Prochazka, Aurelius and Pullin, D. I. (1998) Structure and stability of nonsymmetric Burgers vortices. Journal of Fluid Mechanics, 363 . pp. 199228. ISSN 00221120. https://resolver.caltech.edu/CaltechAUTHORS:PROjfm98

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Abstract
We investigate, numerically and analytically, the structure and stability of steady and quasisteady solutions of the Navier–Stokes equations corresponding to stretched vortices embedded in a uniform nonsymmetric 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 nonsymmetric 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 greaterthan sign]1. A pseudospectral method is used to obtain numerical solutions corresponding to steady and quasisteady vortex states over our whole (R, [lambda]) parameter space including [lambda] where arguments proposed by Moffatt, Kida & Ohkitani (1994) demonstrate the nonexistence of strictly steady solutions. When [lambda][dbl greaterthan sign]1, R[dbl greaterthan sign]1 and [epsilon][identical with][lambda]/R[double lessthan sign]1, we find an accurate asymptotic form for the vorticity in a region 1<r/(2v/[gamma])1/2[lessthanoreq, slant][epsilon]1/2, giving very good agreement with our numerical solutions. This suggests the existence of an extended region where the exponentially small vorticity is confined to a nearly cat'seyeshaped region of the almost twodimensional flow, and takes a constant value nearly equal to [Gamma][gamma]/(4[pi]v)exp[[minus sign]1/(2e[epsilon])] on bounding streamlines. This allows an estimate of the leakage rate of circulation to infinity as [partial partial differential][Gamma]/[partial partial differential]t =(0.48475/4[pi])[gamma][epsilon][minus sign]1[Gamma] exp ([minus sign]1/2e[epsilon]) with corresponding exponentially slow decay of the vortex when [lambda]>1. An iterative technique based on the power method is used to estimate the largest eigenvalues for the nonsymmetric case [lambda]>0. Stability is found for 0[lessthanoreq, slant][lambda][lessthanoreq, slant]1, and a neutrally convective mode of instability is found and analysed for [lambda]>1. Our general conclusion is that the generalized nonsymmetric Burgers vortex is unconditionally stable to twodimensional disturbances for all R, 0[lessthanoreq, slant][lambda][lessthanoreq, slant]1, and that when [lambda]>1, the vortex will decay only through exponentially slow leakage of vorticity, indicating extreme robustness in this case.
Item Type:  Article 

Additional Information:  "Reprinted with the permission of Cambridge University Press." (Received February 2 1997; Revised December 2 1997) We gratefully acknowledge helpful discussions with David Hill, James Buntine, and Ron Henderson. This research was partial supported by NSF Grant CTS9634222. 
Group:  GALCIT 
Subject Keywords:  HOMOGENEOUS TURBULENCE; ISOTROPIC TURBULENCE; STRETCHED VORTICES; INTENSE VORTICITY; MODELS; VORTEX; INTERMITTENCY; ALIGNMENT; DYNAMICS; STRAIN 
Record Number:  CaltechAUTHORS:PROjfm98 
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:PROjfm98 
Alternative URL:  http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=14903&fulltextType=RA&fileId=S0022112098008866 
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ID Code:  3175 
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Deposited On:  18 May 2006 
Last Modified:  02 Oct 2019 23:00 
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