CaltechAUTHORS: Combined
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 12 Nov 2024 13:20:45 -0800On the two-dimensional stability of the axisymmetric Burgers vortex
https://resolver.caltech.edu/CaltechAUTHORS:PROpof95
Year: 1995
DOI: 10.1063/1.868495
The stability of the axisymmetric Burgers vortex solution of the Navierâ€“Stokes equations to two-dimensional perturbations is studied numerically up to Reynolds numbers, R=Gamma/2pinu, of order 104. No unstable eigenmodes for azimuthal mode numbers n=1,..., 10 are found in this range of Reynolds numbers. Increasing the Reynolds number has a stabilizing effect on the vortex.https://resolver.caltech.edu/CaltechAUTHORS:PROpof95Structure and stability of non-symmetric Burgers vortices
https://resolver.caltech.edu/CaltechAUTHORS:PROjfm98
Year: 1998
We investigate, numerically and analytically, the structure and stability of steady and quasi-steady solutions of the Navierâ€“Stokes equations corresponding to stretched vortices embedded in a uniform non-symmetric straining field, ([alpha]x, [beta]y, [gamma]z), [alpha]+[beta]+[gamma]=0, one principal axis of extensional strain of which is aligned with the vorticity. These are known as non-symmetric Burgers vortices (Robinson & Saffman 1984). We consider vortex Reynolds numbers R=[Gamma]/(2[pi]v) where [Gamma] is the vortex circulation and v the kinematic viscosity, in the range R=1[minus sign]104, and a broad range of strain ratios [lambda]=([beta][minus sign][alpha])/([beta]+[alpha]) including [lambda]>1, and in some cases [lambda][dbl greater-than sign]1. A pseudo-spectral method is used to obtain numerical solutions corresponding to steady and quasi-steady vortex states over our whole (R, [lambda]) parameter space including [lambda] where arguments proposed by Moffatt, Kida & Ohkitani (1994) demonstrate the non-existence of strictly steady solutions. When [lambda][dbl greater-than sign]1, R[dbl greater-than sign]1 and [epsilon][identical with][lambda]/R[double less-than sign]1, we find an accurate asymptotic form for the vorticity in a region 11. An iterative technique based on the power method is used to estimate the largest eigenvalues for the non-symmetric case [lambda]>0. Stability is found for 0[less-than-or-eq, slant][lambda][less-than-or-eq, slant]1, and a neutrally convective mode of instability is found and analysed for [lambda]>1. Our general conclusion is that the generalized non-symmetric Burgers vortex is unconditionally stable to two-dimensional disturbances for all R, 0[less-than-or-eq, slant][lambda][less-than-or-eq, slant]1, and that when [lambda]>1, the vortex will decay only through exponentially slow leakage of vorticity, indicating extreme robustness in this case.https://resolver.caltech.edu/CaltechAUTHORS:PROjfm98