scholarly journals Slow Burgers vortices in hot conformal fluids

2011 ◽  
Vol 2011 (5) ◽  
Author(s):  
Jarah Evslin
Keyword(s):  
Burgers Vortices

scholarly journals Vortex and the Balance between Vorticity and Strain Rate

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Václav Kolář ◽  
Jakub Šístek
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Compressible Flows ◽  
High Strain ◽  
Vortex Identification ◽  
Unified Framework ◽  
Cross Sectional ◽  
Duality Property ◽  
Burgers Vortices ◽  
Flow Past A Sphere

A new analysis of the vortex-identification Q-criterion and its recent modifications is presented. In this unified framework based on different approaches to averaging of the cross-sectional balance between vorticity and strain rate in 3D, new relations among the existing modifications are derived. In addition, a new method based on spherical averaging is proposed. It is applicable to compressible flows, and it inherits a duality property which allows its use for identifying high strain-rate zones together with vortices. The new quantity is applied to identification of vortices and high strain-rate zones in the flow around an inclined flat plate, in the flow past a sphere, and for the reconnection process of two Burgers vortices.

scholarly journals Three-Dimensional Stability of Burgers Vortices

2010 ◽  
Vol 302 (2) ◽  
pp. 477-511 ◽  
Author(s):  
Thierry Gallay ◽  
Yasunori Maekawa
Keyword(s):  
Dimensional Stability ◽  
Three Dimensional ◽  
Burgers Vortices

scholarly journals Structure and stability of non-symmetric Burgers vortices

1998 ◽  
Vol 363 ◽  
pp. 199-228 ◽  
Author(s):  
AURELIUS PROCHAZKA ◽  
D. I. PULLIN
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Structure And Stability ◽  
Two Dimensional Flow ◽  
Steady Solutions ◽  
Pseudo Spectral Method ◽  
Burgers Vortices

We investigate, numerically and analytically, the structure and stability of steady and quasi-steady solutions of the Navier–Stokes equations corresponding to stretched vortices embedded in a uniform non-symmetric straining field, (αx, βy, γz), α+β+γ=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=Γ/(2πv) where Γ is the vortex circulation and v the kinematic viscosity, in the range R=1−104, and a broad range of strain ratios λ=(β−α)/(β+α) including λ>1, and in some cases λ[Gt ]1. A pseudo-spectral method is used to obtain numerical solutions corresponding to steady and quasi-steady vortex states over our whole (R, λ) parameter space including λ where arguments proposed by Moffatt, Kida & Ohkitani (1994) demonstrate the non-existence of strictly steady solutions. When λ[Gt ]1, R[Gt ]1 and ε≡λ/R[Lt ]1, we find an accurate asymptotic form for the vorticity in a region 1<r/(2v/γ)1/2[les ]ε1/2, 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's-eye-shaped region of the almost two-dimensional flow, and takes a constant value nearly equal to Γγ/(4πv)exp[−1/(2eε)] on bounding streamlines. This allows an estimate of the leakage rate of circulation to infinity as ∂Γ/∂t =(0.48475/4π)γε−1Γ exp (−1/2eε) with corresponding exponentially slow decay of the vortex when λ>1. An iterative technique based on the power method is used to estimate the largest eigenvalues for the non-symmetric case λ>0. Stability is found for 0[les ]λ[les ]1, and a neutrally convective mode of instability is found and analysed for λ>1. Our general conclusion is that the generalized non-symmetric Burgers vortex is unconditionally stable to two-dimensional disturbances for all R, 0[les ]λ[les ]1, and that when λ>1, the vortex will decay only through exponentially slow leakage of vorticity, indicating extreme robustness in this case.

scholarly journals Existence and Stability of Asymmetric Burgers Vortices

2006 ◽  
Vol 9 (2) ◽  
pp. 243-261 ◽  
Author(s):  
Thierry Gallay ◽  
C. Eugene Wayne
Keyword(s):  
Existence And Stability ◽  
Burgers Vortices

Reconnection of skewed vortices

2014 ◽  
Vol 751 ◽  
pp. 329-345 ◽  
Author(s):  
Y. Kimura ◽  
H. K. Moffatt
Keyword(s):  
Magnetic Flux ◽  
Experimental Evidence ◽  
Time Scale ◽  
Strain Field ◽  
Kinematic Viscosity ◽  
Flux Tubes ◽  
Vortex Reconnection ◽  
Lorentz Forces ◽  
Magnetic Flux Tubes ◽  
Burgers Vortices

AbstractBased on experimental evidence that vortex reconnection commences with the approach of nearly antiparallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly antiparallel, they are annihilated on the strain time-scale, independent of kinematic viscosity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\nu $ in the limit $\nu \rightarrow 0$. When the vortices are skew to each other, they are annihilated under this action over a local extent that increases exponentially in the stretching direction, with clear evidence of reconnection on the same strain time-scale. The initial helicity associated with the skewed geometry is eliminated during the process of reconnection. The model applies equally to the reconnection of weak magnetic flux tubes under the action of a strain field, when Lorentz forces are negligible.

scholarly journals EXISTENCE OF ASYMMETRIC BURGERS VORTICES AND THEIR ASYMPTOTIC BEHAVIOR AT LARGE CIRCULATIONS

2009 ◽  
Vol 19 (05) ◽  
pp. 669-705 ◽  
Author(s):  
YASUNORI MAEKAWA
Keyword(s):  
Asymmetry Parameter ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Solutions ◽  
The Asymmetry ◽  
Burgers Vortices ◽  
Stationary Navier Stokes Equations

The asymmetric Burgers vortices are vortex solutions to the three-dimensional stationary Navier–Stokes equations for viscous incompressible fluids in the presence of an asymmetric background straining flow. The asymmetry of the straining flow is expressed by a non-negative parameter less than 1. The Burgers vortices have been used as a model which expresses tube-like structures of concentrated vorticity fields in turbulence, and they are numerically well investigated especially in the case of large circulation numbers. However, their existence was proved mathematically only when either the asymmetry of the straining flow is not so strong or the circulation number is sufficiently small. In this paper, we prove the existence of asymmetric Burgers vortices for all circulation numbers and each asymmetry parameter less than 1. We also obtain their asymptotic expansion at large circulation numbers, which gives an explanation for a symmetrizing effect by a fast rotation.

The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence

1998 ◽  
Vol 377 ◽  
pp. 65-97 ◽  
Author(s):  
KEIKO K. NOMURA ◽  
GARY K. POST
Keyword(s):  
Isotropic Turbulence ◽  
High Amplitude ◽  
Direct Numerical Simulations ◽  
Principal Strain ◽  
Homogeneous Isotropic Turbulence ◽  
Physical Processes ◽  
Structure And Dynamics ◽  
Principal Axes ◽  
Non Local ◽  
Burgers Vortices

The structure and dynamics of vorticity ω and rate of strain S are studied using direct numerical simulations (DNS) of incompressible homogeneous isotropic turbulence. In particular, characteristics of the pressure Hessian Π, which describe non-local interaction of ω and S, are presented. Conditional Lagrangian statistics which distinguish high-amplitude events in both space and time are used to investigate the physical processes associated with their evolution. The dynamics are examined on the principal strain basis which distinguishes vortex stretching and induced rotation of the principal axes of S. The latter mechanism is associated with misaligned ω with respect to S, a condition which predominates in isotropic turbulence and is dynamically significant, particularly in rotation-dominated regions of the flow. Locally-induced rotation of the principal axes acts to orient ω towards the direction of either the intermediate or most compressive principal strain. The tendency towards compressive straining of ω is manifested at the termini of the high-amplitude tube-like structures in the flow. Non-locally-induced rotation, associated with Π, tends to counteract the locally-induced rotation. This is due to the strong alignment between ω and the eigenvector of Π corresponding to its smallest eigenvalue and is indicative of the controlling influence of the proximate structure on the dynamics. High-amplitude rotation-dominated regions deviate from Burgers vortices due to the misalignment of ω. Although high-amplitude strain-dominated regions are promoted primarily by local dynamics, the associated spatial structure is less organized and more discontinuous than that of rotation-dominated regions.

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