Direct numerical simulations of the elliptic instability of a vortex pair

Laporte, Florent; Corjon, Alexandre

doi:10.1063/1.870357

Cited by 80 publications

(73 citation statements)

References 24 publications

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“…Finally, integration in time is performed by means of a low-storage third-order Runge-Kutta method with maximum CFL number fixed here to 0.5. The code has been used and validated for temporal simulations of corotating (Le Dizès and Laporte, 2002;Nybelen and Paoli, 2009) and counter-rotating (Laporte and Corjon, 2000) vortices, jet-vortex interactions (Paoli et al, 2003), and contrails (Paoli et al, 2004(Paoli et al, , 2013.…”

Section: S Unterstrasser Et Al: Dimension Of Aircraft Plumes: Effecmentioning

confidence: 99%

“…The domain in the transverse direction L x is wide enough to neglect the influence of one vortex on the other across the period boundary. The size of L y is chosen to allow for the most unstable (Crow) mode of the elliptic instability of the counter-rotating vortex pair to develop in the domain (Leweke and Williamson, 1998;Laporte and Corjon, 2000).…”

Section: Simulation Setupmentioning

confidence: 99%

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Dimension of aircraft exhaust plumes at cruise conditions: effect of wake vortices

et al. 2014

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Abstract. The dispersion of aircraft emissions during the vortex phase is studied using a 3-D LES model with Lagrangian particle tracking. The simulations start with a fully rolled-up vortex pair of a type B747/A340 airplane and the tracer centred around the vortex cores. The tracer dilution and plume extent is studied for a variety of ambient and aircraft parameters until aircraft-induced effects have ceased. For typical upper tropospheric conditions, the impact of stratification is more dominant compared to turbulence intensity or vertical wind shear. Moreover, the sensitivity to the initial tracer distribution was found to be weak. Along the transverse direction, the tracer concentrations can be well approximated by a Gaussian distribution, along the vertical a superposition of three Gaussian distributions is adequate. For the studied parameter range, the vertical plume expansion ranges from 400 m to 550 m and cross-sectional area from 4.0 × 10 4 m 2 to 6 × 10 4 m 2 after six minutes. For validation, selected simulations were compared to an alternative LES model and to in-situ NO-measurements.

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Section: S Unterstrasser Et Al: Dimension Of Aircraft Plumes: Effecmentioning

confidence: 99%

Section: Simulation Setupmentioning

confidence: 99%

Dimension of aircraft exhaust plumes at cruise conditions: effect of wake vortices

et al. 2014

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“…Both of these configurations are compared with the case of a cres vortex pair. An example of the elliptic instabilities of a cres vortex pair is shown in Figure 3, with a comparison between the current linear stability analysis prediction and the dns result by Laporte & Corjon [6]. The instability mode has previously been identifed as belonging to the first branch of the Kelvin mode coupling (−1, 1).…”

Section: Stability Analysis Resultsmentioning

confidence: 99%

“…The instability of an equal circulation strength vortex pair (either co-rotating or counter rotating) has been the subject of intense investigation in the past [6,7,9, e.g. ]; owing to its potential application in the aviation industry [15].…”

Section: Introductionmentioning

confidence: 99%

Linear stability analysis of a counter rotating vortex pair of unequal strength

So¹,

Ryan²,

Sheard³

2008

ANZIAMJ

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An elliptic type instability of a counter rotating vortex pair of unequal strength was numerically investigated with a linear stability analysis method. The peak growth rates of the unstable modes were predicted. The instability characteristics were found to differ from an equal strength vortex pair, of either co-rotating or counter rotating vortices. This investigation serves as a fundamental model to the flow of two unequal strength vortices, which can be generated from the ends of aerodynamic surfaces of an aircraft, such as wing tips and ailerons. These results provide predictions of the vortex arrangements likely to develop three dimensional instabilities, which is known to promote the dissipation of the underlying vortex structure.

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“…In three dimensions, a wellseparated vortex pair undergoes an elliptic instability [Leweke and Williamson, 1998] which breaks the two-dimensional structure of the dipole and can lead to turbulence [Laporte and Corjon, 2000] through vortex-tube stretching, a mechanism with requires three-dimensional motion.…”

Section: Three Dimensional Dipole/wall Interactionmentioning

confidence: 99%

Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

Subich

Lamb

Stastna

2013

Numerical Methods in Fluids

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SUMMARYThis paper describes a nonlinear, three‐dimensional spectral collocation method for the simulation of the incompressible Navier–Stokes equations under the Boussinesq approximation, motivated by geophysical and environmental flows. These flows are driven by the interaction of stratified fluid with topography, which this model accurately accounts for by using a mapped coordinate system. The spectral collocation method is implemented with both a Fourier trigonometric expansion and the Chebyshev polynomials, as appropriate for the domain boundary conditions. The coordinate mapping prohibits the use of existing, fast solution methods that rely on the separation of variables, so a preconditioner based on the approximate solution of a corresponding finite‐difference problem with geometric multigrid is used. The model is parallelized with the Message Passing Interface library, and it runs effectively on shared and distributed‐memory systems. Copyright © 2013 John Wiley & Sons, Ltd.

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Direct numerical simulations of the elliptic instability of a vortex pair

Cited by 80 publications

References 24 publications

Dimension of aircraft exhaust plumes at cruise conditions: effect of wake vortices

Dimension of aircraft exhaust plumes at cruise conditions: effect of wake vortices

Linear stability analysis of a counter rotating vortex pair of unequal strength

Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

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