Capillary Waves Research Articles

Smooth stationary water waves with exponentially localized vorticity

We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. A great deal of recent activity has focused on finding waves with nontrivial vorticity \omega . There are now many results on the existence of solutions to this problem for which the vorticity is non-vanishing at infinity, and several authors have constructed waves with \omega having compact support. Our main theorem states that there are large families of stationary capillary-gravity waves that carry finite energy and exhibit an exponentially localized distribution of vorticity. They are solitary waves in the sense that the free surface is asymptotically flat. Remarkably, while their amplitude is small, the kinetic energy is O (1). In this and other respects, they are strikingly different from previously known rotational water waves. To construct these solutions, we exploit a previously unobserved connection between the steady water wave problem on the one hand and singularly perturbed elliptic PDE on the other. Indeed, our result expands the study of spike-layer solutions to free boundary problems with physical relevance.

Surfactant spreading on a deep subphase: Coupling of Marangoni flow and capillary waves

HypothesisSurfactant-driven Marangoni spreading generates a fluid flow characterized by an outwardly moving “Marangoni ridge”. Spreading on thin and/or high viscosity subphases, as most of the prior literature emphasizes, does not allow the formation of capillary waves. On deep, low viscosity subphases, Marangoni stresses may launch capillary waves coupled with the Marangoni ridge, and new dependencies emerge for key spreading characteristics on surfactant thermodynamic and kinetic properties. Experiments and modelingComputational and physical experiments were performed using a broad range of surfactants to report the post-deposition motion of the surfactant front and the deformation of the subphase surface. Modeling coupled the Navier-Stokes and advective diffusion equations with an adsorption model. Separate experiments employed tracer particles or an optical density method to track surfactant front motion or surface deformation, respectively. FindingsMarangoni stresses on thick subphases induce capillary waves, the slowest of which is co-mingled with the Marangoni ridge. Changing Marangoni stresses by varying the surfactant system alters the surfactant front velocity and the amplitude – but not the velocity – of the slowest capillary wave. As spreading progresses, the surfactant front and its associated surface deformation separate from the slowest moving capillary wave.

Effect of atmospheric-pressure plasma irradiation on the surface tension of water

We have shown that measuring the surface tension is a useful scheme to examine the plasma–liquid interface in real-time. The surface tension was measured using a method based on the dispersion relation of an acoustic capillary wave excited on the water surface. The surface tension gradually increased with time, when the water surface was irradiated with the outside region of the spatial afterglow of an atmospheric-pressure plasma. The Marangoni effect associated with the localized increase in the surface tension was observed during the plasma irradiation. The surface tension decreased after the termination of the discharge. A correlation was found between the transient decrease in the surface tension and the variation of the OH radical density in the gas phase. No increase in the surface tension was observed in the solution containing a trapping agent for liquid-phase OH radicals. These experimental results suggest that OH radicals act to increase the surface tension. However, the behavior of the surface tension cannot be explained perfectly by considering only the action of OH radicals.

Gravity–capillary wave interactions generated by moving disturbances: Euler equations framework

The aim of this work is to investigate the interaction of gravity–capillary waves resonantly excited by two moving disturbances along the free surface. The problem is formulated using the full Euler equations, and numerical computations are performed in a simplified domain through the use of a conformal mapping which flattens the free surface. We focus on nearly-critical flows with intermediate capillary effects and characterise their main features. In the supercritical regime, the wave interaction can be strongly nonlinear leading to the onset of wave breaking. In the subcritical regime, depression solitary waves are generated remaining trapped between the disturbances bouncing back and forth. In addition, we notice a dependence of the number of trapped waves on the distance of the disturbances. Furthermore, differently from when only one disturbance is considered, we find that the critical regime captures features from the subcritical and supercritical regime simultaneously.

Interplay of viscosity and surface tension for ripple formation by laser melting

A model for ripple formation on liquid surfaces exposed to an external laser or particle beam and a variable ground is developed. The external incident beam is hereby mechanically coupled to the liquid surface due to surface roughness. Starting from the Navier Stokes equation the coupled equations for the velocity potential and the surface height are derived in a shallow-water approximation with special attention to viscosity. The resulting equations obey conservation laws for volume and momentum where characteristic potentials for gravitation and surface tension are identified analogously to conservative forces. The approximate solutions are discussed in the context of ripple formation in laser materials processing involving melting of a surface by a laser beam. Linear stability analysis provides the formation of a damped wave modified by an interplay between the external beam, the viscosity, and the surface tension. The limit of small viscosity leads to damped gravitational and the limit of high viscosity to capillary waves. The resulting wavelengths are in the order of the ripples occurring in laser welding experiments hinting to the involvement of hydrodynamic processes in their origin. By discussing the response of the system to external periodic excitations with the help of Floquet multipliers, we show that the ripple formation could be triggered by a a periodically modulated external beam, e.g. appropriate repetition rates of an incident laser beam. The weak nonlinear stability analysis provides ranges where hexagonal or stripe structures can appear. The orientation of stripe structures and ripples are shown to be dependent on the incident angle of the laser or particle beam where a minimal angle is reported. Numerical simulations confirm the findings and allow to describe the influence of variable grounds.

Interfaces in incompressible flows

The motion of both internal and surface waves in incompressible fluids under capillary and gravity forces is a major research topic. In particular, we review the derivation of some new models describing the dynamics of gravity-capillary nonlinear waves in incompressible flows. These models take the form of both bidirectional and unidirectional nonlinear and nonlocal wave equations. More precisely, with the goal of telling a more complete story, in this paper we present the results in the works (Cheng in Water Waves 1(1):71-130, 2019; Granero-Belinchón and Ortega in On the motion of gravity-capillary waves with odd viscosity. arXiv:2103.01062, 2021; Granero-Belinchón and Scrobogna in J Diff Equ 276:96–148 1921; SIAM J Appl Math 79(6):2530–2550, 2019; Proc Am Math Soc 148(12):5181–5191, 2020; Phys Fluids 33(10):102115, 2021; Granero-Belinchón and Shkoller in Multiscale Model Simul 15(1):274–308, 2017) together with some new results regarding the well-posedness of the resulting PDEs.

On solitons: Propagation of shallow water waves for the fifth-order KdV hierarchy integrable equation

Abstract This article studies the fifth-order KdV (5KdV) hierarchy integrable equation, which arises naturally in the modeling of numerous wave phenomena such as the propagation of shallow water waves over a flat surface, gravity–capillary waves, and magneto-sound propagation in plasma. Two innovative integration norms, namely, the G ′ G 2 \left(\frac{{G}^{^{\prime} }}{{G}^{2}}\right) -expansion and ansatz approaches, are used to secure the exact soliton solutions of the 5KdV type equations in the shapes of hyperbolic, singular, singular periodic, shock, shock-singular, solitary wave, and rational solutions. The constraint conditions of the achieved solutions are also presented. Besides, by selecting appropriate criteria, the actual portrayal of certain obtained results is sorted out graphically in three-dimensional, two-dimensional, and contour graphs. The results suggest that the procedures used are concise, direct, and efficient, and that they can be applied to more complex nonlinear phenomena.

Generation of surface liquid flow in channels by capillary vibrations and waves

The generation of a directed flow on the water surface in channels with sources and resonators of capillary oscillations is detected and investigated. The surface flow is caused by the movement of the liquid through the gaps between the resonators, as well as between the resonator and the channel walls, under a curved surface that is locally deformed by the sources of capillary vibrations, the transfer of energy of the locally curved surface of the liquid by capillary waves, and the transmission of wave momentum to the particles of the liquid surface in one direction. It is shown that capillary waves together with the energy transfer an excess surface, the flux density of which is equal to the flux of the surface deformation. Moving devices with a capillary-wave accelerator of the surface liquid flow are demonstrated. Keywords: capillary oscillations and waves, surface liquid flow, channel, flux of surface deformation.

Wave Tank Study of Steep Gravity-Capillary Waves and Their Role in Ka-Band Radar Backscatter

Nonlinearity of gravity-capillary waves (GCWs) plays an important role in the wind wave dynamics and in microwave scattering from the sea surface. This study is aimed to investigate in wave tank experiment characteristics of nonlinear features of mechanically generated centimeter-decimeter-wavelength GCW—parasitic capillary ripples (PCRs) and bulge/toe structures, and their contribution in microwave radar return. An optical method of visualization of GCW profile with high spatial resolution was developed to study GCW profile and Ka-band Doppler scatterometer was used to measure backscattering at vertical (VV) and horizontal (HH) polarizations. Dependencies of PCR slopes and bulge curvature on steepness of dm-scale GCW have been obtained and indicated sharp growth in the vicinity of the limiting steepness of order 0.3. PCR slopes and bulge curvature both decreased in the presence of film, but PCR appeared to be stronger suppressed by film than the bulges. The velocities of microwave scatterers retrieved from radar Doppler shifts were found to be consistent with the phase velocities of 4-Hz GCW, but smaller for GCW of lower frequencies. Both the phase velocities and the scatterer’s velocities slowly increased with GCW steepness. Polarization ratio (PR) values decrease with GCW steepness and in the presence of film, thus indicating the enhanced relative contribution of nonpolarized scattering for very steep GCW and when film is applied on the water surface. We consider that the aforementioned results can be explained under an assumption that PCR contributes mostly to Bragg scattering component, while bulge/toe structures contribute to nonpolarized scattering.

Генерация поверхностного потока жидкости в каналах капиллярными колебаниями и волнами

The generation of a directed flow on the water surface in channels with sources and resonators of capillary oscillations is detected and investigated. The surface flow is caused by the movement of the liquid through the gaps between the resonators, as well as between the resonator and the channel walls, under a curved surface that is locally deformed by the sources of capillary vibrations, the transfer of energy of the locally curved surface of the liquid by capillary waves, and the transmission of wave momentum to the particles of the liquid surface in one direction. It is shown that capillary waves together with the energy transfer an excess surface, the flux density of which is equal to the flux of the surface deformation. Moving devices with a capillary-wave accelerator of the surface liquid flow are demonstrated.

Parametric excitation of a gravity–capillary wave by radiation pressure of ultrasound

Parametric instability of a standing gravity–capillary wave is observed in conditions of irradiation of a surface of a liquid by a plane ultrasound beam modulated by amplitude. A threshold value of ultrasound intensity for excitation of the parametric oscillations of the surface is determined, and the frequency response of the process is measured. A mechanism of instability based on sound radiation pressure applied to a liquid surface curved with menisci is suggested.

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

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.

Controllability and stabilization of gravity-capillary surface water waves in a basin

<p style='text-indent:20px;'>The paper concerns the controllability and stabilization of surface water waves in a two-dimensional rectangular basin under the forces of gravity and surface tension. The surface waves are generated by a wave-maker placed at the left side-boundary and it is physical relevant to see whether the surface waves are controllable or can be stabilized using appropriate motion of the wave-maker. Due to the surface tension, an edge condition must be imposed at the contact point between the free surface and a solid boundary. Two types of wave-makers are considered: "flexible" or "rigid". It is shown that the surface waves are approximately controllable, but not exactly controllable, for both "flexible" and "rigid" wave-makers. In addition, under a static feedback to control a "rigid" wave-maker, the strong stability of feedback control system is obtained.</p><p style='text-indent:20px;'> </p><p style='text-indent:20px;'>Correction: The page numbers on each page of the PDF file have been corrected. We apologize for any inconvenience this may cause.</p>

Capillary-wave warp-drive

The generation of surface water flow in channels with sources and resonators of capillary oscillations is detected and investigated. Moving devices with a capillary-wave accelerator of the surface fluid flow are demonstrated. The surface flow of liquid in the channel is generated due to the local deformation of the liquid surface by capillary vibrations and the formation of an excess liquid surface on average near the source and the transport of this surface by waves. Keywords: capillary oscillations and waves, surface liquid flow, channel.

Late Triassic paleowinds from lacustrine wave ripple marks in the Fleming Fjord Group, central East Greenland

Geological evidence of paleoclimate conditions provide important constraints on paleoclimate models. Paleowinds are one of the central paleoclimate parameters in global circulation models used to reconstruct past climatic conditions. However, only a few climate proxies such as eolian dunes and shallow-water wave ripples provide information on paleowind directions. In this study, we present new paleoclimatic data based on lacustrine sediments with wave ripple marks in the Upper Triassic Fleming Fjord Group, central East Greenland deposited at very shallow water depth in the northern part of Pangaea in a mid-latitude, warm-temperate climate. Wave-ripple orientations are measured on 380 individual fossilized wave-rippled beds at four localities in the ~8500 km 2 lacustrine basin. These ripple data are used to establish a geologic wind proxy and are compared to previously published general circulation models. Two wave ripple orientations are observed: The dominant ripple orientation and wave ripple characteristics indicate paleowinds from the Late Triassic SSE and NNW (154.5° and 334.5°), while a subordinate orientation indicate paleowinds from W or E (270° or 90°). This paleowind regime remained stable for at least ~7.5 million years during the mid-late Norian (218.5-211 Ma). These results correspond very well with some general circulation model results that suggest summer winds from the NNW and winter winds from the SSE. Based on the great compatibility between empirical data and general circulation model results, the wind pattern seems to have been greatly influenced by regional, Late Triassic mountain topography in the present-day Greenland and Norway channeling the paleowind in the northernmost part of the pre-Atlantic rift basin (the mid-Norwegian-east Greenland rift system).

Experimental Observation of Capillary Waves Inside a Cavity for Falling Drop

Experimental Observation of Capillary Waves Inside a Cavity for Falling Drop

Influence of ambient air viscosity on the accuracy of measurements of liquid properties in a levitating drop

In this paper, we consider low-amplitude capillary oscillations of a liquid droplet that has a spherical shape in equilibrium and is placed in an immobile light gas volume. In the approximation of low medium viscosity, and under the condition that the media differ greatly in density, a correction to natural frequency was determined and the viscous damping coefficient was estimated. Theoretical predictions were obtained analytically and verified by performing numerical calculations for water or mercury drops in the air. It is shown that the contributions of the viscosity and inertia of the gas to the real frequency of free oscillations of the system are insignificant. As regards the damping factor, the gas viscosity makes a contribution determined by the square root of its kinematic viscosity, which can no longer be neglected. The damping coefficient calculated relative to the liquid contribution linear in viscosity increases as the fourth root of the droplet size. For the water drop of 5 mm diameter, it is about ten percent, and for the mercury drop of the same size, the relative contribution reaches five percent. The results obtained are necessary for improving the "levitating" drop method, which is a variation of the dynamic capillary wave method used for non-contact measurement of viscosity coefficients and surface tension. A generalization of the Lamb formula for calculating liquid viscosity is proposed, which, in addition to the damping decrement of the quadrupole mode and the drop size, includes the density and viscosity of the gas, as well as the natural frequency of the system. The surface tension coefficient can be calculated using the Rayleigh formula, which, as it turns out, does not require a correction.

Dynamics of roller domains under parametric excitation of capillary waves in a square cell with a rounded corner and a rectangular protrusion at the boundary

Dynamics of roller domains under parametric excitation of capillary waves in a square cell with a rounded corner and a rectangular protrusion at the boundary

Comprehensive Review of KY Converter Topologies, Modulation and Control Approaches With Their Applications

In current scenario, the challenging task in designing a DC-DC converter has high voltage gain and small output ripple waves, which researchers deal with highly complicated. Because of its topological and Continuous Conduction Mode (CCM), the KY converters have developed a better converter than all the traditional DC-DC converters to overcome this intricacy of voltage transfer gain and output ripple waves. The KY converters had comparative and various qualities when compared with the boost converter with Synchronous Rectifier (SR). The KY converter is used in photovoltaic and sustainable power applications, which are examined in this study. KY converter incorporates mode-1 and mode-2 operation and its types, for example, one plus D and one plus 2D where the KY can deliver the N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> type of KY converters. This article provides a comprehensive review and investigation of the KY converters, which incorporates their topology with control methodologies, Pulse Width Modulation (PWM) techniques, working activity of KY converters, and types for mode-1 and -2; it interprets the few strategies the KY converter is executed and its applications.

Correlation between Alteration of Sharp-wave Ripple Coupled Cortical Oscillation and Long-term Memory Deficit in Alzheimer Disease Model Mice.

Alzheimer’s disease (AD) is the most common cause of dementia, characterized by prominent episodic memory dysfunction. Recent studies have suggested that there is a sequential mechanism in the memory deficit, with long-term ones preceding short-term ones. However, there is lack of explanation for these symptoms. Interaction between the hippocampus and retrosplenial cortex (RSC) during slow-wave sleep (SWS) is a crucial step for successful long-term memory formation. In particular, sharp-wave ripple (SWR) is a principal hippocampus oscillation that coordinates with RSC activity. To determine the relationship between memory dysfunction and SWR-related oscillation changes in AD, we implanted local field potential electrodes in the hippocampus and RSC of AD model mice (APP/PS1). We found that the SWR-coupled ripple wave increased in the RSC, while the amplitude of the SWR was preserved. In addition, the corresponding delta power in hippocampus and RSC was elevated, together with altered delta synchrony in AD mice. All these findings showed a significant correlation with long-term memory deficits measured in contextual fear conditions. Our study suggests that altered SWR-coupled oscillations are a possible underlying mechanism of episodic memory dysfunction in AD mice.