Abstract:
We describe the effect of vibration on a confined volume of fluid which is density stratified due to its compressibility. We show that internal gravity-acoustic waves can be parametrically destabilized by the vibration. The resulting instability is similar to the classic Faraday instability of surface waves, albeit modified by the compressible nature of the fluid. It may be possible to observe experimentally near a gas-liquid critical point.

Abstract:
The present study focus on evolution of compressible vortex ring generated at the open end of a shock tube through accurate measurement of velocity field using Particle Image Velocimetry (PIV). To investigate the unsteady characteristics of embedded shock-free, low Mach number vortex rings, two cases (shock Mach numbers, and ) are considered for PIV measurements. Time-dependent variations of circulation, core and ring diameters, and ring velocity are calculated from the measured velocity field. Pinching-off process is investigated in detail for both cases. Formation time and the time of complete detachment of the vortex ring from the trailing jet are identified from the velocity and vorticity field. The ring formation is complete at about and 1.65 for and 1.37, respectively, where is time, is fluid velocity behind the shock at exit, and is tube diameter. Complete detachment of the vortex ring from the trailing jet is observed at and 2.9 for and 1.37, respectively. 1. Introduction A vortex ring is a bounded region of vorticity in a fluid in which vortex lines form closed loop. A large volume of research has been published on incompressible vortex rings; for extensive reviews, see Shariff and Leonard [1] and Lim and Nickels [2] and the mathematical details are given in Saffman [3], Lamb [4], and Batchelor [5] and experiments [6, 7]. In recent years, there have been several studies in the area of compressible vortex rings [8–10]. These studies deal with various phenomena such as, sound generation associated with the formation of vortex rings, vortex-vortex interactions, and shock-vortex interaction. Compressible vortex ring generated from the open end of a shock tube at high incident shock Mach number ( ) is an important study due to the presence of shock/expansion waves in the flow field and large variations in thermodynamic and physical properties across the vortex ring. Though the generation mechanism is simple, the unsteady nature of the flow field facilitates understanding of many transient, compressible flow events and associated noise generation mechanism. Shock generated compressible vortex ring at the open end of a duct simulates cold flow from a pulsed detonation engine, where a train of propagating waves are used to generate high transient thrust. It also simulates starting flow field from a rocket nozzle, diesel engine exhaust mufflers, and pulse combustors. Compressible vortex ring emerging from the open end of a shock tube is first studied experimentally by Elder and De Hass [11]. Trajectories of the vortex ring and the incident shock are

Abstract:
Three dimensionality of 3D pulsed second sound wave in He II emitted from a finite size heater is experimentally investigated and theoretically studied based on two-fluid model in this study. The detailed propagation of 3D pulsed second sound wave is presented and reasonable agreement between the experimental and theoretical results is obtained. Heater size has a big influence on the profile of 3D second sound wave. The counterflow between the superfluid and normal fluid components becomes inverse in the rarefaction of 3D second sound wave. The amplitude of rarefaction decreases due to the interaction between second sound wave and quantized vortices, which explains the experimental results about second sound wave near [Phys. Rev. Lett. 73, 2480 (1994)]. The accumulation of dense quantized vortices in the vicinity of heater surface leads to the formation of a thermal boundary layer, and further increase of heating duration results in the occurrence of boiling phenomena. PACS numbers: 67.40.Pm 43.25.+y 67.40.Bz

Abstract:
It is shown that in a rotating compressible fluid the resonant frequencies (measured in a system of reference rotating together with the medium) for the azimuthally running acoustic waves are split into two components. The received results can be of practical significance as a basis of a method of measurements of angular speed of medium and for acoustics of rotating technical devices.

Abstract:
We investigate sound propagation in a moving fluid confined in a randomly corrugated tube. For weak randomness and small fluid velocities $v^{(0)}$, the localization length $\xi$ shows extreme sensitivity to the variation of $v^{(0)}$. In the opposite limit of large fluid velocities, $\xi$ acquires a constant value which is independent of the frequency of the incident sound wave, the degree of randomness and $v^{(0)}$ itself. Finally, we find that the standard deviation $\sigma_{\ln T}$ of the logarithm of transmittance $\ln(T)$ is a universal function of the ensemble average $\langle \ln T\rangle $, which is not affected by the fluid velocity.

Abstract:
A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible non-ideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.

Abstract:
The accompanying fluid dynamics videos visualize the temporal evolution of shock structures and sound waves in and around an under-expanded jet that is impinging on a rigid surface at varying pressure ratios. The recordings were obtained at frame rates of 500 kHz to 1 Mhz using a novel pulsed illumination source based on a high power light emitting diode (LED) which is operated in pulsed current mode synchronized to the camera frame rate.

Abstract:
We consider the dynamics of vortex strings and sound waves in superfluids in the phenomenological Landau-Ginzburg equation. We first derive the vortex equation where the velocity of a vortex is determined by the average fluid velocity and the density gradient near the vortex. We then derive the effective action for vortex strings and sound waves by the dual formulation. The effective action might be useful in calculating the emission rate of sound waves by moving vortex strings.

Abstract:
Consider the dynamics of a gas bubble in an inviscid, compressible liquid with surface tension. Kinematic and dynamic boundary conditions couple the bubble surface deformation dynamics with the dynamics of waves in the fluid. This system has a spherical equilibrium state, resulting from the balance of the pressure at infinity and the gas pressure within the bubble. We study the linearized dynamics about this equilibrium state in a center of mass frame: 1) We prove that the velocity potential and bubble surface perturbation satisfy point-wise in space exponential time-decay estimates. 2) The time-decay rate is governed by scattering resonances, eigenvalues of a non-selfadjoint spectral problem. These are pole singularities in the lower half plane of the analytic continuation of a resolvent operator from the upper half plane, across the real axis into the lower half plane. 3) The time-decay estimates are a consequence of resonance mode expansions for the velocity potential and bubble surface perturbations. 4) For small compressibility (Mach number, a ratio of bubble wall velocity to sound speed, \epsilon), this is a singular perturbation of the incompressible limit. The scattering resonances which govern the anomalously slow time-decay, are {\it Rayleigh resonances}. Asymptotics, supported by high-precision numerical studies, indicate that the Rayleigh resonances which are closest to the real axis satisfy | \frac{\Im \lambda_\star(\epsilon)}{\Re \lambda_\star(\epsilon)} | = {\cal O} (\exp(-\kappa\ \We\ \epsilon^{-2})), \kappa>0. Here, \We denotes the Weber number, a dimensionless ratio comparing inertia and surface tension. 5) To obtain the above results we prove a general result, of independent interest, estimating the Neumann to Dirichlet map for the wave equation, exterior to a sphere.

Abstract:
Hydrodynamic interactions are transmitted by viscous diffusion and sound propagation: the temporal evolution of hydrodynamic interactions by both mechanisms is studied by direct numerical simulation in this paper. The hydrodynamic interactions for a system of two particles in a fluid are estimated by the velocity correlation of the particles. In an incompressible fluid, hydrodynamic interactions propagate instantaneously at the infinite speed of sound, followed by the temporal evolution of viscous diffusion. On the other hand, in a compressible fluid, sound propagates at a finite speed, which affects the temporal evolution of the hydrodynamic interactions by the order of magnitude relation between the time scales of viscous diffusion and sound propagation. The hydrodynamic interactions are characterized by introducing the ratio of these time scales as an interactive compressibility factor.