Onset of wave drag due to generation of capillary-gravity waves by a moving object as a critical phenomenon

The onset of the wave resistance, via generation of capillary-gravity waves of a small object moving with velocity V, is investigated experimentally. Because of the existence of a minimum phase velocity V(c) for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases waves or rotons are produced at V>V(c) due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to sqrt[V-V(c)] for various fluids.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.     

Linear wave interaction at the charged fluid-fluid interface under tangential discontinuity of the velocity field

Capillary wave flow in a two-layer fluid with the upper layer moving parallel to the charged interface at a constant velocity is treated within a linear mathematical model. Interaction between waves excited on the free surface of the upper layer and at the interface results not only in classical Kelvin-Helmholtz instability (at low velocities of the upper layer) but also in oscillatory instability of the interface. The instability increment depends on the fluid density ratio, translational velocity, and charge density at the interface.     

Detection of moving objects and flows in liquids by ultrasonic phase conjugation

The possibility for the application of the method of parametric phase conjugation of ultrasonic waves in measuring the velocity of moving objects and flows is investigated. Results of experimental measurements of the Doppler frequency shift are presented for a low-frequency wave (1 MHz) generated by phase-conjugate waves (10 MHz and 11 MHz) propagating in opposite directions in the presence of a moving scatterer. The super high sensitivity of the phase of the low-frequency wave to variations in the spatial position of the scatterer is used to measure the velocity of the object. The presence of flows in the region of propagation of phase-conjugate waves returned leads to an uncompensated Doppler shift of the phase of the phase-conjugate wave at the primary radiation source. The implementation of this feature of ultrasonic phase conjugation for the detection and measurement of the flow velocities in a liquid is demonstrated experimentally.     

过冷沸腾丝上气泡运动的动态模拟

本文以核态池沸腾100μm铂丝上单个气泡的动力学行为为研究现象进行数值模拟,采用能量方程求解丝上以运动气泡为中心的局部区域内的温度分布,同时引入了在核态池沸腾丝上运动气泡粘性力经验公式,以此来考虑Marangoni驱动力和粘件力相等时的运动气泡稳态速度,最后分析了气泡在运动过程中吸收热量的特性.为理论求解丝上核态沸腾运动气泡的稳态速度和吸热特性积累一些理论根据.     

Sonoelastographic imaging of interference patterns for estimation of shear velocity distribution in biomaterials

The authors have recently demonstrated the shear wave interference patterns created by two coherent vibration sources imaged with the vibration sonoelastography technique. If the two sources vibrate at slightly different frequencies omega and omega+deltaomega, respectively, the interference patterns move at an apparent velocity of (deltaomega/2omega)upsilon(shear), where upsilon(shear) is the shear wave speed. We name the moving interference patterns "crawling waves." In this paper, we extend the techniques to inspect biomaterials with nonuniform stiffness distributions. A relationship between the local crawling wave speed and the local shear wave velocity is derived. In addition, a modified technique is proposed whereby only one shear wave source propagates shear waves into the medium at the frequency omega. The ultrasound probe is externally vibrated at the frequency omega-deltaomega. The resulting field estimated by the ultrasound (US) scanner is proven to be an exact representation of the propagating shear wave field. The authors name the apparent wave motion "holography waves." Real-time video sequences of both types of waves are acquired on various inhomogeneous elastic media. The distribution of the crawling/holographic wave speeds are estimated. The estimated wave speeds correlate with the stiffness distributions.     

Propagation of magnetoacoustic surface waves along static plasma slab surrounded by moving plasma and neutral gas

The existence and propagation of fast and slow magnetoacoustic surface waves (MASW) is investigated in our work by taking a theoretical model of a static plasma slab as the middle layer with a moving plasma region at the top and neutral gas medium as the bottom layer. Applying linear MHD, the dispersion relation is obtained and the propagation of magnetoacoustic surface waves, in the compressional limit for steady flow and for different values of dimensionless wave numbers, is analyzed. Steady flow of plasma along a structured atmosphere may cause enhancement of existing surface modes, disappearance of some modes and generation of new surface wave modes. The possible regions for the propagation of fast and slow surface and body waves for different mass density ratios and magnetic field ratios and with a small flow velocity are studied. Our discussion may help in analyzing more complicated cases.     

Stoneley (interfacial) waves between two magneto-electro-elastic half planes

We investigated the propagation properties of Stoneley waves between two magneto-electro-elastic half planes. Magneto-electro-elastic materials are assumed to possess hexagonal (6 mm) symmetry. Twenty-five sets of magneto-electrical interface conditions were adopted and generalized frequency equations were derived and solved numerically. It was found that, for each set of interface conditions, existing Stoneley waves are always non-dispersive. Numerical results further show that material properties have a significant effect on both the number and velocity of Stoneley waves, and that, although different magneto-electrical interface conditions could influence the existence of Stoneley waves, they have no effect on wave velocities.     

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen （2006） as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song （2005） for second-order solutions for random interfacial waves with steady uniform currents if N = 2.     

Quasidislocation stoneley wave and Eshelby dislocation Scholte wave

A quasidislocation (a dislocationlike entity described here for the first time) moves at the speed of a Stoneley surface wave that travels at the interface between two different elastic solids. An Eshelby glide edge dislocation moves at the speed of a Scholte surface wave that travels at the interface between a solid and an ideal liquid. The quasidislocation and the glide edge dislocation (that moves at the Eshelby velocity) are the Green's functions of their waves. Scholte waves are planar distributions of transonic moving glide edge dislocations. They are not Stoneley waves, although often called by that name, because Stoneley waves are planar distributions of subsonic moving quasidislocations.     

Dispersion of interface waves in sediments with power-law shear speed profiles. I. Exact and approximate analytical results.

In the upper tens of meters of ocean bottom, unconsolidated marine sediments consisting of clay, silt, or fine sand with high porosity are "almost incompressible" in the sense that the shear wave velocity is much smaller than the compressional wave velocity. The shear velocity has very large gradients close to the ocean floor leading to strong coupling of compressional and shear waves in such "soft" sediments. The weak compressibility opens an avenue for developing a theory of elastic wave propagation in continuously stratified soft sediments that fully accounts for the coupling. Elastic waves in soft sediments consist of "fast" waves propagating with velocities close to the compressional velocity and "slow" waves propagating with velocities on the order of the shear velocity. For the slow waves, the theory predicts the existence of surface waves at the ocean-sediment boundary. In the important special case of the power-law depth-dependence of shear rigidity, phase and group velocities of the interface waves are shown to scale as a certain power of frequency. An explicit, exact solution was obtained for the surface waves in sediments characterized by constant density and a linear increase of shear rigidity with depth, that is, for the case of shear speed proportional to the square root of the depth below the sediment-water interface. Asymptotic and perturbation techniques were used to extend the result to more general environments. Theoretical dispersion relations agreed well with numerical simulations and available experimental data and, as demonstrated in a companion paper [D. M. F. Chapman and O. A. Godin, J. Acoust. Soc. Am 110, 1908 (2001)] led to a simple and robust inversion of interface wave travel times for shear velocity profiles in the sediment.     

Surface-plasmon-polariton waves guided by the uniformly moving planar interface of a metal film and dielectric slab

We explored the effects of relative motion on the excitation of surface-plasmon-polariton (SPP) waves guided by the planar interface of a metal film and a dielectric slab, both materials being isotropic and homogeneous. Electromagnetic phasors in moving and non-moving reference frames were related directly using the corresponding Lorentz transformations. Our numerical studies revealed that, in the case of a uniformly moving dielectric slab, the angle of incidence for SPP-wave excitation is highly sensitive to (i) the ratio β of the speed of motion to speed of light in free space and (ii) the direction of motion. When the direction of motion is parallel to the plane of incidence, the SPP wave is excited by p-polarized (but not s-polarized) incident plane waves for low and moderate values of β, while at higher values of β the total reflection regime breaks down. When the direction of motion is perpendicular to the plane of incidence, the SPP wave is excited by p-polarized incident plane waves for low values of β, but s-polarized incident plane waves at moderate values of β, while at higher values of β the SPP wave is not excited. In the case of a uniformly moving metal film, the sensitivity to β and the direction of motion is less obvious.     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

Universal thermal radiation drag on neutral objects

We compute the force on a small neutral polarizable object moving at velocity v--> relative to a photon gas equilibrated at a temperature T. We find a drag force linear in v-->. Its physical basis is related to that in recent formulations of the dissipative component of the Casimir force, i.e., the change in photon momentum in emission and absorption between the moving body and the stationary thermal bath. We estimate the strength of this universal drag force for different dielectric response functions and comment on its relevance in various contexts, especially to radiation-matter coupling in the cosmos.     

Numerical study on trapping and guiding of nanoparticles in a flow using scattering field of laser light

Optical trapping and guiding using laser have been proven to be useful for non-contact and non-invasive manipulation of small objects such as biological cells, organelles within cells, and dielectric particles. We have numerically investigated so far the motion of a Brownian particle suspended in still water under the illumination of a speckle pattern generated by the interference of coherent light scattered by a rough object. In the present study, we investigate numerically the motion of a particle in a water flow under the illumination of a speckle pattern that is at rest or in motion. Trajectory of the particle is simulated in relation with its size, flow velocity, maximum irradiance, and moving velocity of the speckle pattern to confirm the feasibility of the present method for performing optical trapping and guiding of the particle in the flow.     

Chemical instability induced by a shear flow

We predict a new type of instability induced by shear flow in chemical systems. A homogeneous steady state solution of a reaction-diffusion system loses stability in a Poiseuille flow. The instability appears as the speed of the flow increases beyond a certain threshold. This results in a steady pattern moving with the average fluid velocity. The chemical reaction consists of two species (activator and inhibitor) moving with identical velocities. Contrary to Turing's instability, the pattern arises when the activator has a higher diffusivity than the inhibitor.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

Theory of periodic and solitary space charge waves in extrinsic semiconductors

We present a theory of the existence and stability of traveling periodic and solitary space charge wave solutions to a standard rate equation model of electrical conduction in extrinsic semiconductors which includes effects of field-dependent impurity impact ionization. A nondimensional set of equations is presented in which the small parameter β = (dielectric relaxation time) / (characteristic impurity time) 1 plays a crucial role for our singular perturbation analysis. For a narrow range of wave velocities a phase plane analysis gives a set of limit cycle orbits corresponding to periodic traveling waves. while for a unique value of wave velocity we find a homoclinic orbit corresponding to a moving solitary space charge wave of the type experimentally observed in p-type germanium. A linear stability analysis reveals all waves to be unstable under current bias on the infinite one-dimensional line. Finally, we conjecture that solitary waves may be stable in samples of finite length under voltage bias.     

The Force Acting on a Cylinder in a Ring Flow of a Viscous Fluid with a Small Eccentric Displacement

A system consisting of two circular cylinders one inside the other with parallel axes is considered. The outer cylinder of radius R₂ is fixed, and the inner cylinder of radius R₁ rotates with a sufficiently large angular velocity. The region between the cylinders is filled with an incompressible viscous fluid and, in the case of coaxial cylinders, Couette flow along circular trajectories arises. Upon an eccentric small displacement of the axis of the inner cylinder, the symmetry of the flow is disturbed and a force exerted on the inner cylinder by the fluid is created. Within the ideal fluid model, the force depends linearly on the transverse velocities and accelerations of the cylinder. In a viscous fluid, the force depends on the previous motion of the cylinder. It is expressed in terms of the velocity functional by analogy with the Basset force acting on a ball moving in a viscous fluid with a variable velocity.     

Exact solutions of the Korteweg-de Vries equation with a self-consistent source

Exact solutions are found for the Korteweg-de Vries equation with a source satisfying the stationary Schrödinger equation. Each solution describes the evolution of the initial moving wave with one phase velocity to the final moving wave with another phase velocity. The conditions are pointed out under which the phase velocities of these waves may differ in sign. The obtained results are relevant to some problems of hydrodynamics, plasma physics, solid state physics, etc.