Optimal amplification of the Crow instability

2007 ◽  
Vol 19 (11) ◽  
pp. 111703 ◽  
Author(s):  
Vincent Brion ◽  
Denis Sipp ◽  
Laurent Jacquin
Keyword(s):  
Crow Instability

Large eddy simulation of aircraft wake vortices within homogeneous turbulence - Crow instability

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 292-300 ◽  
Author(s):  
Jongil Han ◽  
Yuh-Lang Lin ◽  
David G. Schowalter ◽  
S. P. Arya ◽  
Fred H. Proctor
Keyword(s):  
Large Eddy Simulation ◽  
Homogeneous Turbulence ◽  
Wake Vortices ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Aircraft Wake ◽  
Crow Instability

scholarly journals Crow instability effects on the exhaust plume mixing and condensation

1999 ◽  
Vol 7 ◽  
pp. 66-79 ◽  
Author(s):  
S. Brunet ◽  
F. Garnier ◽  
P. Sagaut
Keyword(s):  
Exhaust Plume ◽  
Crow Instability

Importance of Antisymmetric Modes of the Crow Instability

AIAA Journal ◽  
2017 ◽  
Vol 55 (7) ◽  
pp. 2123-2128 ◽  
Author(s):  
Zhongquan Charlie Zheng ◽  
Jay C. Hardin
Keyword(s):  
Crow Instability

Stability characteristics of a counter-rotating unequal-strength Batchelor vortex pair

2012 ◽  
Vol 696 ◽  
pp. 374-401 ◽  
Author(s):  
Kris Ryan ◽  
Christopher J. Butler ◽  
Gregory J. Sheard
Keyword(s):  
Stokes Equations ◽  
Vortex Pair ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Mode Amplitude ◽  
Nonlinear Growth ◽  
Circulation Ratio ◽  
Secondary Stage ◽  
Aircraft Wake ◽  
Crow Instability

AbstractA Batchelor vortex represents the asymptotic solution of a trailing vortex in an aircraft wake. In this study, an unequal-strength, counter-rotating Batchelor vortex pair is employed as a model of the wake emanating from one side of an aircraft wing; this model is a direct extension of several prior investigations that have considered unequal-strength Lamb–Oseen vortices as representations of the aircraft wake problem. Both solution of the linearized Navier–Stokes equations and direct numerical simulations are employed to study the linear and nonlinear development of a vortex pair with a circulation ratio of$\Lambda = \ensuremath{-} 0. 5$. In contrast to prior investigations considering a Lamb–Oseen vortex pair, we note strong growth of the Kelvin mode$[\ensuremath{-} 2, 0] $coupled with an almost equal growth rate of the Crow instability. Three stages of nonlinear instability development are defined. In the initial stage, the Kelvin mode amplitude becomes sufficiently large that oscillations within the core of the weaker vortex are easily observable and significantly affect the profile of the weaker vortex. In the secondary stage, filaments of secondary vorticity emanate from the weaker vortex and are convected around the stronger vortex. In the tertiary stage, a transition in the dominant instability wavelength is observed from the short-wavelength Kelvin mode to the longer-wavelength Crow instability. Much of the instability growth is observed on the weaker vortex of the pair, although small perturbations in the stronger vortex are observed in the tertiary nonlinear growth phase.

scholarly journals The effects of ambient stratification on the crow instability and subsequent vortex reconnection

1999 ◽  
Vol 7 ◽  
pp. 151-160
Author(s):  
J. F. Garten ◽  
J. Werne ◽  
D. C. Fritts ◽  
S. Arendt
Keyword(s):  
Vortex Reconnection ◽  
Crow Instability

scholarly journals CROW INSTABILITY IN UNITARY FERMI GAS

2013 ◽  
Vol 27 (14) ◽  
pp. 1350097 ◽  
Author(s):  
SANDEEP GAUTAM
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fermi Gas ◽  
Nonlinear Schrodinger Equation ◽  
Vortex Rings ◽  
Zero Temperature ◽  
Sound Waves ◽  
Subsequent Evolution ◽  
Unitary Fermi Gas ◽  
Crow Instability

In this paper, we investigate the initiation and subsequent evolution of Crow instability in an inhomogeneous unitary Fermi gas using zero-temperature Galilei-invariant nonlinear Schrödinger equation. Considering a cigar-shaped unitary Fermi gas, we generate the vortex–antivortex pair either by phase-imprinting or by moving a Gaussian obstacle potential. We observe that the Crow instability in a unitary Fermi gas leads to the decay of the vortex–antivortex pair into multiple vortex rings and ultimately into sound waves.

Within Homogeneous Turbulence: Crow Instability Large Eddy Simulation of Aircraft Wake Vortices

AIAA Journal ◽  
10.2514/2.956 ◽  
2000 ◽  
Vol 38 (2) ◽  
pp. 292-300 ◽  
Author(s):  
Jongil Han ◽  
Yuh-Lang Lin ◽  
David G. Schowalter ◽  
S. Pal Arya ◽  
Fred H. Proctor
Keyword(s):  
Large Eddy Simulation ◽  
Homogeneous Turbulence ◽  
Wake Vortices ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Aircraft Wake ◽  
Crow Instability

The instability of a vortex ring impinging on a free surface

2009 ◽  
Vol 642 ◽  
pp. 79-94 ◽  
Author(s):  
P. J. ARCHER ◽  
T. G. THOMAS ◽  
G. N. COLEMAN
Keyword(s):  
Free Surface ◽  
Vortex Ring ◽  
Radial Direction ◽  
Slenderness Ratio ◽  
Long Wavelength ◽  
Short Waves ◽  
Radial Structure ◽  
Limiting Case ◽  
Crow Instability ◽  
Impermeable Boundary

Direct numerical simulation is used to study the development of a single laminar vortex ring as it impinges on a free surface directly from below. We consider the limiting case in which the Froude number approaches zero and the surface can be modelled with a stress-free rigid and impermeable boundary. We find that as the ring expands in the radial direction close to the surface, the natural Tsai–Widnall–Moore–Saffman (TWMS) instability is superseded by the development of the Crow instability. The Crow instability is able to further amplify the residual perturbations left by the TWMS instability despite being of differing radial structure and alignment. This occurs through realignment of the instability structure and shedding of a portion of its outer vorticity profile. As a result, the dominant wavenumber of the Crow instability reflects that of the TWMS instability, and is dependent upon the initial slenderness ratio of the ring. At higher Reynolds number a short-wavelength instability develops on the long-wavelength Crow instability. The wavelength of the short waves is found to vary around the ring dependent on the local displacement of the long waves.

Direct numerical simulations of the Crow instability and subsequent vortex reconnection in a stratified fluid

2001 ◽  
Vol 426 ◽  
pp. 1-45 ◽  
Author(s):  
J. F. GARTEN ◽  
J. WERNE ◽  
D. C. FRITTS ◽  
S. ARENDT
Keyword(s):  
Growth Rate ◽  
Numerical Model ◽  
Time Scale ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Direct Numerical Simulations ◽  
Reversal Effect ◽  
Vortex Reconnection ◽  
Vertically Propagating ◽  
Crow Instability

The evolution of a vertically propagating three-dimensional vortex pair in ambient stratification is studied with a three-dimensional numerical model. We consider a range of Reynolds (Re) and Froude (Fr) numbers, and initialize the vortex pair in a configuration that promotes growth of the Crow instability (Crow 1970). The growth rate of the instability is Re dependent, and we present a method for extending Crow's model to predict this dependence. We also find that relatively strong ambient stratification (Fr [les ] 2) further alters the growth of the instability via advection by baroclinically produced vorticity. For all of our cases with Fr [ges ] 1 (including our unstratified cases where Fr → ∞), the instability leads to vortex reconnection and formation of a vortex ring. A larger Re delays the commencement of the reconnection, but it proceeds more rapidly once it does commence. We compute a reconnection time scale (tR), and find that tR ∼ 1/Re, in agreement with a model formulated by Shelley et al. (1993). We also discuss a deformative/diffusive effect (related to yet distinct from the curvature reversal effect discussed by Melander & Hussain 1989) which prevents complete reconnection. Ambient stratification (in the range Fr [ges ] 1) accelerates the reconnection and reduces tR by an amount roughly proportional to 1/Fr. For some Fr, stratification effects overwhelm the deformative effect, and complete reconnection results.

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