[en] The stability of the spherical shape of the free surface of a gas bubble compressed by an incompressible fluid as it appears in the inertial confinement fusion problem is considered. (i) The equations derived by Prosperetti [Accad. Naz. Lincei 62, 196 (1977)] generalizing the Plesset equation are recovered in cases when the outer fluid is nonviscous, the flow being not potential, and it is shown that vorticity may change drastically the results of the potential case. (ii) In the case of viscous external fluid, the equations derived by Prosperetti [Q. Appl. Math. 1, 399 (1977)] and other external conditions on a sphere of finite radius are derived. (iii) Assuming that the time scale of the dynamics of the spherical bubble is large with respect to the time scale of the perturbation (frozen assumption), the linear stability of the collapsing bubble is studied numerically. The parameters are here (a) an inertia force (related with acceleration R of the radius of the bubble), (b) the Reynolds number built with the decaying rate of the bubble, (c) surface tension, and (d) the aspect ratio (ratio between the gap width of the viscous fluid and the radius of the bubble). It is shown that the spherical shape is always linearly unstable in the absence of surface tension. In the presence of surface tension, there is a critical inertia parameter value and the most dangerous mode is always stationary. For the case of a large surface tension, the spherical wavenumber l of the most dangerous mode, is low. Finally, it is shown that the Rayleigh--Taylor instability might only be observed for both small aspect ratio and Reynolds number, depending on the surface tension

[en] Integration of the compressible Navier--Stokes equations shows that large amplifications of eddy kinetic energy are possible during the cylindrical implosion of two-dimensional randomized eddy structures. In the limit of vanishingly small initial eddy kinetic energy and viscosity, the amplification of the kinetic energy, and the density fluctuations associated with the eddies, is consistent with assumption that the angular momentum of individual eddies is conserved during the implosion. With increasing initial eddy kinetic energy, nonlinear effects reduce the amplification by a factor approximately exponential in the product of the compression and the ratio of the initial eddy kinetic energy to the implosion kinetic energy

[en] High-frequency electromagnetic (EM) fields are investigated for the levitation of thin horizontal sheets of liquid metal. A magnetic configuration is analyzed in which inductance stabilization provides global stability and magnetic flux compression provides local stability. Stability analysis indicates that frequencies greater than about 24 kHz are desirable to stably levitate 6 mm thick steel. For stability in systems without active feedback, a conducting screen is required below the metal, with a gap between the screen and the molten metal of no more than twice the metal thickness. Experiments in which 10 kHz EM fields were used to statically levitate sheets of molten tin indicate that dominant magnetohydrodynamic instabilities are of the Rayleigh--Taylor type and correspond to theory

[en] A systematic study of the hypersonic limit of a heavy species diluted in a much lighter gas is made via the Fokker--Planck equation governing its velocity distribution function. In particular, two different hypersonic expansions of the Fokker--Planck equation are considered, differing from each other in the momentum equation of the heavy gas used as the basis of the expansion: in the first of them, the pressure tensor is neglected in that equation while, in the second expansion, the pressure tensor term is retained. The expansions are valid when the light gas Mach number is O(1) or larger and the difference between the mean velocities of light and heavy components is small compared to the light gas thermal speed. They can be applied away from regions where the spatial gradient of the distribution function is very large, but it is not restricted with respect to the temporal derivative of the distribution function. The hydrodynamic equations corresponding to the lowest order of both expansions constitute two different hypersonic closures of the moment equations. For the subsequent orders in the expansions, closed sets of moment equations (hydrodynamic equations) are given. Special emphasis is made on the order of magnitude of the errors of the lowest-order hydrodynamic quantities. It is shown that if the heat flux vanishes initially, these errors are smaller than one might have expected from the ordinary scaling of the hypersonic closure. Also it is found that the normal solution of both expansions is a Gaussian distribution at the lowest order

[en] Waves that occur at the interface of a thin, horizontal liquid film sheared by a concurrent turbulent gas flow are investigated. Observations using liquids in the range of 13--15 cP indicate that broad-crested, steady, periodic waves appear as the gas velocity is increased above the point of neutral stability. For a sufficiently large gas Reynolds number, steady solitary waves appear. These travel at speeds significantly faster than the periodic waves. However, if the liquid flow rate is increased, solitary waves do not form. To quantitatively describe the waves, a weakly nonlinear wave equation is derived using boundary-layer approximations. The equation is valid for liquid Reynolds numbers of O (1--100) and reveals the presence of both kinematic and dynamic processes, which may (i) act together or (ii) singularly dominate the wave field. For the latter case, reduced forms of the evolution equation are derived. Linear stability analysis of the complete equation and its reduced forms is used to determine the parameter ranges where either dynamic or kinematic processes dominate. The evolution equation in its nonlinear forms should be capable of describing and predicting the amplitudes, shapes, and interactions of finite amplitude waves

[en] The results of large eddy simulation (LES) of the Navier--Stokes equations are used to evaluate the validity of Taylor's hypothesis of frozen turbulence, which states that the time derivative of some instantaneous quantity is proportional to its derivative in the streamwise direction, for incompressible plane channel flow. Time and space derivatives in the streamwise direction of the velocity components are, in fact, found to be well correlated. Root-mean-square fluctuations of the terms in Taylor's hypothesis also support the validity of this hypothesis above the buffer layer. The good agreement between LES and experimental results indicates that errors in the evaluation of derivatives in the streamwise direction are due mostly to insufficient resolution

[en] A series of experiments has been conducted in a lid-driven cavity of square cross section (depth = width = 150 mm) for Reynolds numbers (Re, based on lid speed and cavity width) between 3200 and 10 000, and spanwise aspect ratios (SAR) between 0.25:1 and 1:1. Flow visualization using polystyrene beads and two-dimensional laser-Doppler anemometer (LDA) measurements have shed new light on the momentum transfer processes within the cavity. This paper focuses on the variation, with Re and SAR, of the mean and the rms velocities profiles, as well as the /similar to/(U'V') profile, along the horizontal and vertical centerlines in the symmetry plane. In addition, the contribution of the large-scale ''organized structures,'' and the high-frequency ''turbulent'' velocity fluctuations to the total rms is examined. At low Re, the organized structures account for most of the energy contained in the flow irrespective of SAR. As the Re increases, however, so does the energy content of the higher frequency fluctuations. This trend is not independent of SAR; a reduction in the SAR causes the ''organized structures'' to again become more evident

[en] Very little attention has been given, so far, to the problem of the propagation of axisymmetric second-sound shock waves, although they may occur in practical applications. In this paper, research on the propagation of moderate cylindrical heat pulses in superfluid helium is reported. A theoretical model is built based on the experimental observation of the evolution of the structure of rectangular heat pulses. The agreement between the experimental measurements and the theoretical calculations of the evolution of the main parameters is very satisfactory

[en] It is shown that the hypothesis of independent increments for velocity, which is widely used by many authors [e.g., A. M. Obukhov, Adv. Geophys. 6, 113 (1959)] in the Lagrangian description of turbulence, is inconsistent with the Navier--Stokes equations in a fundamental way. A more general Lagrangian description of turbulent velocity such as the Markov process with dependent increments, which recognizes the condition of incompressibility and the important phenomenon of intermittency, is proposed. A model of intermittent relative motion of fluid particles in turbulent flow is presented. The high-order Lagrangian moments and the probability distribution are obtained. The distribution for the intermittent vorticity is also proposed

[en] Combining the reversibility of advection by a Stokes flow with the irreversibility of diffusion leads to a separation strategy for diffusing substances. This basic idea goes back to Taylor and Heller. It is shown here that the sensitivity of the method can be greatly enhanced by making the advection chaotic. The separation is particularly efficient when the thinnest structures resulting from advection are made comparable in size to a diffusion length. Simple heuristic estimates based on an understanding of chaotic motion and diffusion lead to a certain scaling that is seen in numerical experiments on this separation method