The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Monika Nitsche - One of the best experts on this subject based on the ideXlab platform.
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singularity formation in a cylindrical and a spherical vortex sheet
Journal of Computational Physics, 2001Co-Authors: Monika NitscheAbstract:Abstract The evolutions of the planar and Axisymmetric vortex sheets generated by the impulsive motion of a cylinder and a sphere, respectively, are compared numerically. The numerical method addresses difficulties that occur in the Axisymmetric case near the axis of symmetry. The planar vortex sheet is known to develop a branch point singularity in finite time. Comparison of the planar and Axisymmetric solutions indicates that the Axisymmetric sheet develops a branch point singularity as well, and that it is of the same order p as the planar singularity. The value of p is consistent with 3/2.
Steven A. Balbus - One of the best experts on this subject based on the ideXlab platform.
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Axisymmetric and non-Axisymmetric magnetostrophic MRI modes
Physics of the Earth and Planetary Interiors, 2013Co-Authors: Ludovic Petitdemange, Emmanuel Dormy, Steven A. BalbusAbstract:Abstract The magnetorotational-instability is central to the understanding of many astrophysical magnetohydrodynamic flows (in particular accretion discs). We have recently shown that a modified version of this instability, the magnetostrophic MRI (MS-MRI), is relevant to the dynamics of the Earth liquid core ( Petitdemange et al., 2008 ). Our previous study used a purely axial imposed magnetic field and considered only Axisymmetric instabilities. We investigate here the effects of a large scale toroidal magnetic field on the development and saturation of the MS-MRI both in an Axisymmetric setup and in fully three-dimensional configurations. We use direct numerical modeling of the full MHD equations (both in the linear and non-linear regimes) in a spherical geometry. We interpret our results using WKB expansions and shearing coordinates. We find that three-dimensional MS-MRI modes exhibit a strong helical structure for parameters relevant to planetary interiors. Three-dimensional MS-MRI modes share some similarities with their Axisymmetric counterparts. They are amplified on the same short timescale. When non-linear effects become significant, they act to decrease the shear. During saturation, the magnetic structure expands spatially, while drifting at a constant rate along the direction of the rotation axis. A striking result is that an m = 1 mode can dominate in the non-linear regime when a sufficiently large toroidal field is present. Three-dimensional MS-MRI modes could play an important role in planetary interior dynamics. They can cause rapid magnetic field variations and also act to limit the shear in the conducting liquid core.
James G. Simmonds - One of the best experts on this subject based on the ideXlab platform.
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An asymptotic analysis of end effects in the Axisymmetric deformation of elastic tubes weak in shear: Higher-order shell theories are inadequate and unnecessary☆
International Journal of Solids and Structures, 1992Co-Authors: James G. SimmondsAbstract:Abstract This paper specializes to a semi-infinite tube Morgan's (Int. J. Solids Structures10, 837–852, 1974) two-stress-function formulation of the equations for the Axisymmetric deformation of a linearly elastic transversely isotropic cylindrical body free of surface tractions. The ratio of the tube's shear modulus to its radial (transverse) extensional modulus is taken to be of the order of magnitude of the square root of its thickness to its mean radius. The equations are solved by formal asymptotic expansion in (fractional) powers of the thickness to radius ratio for four canonical sets of end conditions: (A) axisymmctric equilibrated tractions : (B) and (C). two different combinations of tractions and displacements: and (D) axisymmctric radial and axial displacements. The solutions exhibit interior (i.e. shell-like) parts and wide and narrow boundary (or edge) layers, the latter containing components that vary extremely rapidly through the thickness of the tube. The analysis focuses on computing the lowest-order correction, both in the interior and in the boundary layers, to classical shell theory. It is shown that in cases (A)- (C) the interior correction to classical shell theory—that is, those effects so-called higher-order shell theories attempt to capture—can (ultimately) be determined directly, in terms of the edge data, but that in case of prescribed displacements (D), the computation of (three-dimensional) boundary-layer effects is essential. These conclusions are consistent with those for elastically isotropic shells found by Gregory and Wan (1992) who used ingenious arguments based on the Betti Reciprocity Principle.
Andrew W Cary - One of the best experts on this subject based on the ideXlab platform.
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Axisymmetric and Non-Axisymmetric Initiation of Vortex Breakdown
2003Co-Authors: Andrew W Cary, David L DarmofalAbstract:Abstract : The onset of Axisymmetric (bubble) and non-Axisymmetric (spiral) modes of breakdown is studied numerically for swirling pipe flows. The authors have found that the onset of Axisymmetric vortex breakdown occurs when the vortex attains local criticality. A transient simulation of the evolution of vortex breakdown revealed that downstream-running waves are trapped approximately at the location of flow criticality. These trapped waves are slowly amplified and eventually result in the bubble breakdown region with reversed flow and enlarged core size. Non-Axisymmetric disturbances were found to decay on columnar base flows; however, for base flows with bubble breakdown, non-Axisymmetric disturbances were amplified. These amplified disturbances resulted in the formation of spiral breakdown. If the base flow inlet swirl was only slightly larger than that leading to Axisymmetric breakdown, a nearly columnar solution was obtained, suggesting that weak asymmetry may help to stabilize the columnar solution branch. The numerical simulations also revealed that most of the energy in spiral breakdown is contained in the first few non-Axisymmetric modes of variation. (10 figures, 38 refs.)
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Evolution of Asymmetries in Vortex Breakdown
29th AIAA Fluid Dynamics Conference, 1998Co-Authors: Andrew W Cary, David L Darmofal, Kenneth G PowellAbstract:The influence of weak asymmetric disturbances on an Axisymmetric swirling flow is examined through numerical simulation. To track the evolution of asymmetries, the incompressible Navier-Stokes equations are Fourier-decomposed in the azimuthal direction and integrated forward in time. Beginning with an Axisymmetric solution, an asymmetric disturbance is added at the inlet of a converging-diverging nozzle and allowed to propagate. For Axisymmetric flows which do not exhibit vortex breakdown, the disturbance is merely convected and dissipated. The presence of Axisymmetric breakdown, however, amplifies the disturbance and large changes occur in the flow structures. Depending on the Axisymmetric swirl ratio, non-Axisymmetric solutions range from no apparent breakdown, to the spiral mode, and, at larger swirl ratios, to an oscillation between the spiral mode and the bubble mode. For swirl ratios corresponding to a weak Axisymmetric breakdown, asymmetry creates a "relieving effect" which eliminates the recirculation zone, resulting in a smooth solution with only weak asymmetries.
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onset of the spiral mode of vortex breakdown
35th Aerospace Sciences Meeting and Exhibit 1997, 1997Co-Authors: Andrew W Cary, David L Darmofal, Kenneth G PowellAbstract:The three-dimensional nature of vortex breakdown, while widely recognized, has seldom been included in the analytical investigations and, until recently, the numerical simulations of this phenomenon. The principle asymmetric effects are examined by considering the impact that a weak perturbation has on an Axisymmetric vortex. It is demonstrated that large Axisymmetric strain rates are required for a non-Axisymmetric perturbation to grow. Simulations bear out this fact by showing significant asymmetric behavior only after a critical swirl is exceeded which leads to breakdown in an Axisymmetric flow. This result supports previous investigations which predict breakdown for an Axisymmetric flow, despite their inability to fully capture the complexity of the breakdown topology. Furthermore, this finding indicates that vortex breakdown may be a predominantly Axisymmetric occurrence which is complicated by three-dimensional effects.
A.-m. Zhang - One of the best experts on this subject based on the ideXlab platform.
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An accurate SPH Volume Adaptive Scheme for modeling strongly-compressible multiphase flows. Part 2: Extension of the scheme to cylindrical coordinates and simulations of 3D Axisymmetric problems with experimental validations
Journal of Computational Physics, 2020Co-Authors: P.-n. Sun, D. Le Touzé, Guillaume Oger, A.-m. ZhangAbstract:Abstract The present work is dedicated to extending the strongly-compressible multiphase SPH Volume Adaptive Scheme (see [22] ) from Cartesian to cylindrical polar coordinates for addressing Axisymmetric problems. By omitting the gradient in the circumferential direction, an Axisymmetric-SPH model is developed. Three-dimensional Axisymmetric problems including rising bubbles, expanding or collapsing bubbles are conveniently and efficiently simulated using the proposed Axisymmetric-SPH model. Contrary to the purely three-dimensional SPH model established in Cartesian coordinates, with the Axisymmetric model, sufficient particle resolutions can be easily adopted to reach converged simulations of complex problems. Axisymmetric-SPH results are validated either using experimental data or other numerical results. In the Axisymmetric-SPH model, a convenient and effective way of avoiding singularity at the axis is presented. In addition, the Volume Adaptive Scheme (VAS), originally developed for compressible flow simulations with large volume variations in Cartesian coordinates, is shown to be a crucial tool to adjust particle volumes in the Axisymmetric-SPH model for all flow cases, including both weakly-compressible and strongly-compressible flows.
