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  • 1
    Electronic Resource
    Electronic Resource
    Development of singular solutions to the axisymmetric Euler equations (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1472-1491 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A variety of initially smooth axisymmetric flows with swirl are simulated with a variable mesh, finite-difference code with particular attention paid to the production of large (divergent) vorticity. Away from the symmetry axis, the evolution is entirely consistent with expectations based on the isomorphism with two-dimensional convection. Vortex sheets form on the leading face of "plumes'' and their trailing edges roll up. When a "plume'' begins to fission, a cusp develops at the cleavage point via a Rayleigh–Taylor-like instability and the maximum (three-dimensional) vorticity diverges, approximately, as inverse time squared. For technical reasons, the Boussinesq approximation was employed for this part of the simulation which observed, overall, a 106 increase in vorticity. The diverging strain was generated progressively more locally, justifying the approximation. Analytic estimates are provided which significantly constrain the singular solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858422
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  • 2
    Electronic Resource
    Electronic Resource
    Effect of an externally applied electric field on excitation propagation in the cardiac muscle (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 4 (1994), S. 547-555 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Classical theory of potential distribution in cardiac muscle (cable theory) postulates that all effects of electric field (internally or externally applied) should decay exponentially with a space constant of the order of the tissue space constant (∼1 mm). Classical theory does not take into account the cellular structure of the heart. Here, we formulate a mathematical model of excitation propagation taking into account cellular gap junctions. Investigation of the model has shown that the classical description is correct on the macroscopic scale only. At microscopic scale, electric field is modulated with a spatial period equal to the cell size (Plonsey and Barr), with the zero average. A very important new feature found here is that this effect of electric field does not decay at arbitrary big distances from the electrode. It opens the new way to control the excitation propagation in the cardiac muscle. In particular, we show that electric field can modify the velocity of propagation of an impulse in cardiac tissue at arbitrary big distances from electrode. In 2-dimensions, it can make rotating waves drift. To test these predictions, experiments with cardiac preparations are proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166046
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  • 3
    Electronic Resource
    Electronic Resource
    Small-scale properties of scalar and velocity differences in three-dimensional turbulence (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 3974-3984 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Turbulent flows are known to concentrate strong vorticity in vortex tubes, giving rise to large velocity jumps across the tubes. When a passive scalar is advected by the flow, very steep scalar fronts separate well-mixed regions, and result in large scalar differences. The properties of these large jumps are investigated by studying the probability distribution functions of velocity, scalar differences as a function of the separation between the points, of the Reynolds and of the Prandtl number. Over the range of parameters covered by the direct numerical simulations reported here (20≤Rλ≤90 and 1/32≤Pr≤1), it is found that the widths of the velocity (respectively, the scalar) jumps scale like the Kolmogorov length (respectively, like the Batchelor length). For both the scalar and the velocity, the large differences over small distance become rarer as the Reynolds number increases. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868387
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  • 4
    Electronic Resource
    Electronic Resource
    A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2118-2132 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The mixing of a passive scalar in the presence of a mean gradient is studied in three dimensions by direct numerical simulations. The driving velocity field is either a solution of the three-dimensional (3-D) Navier–Stokes equations, at a microscale Reynolds number in between 20 and 70, and with a Prandtl number varying between 1/8 and 1, or a solution of the Euler equation restricted to a shell of wave numbers, which formally corresponds to an infinite Prandtl number. The probability distribution function (PDF) of the scalar gradients parallel and perpendicular to the direction of the mean gradient are studied. The gradients parallel to the mean gradient have a skewness of order 1 in the range of Péclet number considered. The PDFs are sharply peaked and their maxima correspond to a perfect mixing of the scalar. The PDF of the scalar gradient perpendicular to the mean gradient are reasonably well fit by stretched exponentials. Similar properties are observed for the restricted Euler model. In physical space, the scalar is well mixed in large domains, separated by narrow regions, where very large gradients concentrate. These "cliffs'' are found to sit in regions where the flow is hyperbolic, whereas the scalar gradients are much weaker where the flow is elliptic. The present results are generally in agreement with the conclusions reached in a comparable study in two dimensions by Holzer and Siggia (to appear in Phys. Fluids). The stretching acting on the scalar is studied by computing various correlations between scalar gradient and velocity derivatives, as well as the correlations between vorticity and scalar gradient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868216
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  • 5
    Electronic Resource
    Electronic Resource
    Collapsing solutions to the 3-D Euler equations (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 220-241 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A three-dimensional adaptive mesh code is used to search for singularities in the incompressible Euler equations. For the initial conditions examined, the maximum vorticity eventually grows only exponentially. The small scales are quasi-two-dimensional and the vorticity has a pronounced tendency to develop sharp jumps in magnitude. The vorticity is very nearly parallel to the eigenvector of the rate-of-strain matrix whose eigenvalue is the smallest in magnitude. This eigenvalue is positive and much smaller than the others.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857824
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  • 6
    Electronic Resource
    Electronic Resource
    A numerical study of pressure fluctuations in three-dimensional, incompressible, homogeneous, isotropic turbulence (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2071-2083 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Pressure fluctuations in incompressible turbulence are studied by direct numerical simulations of the three-dimensional (3-D) Navier–Stokes equations. The pressure probability distribution function (PDF) is shown to have an exponential tail on the negative side, and to be independent of the Reynolds number for Reλ(approximately-less-than)60. At higher Reynolds numbers, the low pressure part of the pressure PDF becomes super exponential. The joint PDFs of strain, vorticity, and pressure (considered pairwise) show a strong dissymmetry between positive and negative pressure fluctuations. The results obtained from the numerical solutions of the Navier–Stokes equations are compared with a Gaussian velocity field. The two statistical ensembles are shown to lead to quantitatively different results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868213
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  • 7
    Electronic Resource
    Electronic Resource
    Formation and interaction of intense vortex sheets in 3-dimensional, incompressible, hydrodynamics (1994)
    Springer
    Meccanica 29 (1994), S. 343-350 
    Details
    ISSN: 1572-9648
    Keywords: Turbulent flows ; Singularities ; Vortex dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Sono considerate varie questioni correlate con la fisica dei flussi non-viscosi. La nascita di strati di forti vortici è stata ripetutamente osservata nella simulazione delle equazioni tridimensionali, per diverse condizioni iniziali. Nel caso di flussi di Eulero assialsimmetrici, l'origine di questi piani può essere facilmente compresa con l'aiuto di una analogia con i flussi guidati termicamente. Viene inoltre proposto un più generale meccanismo per giustificare questi strati e si passano in rassegna brevemente questioni riguardanti le singolarità. Infine, vengono presentati alcuni risultati preliminari sulla connessione tra i piani formantisi in flussi non viscosi ed i vortici tubolari osservati nei flussi ad alti numeri di Reynolds.
    Notes: Abstract Various questions related to the physics of inviscid flows are reviewed. The emergence of strong vortex sheets has repeatedly been observed in the simulation of the 3-dimensional equations, with a variety of initial conditions. In the case of axisymmetric Euler flows, the origin of these sheets can be easily understood with the help of an analogy with thermally driven flows. A more general mechanism to explain these sheets is proposed. Questions of singularities are briefly reviewed. Lastly, preliminary results on the connection between the sheets forming in inviscid flows, and the vortex tubes observed in high Reynolds number flows are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00987569
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  • 8
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    Exponential tails and random advection (1991)
    American Physical Society
    Details
    Publication Date: 1991-06-10
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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  • 9
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    Finite-time singularities in the axisymmetric three-dimension Euler equations (1992)
    American Physical Society
    Details
    Publication Date: 1992-03-09
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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  • 10
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    A numerical study of pressure fluctuations in three‐dimensional, incompressible, homogeneous, isotropic turbulence (1994)
    American Institute of Physics
    Details
    Publication Date: 1994-06-01
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
    Published by American Institute of Physics
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