary-Gravity Wave Turbulence
An analytical solution is presented for deriving inertial spectra of capillary-gravity waves. The theory successfully explains dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves.
multi-wave↗
On two-dimensional packets of capillary-gravity waves
The motion of a two-dimensional packet of capillary-gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear Schroedinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary-gravity wave is less than or greater than the velocity of long gravity waves. These equations are used to examine the stability of the Stokes capillary-gravity wave train. The analysis reveals the existence of a resonant interaction between a capillary-gravity wave and a long gravity wave. The interaction requires that the liquid depth be small in comparison with the wavelength of the (long) gravity waves and the evolution equations describing the dynamics of this interaction are derived.
Djordjevic, V. D.↗
A Simple Theory of Capillary-Gravity Wave Turbulence
Employing a recently proposed 'multi-wave interaction' theory [JFM, 243, 623-625], spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The resultant absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear Rossby waves) intractable by small-perturbation techniques, even in the weak turbulence limit. The analytical solution obtained in the present work is shown to be in good agreement with experimental data. Its low- and high-frequency limits yield power-laws characterizing spectra of purely gravity and capillary waves, respectively. In the limits of weak and strong linearity, these reduce of the Zakharov-Filonenko and Phillips spectra, respectively.
Glazman, Roman E.↗
Monitoring the sea surface with a short pulse radar
A solution is presented for the scattering of short pulses from a stochastic, corrugated surface relative to the sea for the case of a narrow-beam transmitting antenna pointing near nadir. The spectrum of the received power and its time history are calculated and this solution is used to show that a measure of the variance of the surface ordinant can be obtained from the backscattered power. Included explicitly in the analysis is the finite nature of the source and the role of the small-scale wave structure (capillary wave range). It is shown that when sufficiently short pulses are transmitted, one can obtain a measure of the variance of the large scale surface ordinant from either the temporal spacing of the peaks in the returned power or from the envelope of the spectrum of the received power. Assuming an appropriate model for the statistics and spectrum of the surface ordinate, the variance can be used to compute the wind speed and the significant wave height of the surface.
Le Vine, D. M.↗
Using a microgravity environment to probe wave turbulence
The experimental key to observing stochasticity or turbulence in a distribution of interacting propagating waves is the achievement of high amplitude and the use of a medium with a large coefficient of nonlinearity. The research indicates that capillary waves are the best means of observing this phenomenon; however, gravitational modifications of the capillary wave dispersion law greatly reduce the large coefficient of nonlinearity. Thus, a search for wave turbulence in a large drop of fluid that is positioned in a microgravity experiment was conducted. Capillary waves that run around the surface of the drop are excited, and their power spectrum and higher order correlations are analyzed for wave turbulence. The theoretical calculations indicate that modulations of the power spectrum should propagate as second sound waves. These issues have consequences for signal processing and plasma confinement.
Putterman, S.↗