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[en] Benard convection, in containers with large aspect ratio, exhibits space-filling cellular patterns, with the degree of disorder varying with the temperature difference driving the convective instability. I shall show that the structure of cellular networks can be explained by elementary topological transformations (which act like collisions in statistical mechanics to keep the network in statistical equilibrium, but also govern the motion of topological dislocations in the network). I shall also discuss the dynamics of cells in the network, in terms of a (molecular dynamics) modelization by Telley, and show why such a simple model can also be realistic. This work relates to the subject ''geometry and topology of stirred fluid regions'' mentioned in the announcements for the Symposium. [Work at Argonne supported by U.S. Department of Energy Contract No. W-31-109-ENG-38.]

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[en] Linearized Euler equations of a general stationary multiple layer stratified system for both compressible and incompressible inviscid fluids are analyzed. The main result is that many features of a multilayer system are universal, in the sense they do not depend on such details as the number of layers, their thicknesses, equations of state for the fluids, and equilibrium density distributions. Necessary and sufficient conditions of stability are determined. For compressible fluids, it is possible for the system to be unstable even if there is no density inversion anywhere. It is shown that a compressible system is always more unstable than the corresponding incompressible one. A universal upper bound for the growth rate for a given perturbation wave number is given. General Rayleigh--Taylor unstable modes are characterized, and the range of unstable wave numbers is determined. Properties of stable modes are discussed. Numerical algorithms for solving the eigenvalue problem of the set of linearized Euler equations are given

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[en] A study of the interaction of an electrostatic field with a thin liquid film flowing under gravity down an inclined plane is presented. First, the effect of the electric field on the stability of the film flow is examined. Next, several limits of the equations of motion are investigated analytically, and then compared with an explicit numerical calculation of the equations of motion. Also, applications of these calculations to a proposed electrostatic liquid film space radiator are discussed

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[en] The results of detailed numerical simulations of the Richtmyer--Meshkov instability of the interface between layers of air and either helium or SF

_{6}in a shock tube are reported. Two- and three-dimensional simulations based on both the Euler and Navier--Stokes equations were obtained by a finite difference method that employs a front-tracking technique to keep the interface sharp. The nature of the flow patterns induced by the instability is discussed. The results of a numerical resolution study and a demonstration of the influence of boundary layers are presented also. Agreement with experimental data is found to be satisfactory, with the exception of the initial instability growth ratePrimary Subject

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[en] The problem of a dynamic liquid bridge between moving parallel plates is introduced. For the case of the Stokes flow in a cylindrical bridge driven by a slow change of the distance between the plates, an exact infinite-series solution is constructed, without invoking the lubrication approximation which was never surmounted in previous theories of dynamic liquid bridges. The boundary conditions at the free surface are fully satisfied, and the singularities of physical quantities at the moving contact line are avoided by allowing a minute but nonzero slip velocity. It is shown that, for narrower bridges, the ''nonlubricative'' contribution to hydrodynamic forces may become comparable with the force associated with the lubrication approximation

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[en] Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

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[en] Exact solutions are presented for a steady stream of bubbles in a Hele--Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area and distance between bubbles, the speed of the bubble remains arbitrary when surface tension is neglected. However, numerical and analytical evidence indicates that this arbitrariness is removed by the effect of surface tension. The branch of solutions that corresponds to the McLean--Saffman finger solution were primarily studied. A dramatic increase was observed in bubble speeds when the distance between bubbles is on the order of a bubble diameter, which may have relevance to experiments done by Maxworthy [J. Fluid Mech. 173, 95 (1986)]

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[en] The effect of anisotropic dispersion on nonlinear viscous fingering in miscible displacements is examined. The formulation admits dispersion coefficient-velocity field couplings (i.e., mechanical dispersivities) appropriate to both porous media and Hele--Shaw cells. A Hartley transform-based scheme is used to numerically simulate unstable miscible displacement. Several nonlinear finger interactions were observed. Shielding, spreading, tip splitting, and pairing of viscous fingers were observed here, as well as in isotropic simulations. Multiple coalescence and fading were observed in simulations with weak lateral dispersion, but not for isotropic dispersion. Transversely and longitudinally averaged one-dimensional concentration histories demonstrate the rate at which the mixing zone broadens and the increase in lateral scale as the fingers evolve when no tip splitting occurs. These properties are insensitive to both the dispersion anisotropy and the Peclet number at high Peclet number and long times. This suggests the dominance of finger interaction mechanisms that are essentially independent of details of the concentration fields and governed fundamentally by pressure fields

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[en] The linear stability of core-annular flow in rotating pipes is analyzed. Attention is focused on the effects of rotating the pipe and the difference in density of the two fluids. Both axisymmetric and nonaxisymmetric disturbances are considered. Major effects of the viscosity ratio, interfacial tension, radius ratio, and Reynolds number are included. It is found that for two fluids of equal density the rotation of the pipe stabilizes the axisymmetric (n=0) modes of disturbances and destabilizes the nonaxisymmetric modes. Except for small R, where the axisymmetric capillary instability is dominant, the first azimuthal mode of disturbance |n|=1 is the most unstable. When the heavier fluid is outside centripetal acceleration of the fluid in the rotating pipe is stabilizing; there exists a critical rotating speed above which the flow is stabilized against capillary instability for certain range of small R. When the lighter fluid is outside the flow is always unstable

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[en] One of the principal shortcomings of the computer models that are presently used for two-dimensional explosive engineering design is their inadequate treatment of the explosive's detonation reaction zone. Current methods lack the resolution to both calculate the broad gas expansion region and model the thin reaction zone with reasonable detail. Recently an alternative method for modeling the reaction zone has been developed. This method applies when the radius of curvature of the shock is large compared to the reaction-zone length. In this limit, the dynamics of the interaction between the chemical heat release and the two-dimensional flow in the reaction zone is quasisteady. It is summarized by a relation D/sub n/(κ), between the local normal shock velocity D/sub n/ and shock curvature κ. When this relation is combined with the kinematic surface condition (an equation that describes how disturbances move along the shock), the two-dimensional reaction-zone calculation is reduced to a one-dimensional calculation

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