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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
    Spiral wave drift induced by stimulating wave trains (2001)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 11 (2001), S. 487-494 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We investigate the drift of a spiral wave core in a homogeneous excitable medium under the influence of a periodic stimulation by wave trains close to the core. Two important results were found. First, as opposed to existing theories of spiral wave drift, we observe drift induced by wave trains with periods larger than the period of the freely rotating spiral wave. Second, when investigating the drift of meandering spirals we found that the property of meandering of spirals is not robust against periodic stimulations. Simple phenomenological arguments are provided to explain these observations. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1395624
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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Vortex dynamics and the existence of solutions to the Navier–Stokes equations (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1606-1626 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Biot–Savart model for a vortex filament predicts a finite time singularity in which the maximum velocity diverges as (t*−t)−1/2 for the time t tending to t*. The filament pairs with itself, yet remains locally smooth even though the characteristic length scales as (t*−t)1/2. A multiscale perturbative treatment of the Euler equations is developed for solutions that are locally a two-dimensional vortex dipole centered on a slowly varying three-dimensional space curve. For short periods of time the Euler and Biot–Savart solutions agree. Provided this correspondence persists, a sufficiently small viscosity ν will not control the divergence in the maximum velocity until it is of order exp(cst/ν), where cst is a constant of order the filament circulation. Singularities in the Navier–Stokes equations cannot be easily dismissed. The most questionable step in the arguments presented occurs for ν=0, namely whether the Euler vortex dipole solutions break down when they self-stretch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866226
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  • 8
    Electronic Resource
    Electronic Resource
    Turbulence in homogeneous shear flows (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 3112-3127 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Homogeneous shear flows with an imposed mean velocity U=Syxˆ are studied in a period box of size Lx×Ly×Lz, in the statistically stationary turbulent state. In contrast with unbounded shear flows, the finite size of the system constrains the large-scale dynamics. The Reynolds number, defined by Re≡SL2y/ν varies in the range 2600≤Re≤11300. The total kinetic energy and enstrophy in the volume of numerical integration have large peaks, resulting in fluctuations of kinetic energy of order 30%–50%. The mechanism leading to these fluctuations is very reminiscent of the "streaks'' responsible for the violent bursts observed in turbulent boundary layers. The large scale anisotropy of the flow, characterized by the two-point correlation tensor 〈uiuj〉 depends on the aspect ratio of the system. The probability distribution functions (PDF) of the components of the velocity are found to be close to Gaussian. The physics of the Reynolds stress tensor, uv, is very similar to what is found experimentally in wall bounded shear flows. The study of the two-point correlation tensor of the vorticity 〈ωiωj〉 suggests that the small scales become isotropic when the Reynolds number increases, as observed in high Reynolds number turbulent boundary layers. However, the skewness of the z component of vorticity is independent of the Reynolds number in this range, suggesting that some small scale anisotropy remains even at very high Reynolds numbers. An analogy is drawn with the problem of turbulent mixing, where a similar anisotropy is observed. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869100
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  • 9
    Electronic Resource
    Electronic Resource
    A model of bubble dynamics in a Hele–Shaw cell (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 752-763 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A model of the interaction of small, well-separated bubbles of one fluid propagating through another "resident'' fluid in a Hele–Shaw cell is introduced and studied. In the model each bubble acts on the others by setting up a velocity field of the dipole type. A system of ordinary differential equations is developed for the bubble positions. The system is solved completely for the two-bubble problem. The three-bubble problem is addressed by numerical simulations. A set of self-similar motions are also found analytically. The dynamics of rows of bubbles is investigated analytically and via numerical simulations. Although clearly an extreme idealization, the model appears to shed considerable light on what to expect in laboratory experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866811
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  • 10
    Electronic Resource
    Electronic Resource
    A model of wave dynamics in the far wake of a cylinder (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 1969-1979 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Interesting interactions in the far wake behind a cylinder, leading in particular to the appearance of a strong secondary oblique wave, have recently been discovered experimentally by Williamson and Prasad [J. Fluid Mech. 256, 269, 315 (1993)]. They are induced from a very small amount of noise, added to the decaying primary wave. The problem is investigated theoretically with simple amplitude equations, based on temporal instability of the small amplitude waves. The symmetry of the wake flow requires that quadratic interactions arise only among triads of wave numbers involving one varicose and two sinuous waves, or three varicose waves. As the primary wave, corresponding to vortex shedding, is sinuous, the interacting secondary waves must be of opposite parities. In this case, it is found that the sinuous wave will always prevail downstream. The preferential appearance of the secondary oblique wave in the far wake can be reproduced by letting an initially very small varicose parallel wave interact with the primary wave. The secondary oblique wave results from a classical three-wave, quadratic nonlinear interaction between the waves. In addition, our model reproduces the observation that upon increasing the noise amplitude the oblique wave appears sooner (further upstream) in the wake. The occurrence of parallel waves very far downstream, which depends on the frequency relationship between the waves, can be understood by considering the interactions between parallel and oblique secondary waves of both parities. We propose a reasonable scenario explaining the experimental observations of Williamson and Prasad. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869316
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