Elliptic instability of a curved Batchelor vortex

Blanco–Rodríguez, Francisco J.; Dizès, Stéphane Le

doi:10.1017/jfm.2016.533

Cited by 26 publications

(47 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to a normalisation mistake, a systematic error has been made in the values of the coefficients R AB and R BA in the dispersion relation (4.7) of Blanco-Rodríguez & Le Dizès (2016). The correct values are twice those indicated in this paper for all the modes.…”

Section: Appendix D Elliptic Instability Of a Curved Batchelor Vortementioning

confidence: 67%

“…By contrast, the elliptic instability characteristics in helices depend on the helix pitch and on the number of helices (Blanco-Rodríguez & Le Dizès 2016). Whether the curvature instability dominates the elliptic instability must then be analysed on a case by case basis.…”

Section: Resultsmentioning

confidence: 99%

“…We provide theoretical predictions for a curved vortex when the underlying vortex structure is a Batchelor vortex (Gaussian axial velocity and axial vorticity). This work is the follow-up of Blanco-Rodríguez & Le Dizès (2016), hereafter BRLD16, where another short-wavelength instability, the elliptic instability, was analysed using the same theoretical framework.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Curvature instability of a curved Batchelor vortex

Blanco–Rodríguez

Dizès

2017

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

In this paper, we analyse the curvature instability of a curved Batchelor vortex. We consider this short-wavelength instability when the radius of curvature of the vortex centerline is large compared to the vortex core size. In this limit, the curvature instability can be interpreted as a resonant phenomenon. It results from the resonant coupling of two Kelvin modes of the underlying Batchelor vortex with the dipolar correction induced by curvature. The condition of resonance of the two modes is analysed in detail as a function of the axial jet strength of the Batchelor vortex. Contrarily to the Rankine vortex, only a few configurations involving m = 0 and m = 1 modes are found to become the most unstable. The growth rate of the resonant configurations is systematically computed and used to determine the characteristics of the most unstable mode as a function of the curvature ratio, the Reynolds number, and the axial flow parameter. The competition of the curvature instability with another short-wavelength instability, which was considered in a companion paper [Blanco-Rodríguez & Le Dizès, Elliptic instability of a curved Batchelor vortex, J. Fluid Mech. 804, 224-247 (2016)], is analysed for a vortex ring. A numerical error found in this paper which affects the relative strength of the elliptic instability is also corrected. We show that the curvature instability becomes the dominant instability in large rings as soon as axial flow is present (vortex ring with swirl).

show abstract

Section: Appendix D Elliptic Instability Of a Curved Batchelor Vortementioning

confidence: 67%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Curvature instability of a curved Batchelor vortex

Blanco–Rodríguez

Dizès

2017

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, in the case of Batchelor vortices, this configuration has been shown to stabilize with increased axial flow, and be replaced by other unstable resonance configurations [42,43]. Recently, the elliptic instability of curved Batchelor vortices has been investigated by Blanco-Rodríguez and Le Dizès [51]. These authors computed the growth rates for certain combinations of Kelvin modes using the following equation…”

Section: Elliptic Instabilitiesmentioning

confidence: 99%

“…One also has that ε = Ra/(R 2 + L 2 ), and as before, = L/R is the dimensionless reduced pitch. Approximate relations for the other coefficients appearing in (31) are given in Appendix C of [51] (note also the corrigendum to some of these relations appended to [47]). The Reynolds number used in (31) is defined as Re = Re/(2π).…”

Section: Elliptic Instabilitiesmentioning

confidence: 99%

Numerical realization of helical vortices: application to vortex instability

Brynjell-Rahkola

Henningson

2019

Theor. Comput. Fluid Dyn.

View full text Add to dashboard Cite

The need to numerically represent a free vortex system arises frequently in fundamental and applied research. Many possible techniques for realizing this vortex system exist but most tend to prioritize accuracy either inside or outside of the vortex core, which therefore makes them unsuitable for a stability analysis considering the entire flow field. In this article, a simple method is presented that is shown to yield an accurate representation of the flow inside and outside of the vortex core. The method is readily implemented in any incompressible Navier-Stokes solver using primitive variables and Cartesian coordinates. It can potentially be used to model a wide range of vortices but is here applied to the case of two helices, which is of renewed interest due to its relevance for wind turbines and helicopters. Three-dimensional stability analysis is performed in both a rotating and a translating frame of reference, which yield eigenvalue spectra that feature both mutual inductance and elliptic instabilities. Comparison of these spectra with available theoretical predictions is used to validate the proposed baseflow model, and new insights into the elliptic instability of curved Batchelor vortices are presented. Furthermore, it is shown that the instabilities in the rotating and the translating reference frames have the same structure and growth rate, but different frequency. A relation between these frequencies is provided.

show abstract

High-speed volumetric particle tracking measurements of unstable helical vortex pairs

2023

View full text Add to dashboard Cite

We present results from an experimental study investigating pairs of helical vortices generated by a one-bladed rotor in hovering conditions. Time-resolved volumetric Lagrangian particle tracking measurements are conducted in a water tunnel to analyze the three-dimensional development of the vortex system. The vortex pairs are generated by a specific tip design, which allows splitting the single tip vortex into two vortices, whose characteristics depend on the geometric fin parameters. The objective of this procedure is the modification of the tip vortex structure, in order to minimize negative effects caused by fluid–structure interactions in applications involving rotors. Certain vortex configurations are affected by centrifugal instabilities, which result in an immediate pronounced growth of the vortex cores. As a consequence of the instability, secondary vortex structures are formed between the unstable cores. The presence of these structures results in an accelerated break-up of the cores, causing them to merge. In order to investigate the influence of the trailing vorticity layer shed from the inner part of the blade, two blade designs with different radial circulation distributions are considered. The measurements are able to track the evolution of the vorticity layer and the secondary structures, providing new insights into the instability of closely spaced vortex pairs with varying circulation ratios.

show abstract

Elliptic instability of a curved Batchelor vortex

Cited by 26 publications

References 32 publications

Curvature instability of a curved Batchelor vortex

Curvature instability of a curved Batchelor vortex

Numerical realization of helical vortices: application to vortex instability

High-speed volumetric particle tracking measurements of unstable helical vortex pairs

Contact Info

Product

Resources

About