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Axisymmetry

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H M Blackburn – One of the best experts on this subject based on the ideXlab platform.

  • three dimensional instability and state selection in an oscillatory axisymmetric swirling flow
    Physics of Fluids, 2002
    Co-Authors: H M Blackburn

    Abstract:

    Previous studies of the flow created inside a cylindrical cavity (radius R, height H) of fluid by a single rotating end wall have shown that over a range of cylinder aspect ratios 1.6≲H/R≲2.8, the first unsteady flows to bifurcate with increasing Reynolds number retain Axisymmetry, and subsequent bifurcations break Axisymmetry to give solutions with modulated rotating wave (MRW) states. The underlying axisymmetric components of these MRW flows are nearly indistinguishable from corresponding axisymmetric flows at the same Reynolds numbers. Of the three solution branches so far identified for this flow at H/R=2.5, only one both supports MRWs and has a simple limit-cycle underlying axisymmetric flow. Here, we carry out three-dimensional Floquet stability analysis of this branch of axisymmetric solutions and demonstrate that only a subset of the linearly unstable MRWs are observed asymptotically at large times for full Navier–Stokes solutions. Stability analysis of the time-average axisymmetric flow shows rot…

Wei Yao – One of the best experts on this subject based on the ideXlab platform.

  • asymptotic Axisymmetry of the subsonic traveling waves to the gross pitaevskii equation
    Communications in Contemporary Mathematics, 2011
    Co-Authors: Juncheng Wei, Wei Yao

    Abstract:

    In this paper we show the asymptotic Axisymmetry of subsonic traveling waves of finite energy to the Gross–Pitaevskii equation. In particular, using a new Hamiltonian identity, we prove that the momentum in the orthogonal directions must vanish.

  • ASYMPTOTIC Axisymmetry OF THE SUBSONIC TRAVELING WAVES TO THE GROSS–PITAEVSKII EQUATION
    Communications in Contemporary Mathematics, 2011
    Co-Authors: Juncheng Wei, Wei Yao

    Abstract:

    In this paper we show the asymptotic Axisymmetry of subsonic traveling waves of finite energy to the Gross–Pitaevskii equation. In particular, using a new Hamiltonian identity, we prove that the momentum in the orthogonal directions must vanish.

Arash Kheradvar – One of the best experts on this subject based on the ideXlab platform.

  • Effect of the Mitral Valve’s Anterior Leaflet on Axisymmetry of Transmitral Vortex Ring.
    Annals of Biomedical Engineering, 2015
    Co-Authors: Ahmad Falahatpisheh, Niema M. Pahlevan, Arash Kheradvar

    Abstract:

    The shape and formation of transmitral vortex ring are shown to be associated with diastolic function of the left ventricle (LV). Transmitral vortex ring is a flow feature that is observed to be non-axisymmetric in a healthy heart and its inherent asymmetry in the LV assists in efficient ejection of the blood during systole. This study is a first step towards understanding the effects of the mitral valve’s anterior leaflet on transmitral flow. We experimentally study a single-leaflet model of the mitral valve to investigate the effect of the anterior leaflet on the Axisymmetry of the generated vortex ring based on the three-dimensional data acquired using defocusing digital particle image velocimetry. Vortex rings form downstream of a D-shaped orifice in presence or absence of the anterior leaflet in various physiological stroke ratios. The results of the statistical analysis indicate that the formed vortex ring downstream of a D-shaped orifice is markedly non-axisymmetric, and presence of the anterior leaflet improves the ring’s Axisymmetry. This study suggests that the improvement of Axisymmetry in presence of the anterior leaflet might be due to coupled dynamic interaction between rolling-up of the shear layer at the edges of the D-shaped orifice and the borders of the anterior leaflet. This interaction can reduce the non-uniformity in vorticity generation, which results in more axisymmetric behavior compared to the D-shaped orifice without the anterior leaflet.

  • A measure of Axisymmetry for vortex rings
    European Journal of Mechanics B-fluids, 2014
    Co-Authors: Ahmad Falahatpisheh, Arash Kheradvar

    Abstract:

    Abstract There are many conditions in which a vortex ring deviates from Axisymmetry. The shape of a three dimensional vortex ring represents the Axisymmetry of propulsion, which has applications in animal locomotion (e.g., the free-swimming of a jellyfish), rocket and marine propulsion devices as well as blood flow through the heart valves. No fluid dynamics’ measure is yet defined to quantify the Axisymmetry of a three dimensional vortex ring with a single value. The non-Axisymmetry exists, for instance, in the vortex ring formed downstream of the mitral valve of healthy hearts, and helps efficient blood momentum transfer from the left atrium toward the aorta. Here, we introduce an index that measures the deviation of a vortex ring from Axisymmetry. This index examines the spectrum of the impulse of a naturally-formed vortex ring and expresses the deviation from Axisymmetry in terms of the vortex’s impulse. We show that the Axisymmetry index is related to the second moment of the vorticity distribution of the ring, i.e., as the second moment of vorticity on one side increases compared to the other side, the Axisymmetry index decreases accordingly.