Two-dimensional Euler flows in slowly deforming domains

We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow compared to the fluid motion. The Eulerian flow is found to remain approximately steady throughout the evolution. At leading order, the velocity field depends instantaneously on the shape of the domain boundary, and it is determined by the steadiness and vorticity-preservation conditions. This is made explicit by reformulating the problem in terms of an area-preserving diffeomorphism g_Λ which transports the vorticity. The first-order correction to the velocity field is linear in the boundary velocity, and we show how it can be computed from the time derivative of g_Λ.The evolution of the Lagrangian position of fluid particles is also examined. Thanks to vorticity conservation, this position can be specified by an angle-like coordinate along vorticity contours. An evolution equation for this angle is derived, and the net change in angle resulting from a cyclic deformation of the domain boundary is calculated. This includes a geometric contribution which can be expressed as the integral of a certain curvature over the interior of the circuit that is traced by the parameters defining the deforming boundary.A perturbation approach using Lie series is developed for the computation of both the Eulerian flow and geometric angle for small deformations of the boundary. Explicit results are presented for the evolution of nearly axisymmetric flows in slightly deformed discs.     

Near-field ultrasound tomography

In this paper, a near-field tomographic solution is introduced to solve the imaging problem of fluid objects assumed to be weakly heterogeneous (Born approximation) and excited by spherical waves. The solution to the forward problem is based on the Huygens-Fresnel principle which describes the scattered field as the result of the interference scheme of all the secondary spherical waves. From the derivation of the scattered field, a new Fourier transform that has been called the elliptical Fourier transform is defined: It differs from the standard Fourier transform in that instead of a plane wave decomposition, a harmonic ellipsoidal wave decomposition is obtained. Based on this spectral analysis, a near-field Radon transform is designed that complements the "far-field tools" published in diffraction tomography literature. Then, assuming that the measuring distance is greater than one wavelength, the feasibility of reconstructing either the impedance or the velocity maps of an acoustical (perfect fluid) model is demonstrated. Numerical simulations were performed which confirmed the validity of the theory presented here; a theory which has many potential applications in future wave theory research.     

Propagation of sound waves through a spatially homogeneous but smoothly time-dependent medium

The propagation of sound through a spatially homogeneous but non-stationary medium is investigated within the framework of fluid dynamics. For a non-vortical fluid, especially, a generalized wave equation is derived for the (scalar) potential of the fluid velocity distribution in dependence of the equilibrium mass density of the fluid and the sound wave velocity. A solution of this equation for a finite   transition period τ$\tau$ is determined in terms of the hypergeometric function for a phenomenologically realistic, sigmoidal change of the mass density and sound wave velocity. Using this solution, it is shown that the energy flux of the sound wave is not conserved but increases always   for the propagation through a non-stationary medium, independent of whether the equilibrium mass density is increased or decreased. It is found, moreover, that this amplification of the transmitted wave arises from an energy exchange with the medium and that its flux is equal to the (total) flux of the incident and the reflected wave. An interpretation of the reflected wave as a propagation of sound backward in time is given in close analogy to Feynman and Stueckelberg for the propagation of anti-particles. The reflection and transmission coefficients of sound propagating through a non-stationary medium is analyzed in more detail for hypersonic waves with transition periods τ$\tau$ between 15 and 200 ps as well as the transformation of infrasound waves in non-stationary oceans.     

General relativistic shock waves in fluids for which pressure equals energy density

A shock wave in a self-gravitating fluid obeying the equation of state: pressure equal to energy density is shown to travel with the velocity of light in a space-time determined by the Einstein field equations. The jump conditions that must be satisfied by the hydrodynamic variables are derived and discussed as are those that must be satisfied by the metric tensor and its derivatives. The latter conditions are obtained by using a variational principle.     

A two-dimensional cochlear fluid model based on conformal mapping

Using conformal mapping, fluid motion inside the cochlear duct is derived from fluid motion in an infinite half plane. The cochlear duct is represented by a two-dimensional half-open box. Motion of the cochlear fluid creates a force acting on the cochlear partition, modeled by damped oscillators. The resulting equation is one-dimensional, more realistic, and can be handled more easily than existing ones derived by the method of images, making it useful for fast computations of physically plausible cochlear responses. Solving the equation of motion numerically, its ability to reproduce the essential features of cochlear partition motion is demonstrated. Because fluid coupling can be changed independently of any other physical parameter in this model, it allows the significance of hydrodynamic coupling of the cochlear partition to itself to be quantitatively studied. For the model parameters chosen, as hydrodynamic coupling is increased, the simple resonant frequency response becomes increasingly asymmetric. The stronger the hydrodynamic coupling is, the slower the velocity of the resulting traveling wave at the low frequency side is. The model's simplicity and straightforward mathematics make it useful for evaluating more complicated models and for education in hydrodynamics and biophysics of hearing.     

Acoustic wave in a suspension of magnetic nanoparticle with sodium oleate coating

The ultrasonic propagation in the water-based magnetic fluid with doubled layered surfactant shell was studied. The measurements were carried out both in the presence as well as in the absence of the external magnetic field. The thickness of the surfactant shell was evaluated by comparing the mean size of magnetic grain extracted from magnetization curve with the mean hydrodynamic diameter obtained from differential centrifugal sedimentation method. The thickness of surfactant shell was used to estimate volume fraction of the particle aggregates consisted of magnetite grain and surfactant layer. From the ultrasonic velocity measurements in the absence of the applied magnetic field, the adiabatic compressibility of the particle aggregates was determined. In the external magnetic field, the magnetic fluid studied in this article becomes acoustically anisotropic, i.e., velocity and attenuation of the ultrasonic wave depend on the angle between the wave vector and the direction of the magnetic field. The results of the ultrasonic measurements in the external magnetic field were compared with the hydrodynamic theory of Ovchinnikov and Sokolov (velocity) and with the internal chain dynamics model of Shliomis, Mond and Morozov (attenuation).     

Stability of magnetohydrodynamic stratified shear flows

Summary The linear stability of a stratified shear flow of a perfectly conducting bounded fluid in the presence of a magnetic field aligned with the flow and buoyancy forces has been studied under Boussinesq approximation. A new upper bound has been obtained for the range of real and imaginary parts of the complex wave velocity for growing perturbations. The upper bound depends on minimum Richardson number, wave number, Alfvén velocity and basic flow velocity. H?iland's necessary criterion for instability of hydrodynamic stratified homogeneous shear flow is modified and its analog for nonhomogeneous magnetohydrodynamic cases is derived. Finally the upper bound for the growth rate ofKC _i and its variants, whereK is the wave number andC _i the imaginary part of complex wave velocity, is derived as the necessary condition of instability. All estimates remain valid even when the minimum richardson numberJ ₁, for some practical problems, exceeds 1/4 for growing perturbations. The authors of this paper have agreed to not receive the proofs for correction.     

A minimum photon “rest mass” — Using Planck's constant and discontinuous electromagnetic waves

Reasons for taking1/2h/c ² in cgs units as an equivalent in grams for the photon “rest mass” are given. Its numerical value of3.68×10 ^?48 g corresponds to the minimum mass equivalent energy for one half-cycle of an electromagnetic dipole field distribution, which is discontinuous. For the fluid models that are discussed, this field distribution corresponds somewhat to a hydrodynamic toroidal vortex which is stationary—if we use toroidal coordinates and assume that the ring origin has the radial velocity c, that the gauge is defined by the ring origin diameter, and that free space is represented by a two-fluid model (the fluids oppositely charged). There are mappings which can transform such toroidal entities (photons) into spherical ones. The toroidal entities are possible candidates for the role of “hidden variables.”     

Complex singularity of a stokes wave

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase in the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value H _max/λ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave. Here, H is the wave height and λ is the wavelength. We simulated fully nonlinear Euler equations, reformulated in terms of conformal variables, to find Stokes waves for different wave heights. Analyzing spectra of these solutions we found in conformal variables, at each Stokes wave height, the distance ν _c from the lowest singularity in the upper half-plane to the real line which corresponds to the fluid free surface. We also identified that this singularity is the square-root branch point. The limiting Stokes wave emerges as the singularity reaches the fluid surface. From the analysis of data for ν _c → 0 we suggest a new power law scaling ν _c ∝ (H _max ? H)^3/2 as well as new estimate H _max/λ ? 0.1410633.     

Amplification and change in velocity of acoustic waves due to external temperature gradient in piezoelectric semiconductors

Using hydrodynamic equations we calculate the attenuation/amplification coefficient of an acoustic wave and the change in its velocity due to an external temperature gradient in piezoelectric semiconductors. The numerical results have been presented for a typical case of Indium Antimonide. The present analysis is valid in the low frequency region only (i.e. ql ? 1).     

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.     

Breakdown of hydrodynamics in a simple one-dimensional fluid

We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches; e.g., the hydrodynamic profiles relax algebraically toward their equilibrium values. Deviations from local thermodynamic equilibrium are persistent, decaying as a power law of the distance to the shock layer. Nonequipartition is observed infinitely far from the shock wave, and the velocity-distribution moments exhibit multiscaling. These results question the validity of simple hydrodynamic theories to understand collective behavior in 1D fluids.     

Convective motion and transfer of force by many-body hydrodynamic interaction

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. When the bodies are carried along by an incident flow without exerting forces or torques on the fluid then their translational and rotational velocities are linearly related to the incident flow velocity by convection kernels. In the absence of an incident flow, but with applied forces and torques, the force density acting on the fluid is linearly related to the forces and torques by transfer kernels. We show that the convection and transfer kernels are simply related by a symmetry relation. For freely moving bodies the force density exerted on the fluid is related to the incident flow by a convective friction kernel. We show that this kernel is symmetric.     

Coupled hydrodynamic-acoustic modeling of sound generated by impacting cylindrical water jets

A coupled hydrodynamic-acoustic model describing acoustic propagation in a fluid containing multiple bubbles is proposed and applied to simulate noise generated by impacting water jets. The total pressure is decomposed into a "hydrodynamic" part and an "acoustic" part and computed using different schemes. The hydrodynamic pressure field is calculated independently using a generalized hydrodynamic model, and the pressure variations serve as sources in the wave equation for the acoustic pressure. A numerical algorithm developed to calculate wave propagation in an irregular region is used to account for the existence of the cavities. Noise generated by the impact of two cylindrical water jets is predicted. The computed near-field pressure is compared with the experimental data.     

Analysis of peristaltic flow of Jeffrey six constant nano fluid in a vertical non-uniform tube

Peristaltic flow of non-Newtonian nano fluid through a non-uniform surface has been investigated in this paper. The fluid motion along the wall of the surface is caused by the sinusoidal wave traveling with constant speed. The governing equations are converted into cylindrical coordinate system and assuming low Reynolds number and long wave length partial differential equations are simplified. Analytically solutions of the problem are obtained by utilizing the homotopy perturbation method (HPM). In order to insight the impact of embedded parameters on temperature, concentration and velocity some graphs are plotted for different peristaltic waves. At the end, some observations were made from the graphical presentation that velocity, pressure rise and nano particle concentration are increasing function of thermophoresis parameter N_t while temperature and frictional forces show opposite trend.     

Kerr–Newman-AdS black hole surrounded by perfect fluid matter in Rastall gravity

The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to \(T^{\mu \nu }_{~~;\mu }=\lambda R^{,\nu }\). In this work, we derive the Kerr–Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman–Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy (\(\omega =-\,2/3\)) and the perfect fluid dark matter (\(\omega =-\,1/3\)). Firstly, the Rastall parameter \(\kappa \lambda \) could be constrained by the weak energy condition and strong energy condition. Secondly, by analyzing the number of roots in the horizon equation, we get the range of the perfect fluid matter intensity \(\alpha \), which depends on the black hole mass M and the Rastall parameter \(\kappa \lambda \). Thirdly, we study the influence of the perfect fluid dark matter and dark energy on the ergosphere. We find that the perfect fluid dark matter has significant effects on the ergosphere size, while the dark energy has smaller effects. Finally, we find that the perfect fluid matter does not change the singularity of the black hole. Furthermore, we investigate the rotation velocity in the equatorial plane for the KN-AdS black hole with dark energy and perfect fluid dark matter. We propose that the rotation curve diversity in Low Surface Brightness galaxies could be explained in the framework of the Rastall gravity when both the perfect fluid dark matter halo and the baryon disk are taken into account.     

固体吸附式制冷中热波循环的分析研究

1引言由Tehernev博士和S．V．Shelton教授提出的热波循环，是吸附式制冷中引起广泛兴趣的一种循环方式。其特点是高效回热，Shelton采用斜波法［‘］和方波法［‘］分析了热波循环，回热率达70％，热泵工况COP超过1．6。其它学者作了改进研究［‘并热波循环的模拟效果很好，但实验方面进展相当缓慢。采用螺旋板式换热器作吸附器，也发现热波循环的运行效果很不理想问。目前，相关的文献主要是系统模拟，而对其关键，热波的形成、特性研究较少。另外，研究侧重于系统性能（COP），对能量密度（SPD）考虑较少。本文将从传热的角度分析热…