The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Stéphane Le Dizès - One of the best experts on this subject based on the ideXlab platform.
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Curvature instability of a curved Batchelor vortex
Journal of Fluid Mechanics, 2017Co-Authors: Francisco J. Blanco-rodríguez, Stéphane Le DizèsAbstract: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 centreline is large compared with 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. In contrast 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, J. Fluid Mech., vol. 804, 2016, pp. 224–247), 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).
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Curvature instability of a curved Batchelor vortex
Journal of Fluid Mechanics, 2017Co-Authors: Francisco J. Blanco-rodríguez, Stéphane Le DizèsAbstract: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).
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Elliptic instability of a curved Batchelor vortex
Journal of Fluid Mechanics, 2016Co-Authors: Francisco J. Blanco-rodríguez, Stéphane Le DizèsAbstract:The occurrence of the elliptic instability in rings and helical vortices is analysed theoretically. The framework developed by Moore & Saffman ( Proc. R. Soc. Lond. A, vol. 346, 1975, pp. 413–425), where the elliptic instability is interpreted as a resonance of two Kelvin modes with a strained induced correction, is used to obtain the general stability properties of a curved and strained Batchelor vortex. Explicit expressions for the characteristics of the three main unstable modes are obtained as a function of the axial flow parameter of the Batchelor vortex. We show that vortex curvature adds a contribution to the elliptic instability growth rate. The results are applied to a single vortex ring, an array of alternate vortex rings and a double helical vortex.
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Elliptic instability in a strained Batchelor vortex
Journal of Fluid Mechanics, 2007Co-Authors: Laurent Lacaze, Kris Ryan, Stéphane Le DizèsAbstract:The elliptic instability of a Batchelor vortex subject to a stationary strain field is considered by theoretical and numerical means in the regime of large Reynolds number and small axial flow. In the theory, the elliptic instability is described as a resonant coupling of two quasi-neutral normal modes (Kelvin modes) of the Batchelor vortex of azimuthal wavenumbers m and m + 2 with the underlying strain field. The growth rate associated with these resonances is computed for different values of the azimuthal wavenumbers as the axial flow parameter is varied. We demonstrate that the resonant Kelvin modes m = 1 and in =-1 which are the most unstable in the absence of axial flow become damped as the axial flow is increased. This is shown to be due to the appearance of a critical layer which damps one of the resonant Kelvin modes. However, the elliptic instability does not disappear. Other combinations of Kelvin modes m=-2 and m=0, then in = -3 and in = -1 are shown to become progressively unstable for increasing axial flow. A complete instability diagram is obtained as a function of the axial flow parameter for several values of the strain rate and Reynolds number. The numerical study considers a system of two counter-rotating Batchelor vortices in which the strain field felt by each vortex is due to the other vortex. The characteristics of the most unstable linear modes developing on the frozen base flow are computed by direct numerical simulations for two axial flow parameters and compared to the theory
Pablo D. Mininni - One of the best experts on this subject based on the ideXlab platform.
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Decay of Batchelor and Saffman rotating turbulence.
Physical Review E, 2012Co-Authors: Tomas Teitelbaum, Pablo D. MininniAbstract:The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two canonical self-preserving solutions of the von K\'arm\'an--Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra $\ensuremath{\sim}{k}^{4}$ (Batchelor turbulence) and $\ensuremath{\sim}{k}^{2}$ (Saffman turbulence) and show that, while a self-similar decay can not be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two- and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von K\'arm\'an--Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.
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Decay of Batchelor and Saffman rotating turbulence.
Physical review. E Statistical nonlinear and soft matter physics, 2012Co-Authors: Tomas Teitelbaum, Pablo D. MininniAbstract:The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two canonical self-preserving solutions of the von Kármán-Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra ∼k^{4} (Batchelor turbulence) and ∼k^{2} (Saffman turbulence) and show that, while a self-similar decay can not be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two- and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von Kármán-Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.
Francisco J. Blanco-rodríguez - One of the best experts on this subject based on the ideXlab platform.
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Curvature instability of a curved Batchelor vortex
Journal of Fluid Mechanics, 2017Co-Authors: Francisco J. Blanco-rodríguez, Stéphane Le DizèsAbstract: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 centreline is large compared with 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. In contrast 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, J. Fluid Mech., vol. 804, 2016, pp. 224–247), 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).
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Optimal response of Batchelor vortex
Physics of Fluids, 2017Co-Authors: Francisco J. Blanco-rodríguez, Jesús Óscar Rodríguez-garcía, L. Parras, Carlos Del PinoAbstract:The optimal response of the Batchelor vortex is studied by considering the time-harmonically forced problem with frequency ω. High variance levels are sustained in this system under periodic forcing. The optimal response is largest when the input frequency is null in the axisymmetric case (m = 0). In addition, the axial flow does not play a relevant part in determining the optimal response. When considering helical modes |m| = 1, perturbations are excited through a resonance mechanism at moderate and large wavelengths. At smaller wavelengths, a large response is excited by steady forcing. Regarding the axial flow, the response is largest when the axial velocity intensity is near to zero. For perturbations with larger azimuthal wavenumbers |m| > 1, the magnitude of the response is smaller than those for helical modes. Therefore, studying the response for |m| > 1 is of no interest.
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Curvature instability of a curved Batchelor vortex
Journal of Fluid Mechanics, 2017Co-Authors: Francisco J. Blanco-rodríguez, Stéphane Le DizèsAbstract: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).
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Elliptic instability of a curved Batchelor vortex
Journal of Fluid Mechanics, 2016Co-Authors: Francisco J. Blanco-rodríguez, Stéphane Le DizèsAbstract:The occurrence of the elliptic instability in rings and helical vortices is analysed theoretically. The framework developed by Moore & Saffman ( Proc. R. Soc. Lond. A, vol. 346, 1975, pp. 413–425), where the elliptic instability is interpreted as a resonance of two Kelvin modes with a strained induced correction, is used to obtain the general stability properties of a curved and strained Batchelor vortex. Explicit expressions for the characteristics of the three main unstable modes are obtained as a function of the axial flow parameter of the Batchelor vortex. We show that vortex curvature adds a contribution to the elliptic instability growth rate. The results are applied to a single vortex ring, an array of alternate vortex rings and a double helical vortex.
I Hager - One of the best experts on this subject based on the ideXlab platform.
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Subtalar arthrodesis with the combined Batchelor–Grice technique
Foot and Ankle Surgery, 2004Co-Authors: M Vlachou, D Demetriades, I HagerAbstract:Abstract Eight patients (13ft) with progressive neuromuscular planovalgus foot deformity, underwent an extraarticular subtalar arthrodesis with the combined Batchelor–Grice procedure. All patients were ambulant and received conservative treatment with braces and special orthopaedic shoes prior to operation. Postoperatively the feet were immobilized in short casts for six weeks. Evaluation was based on the appearance of the feet, the clinical symptoms and X-ray measurements. Solid fusion and sustained correction, took place in all feet. Foot appearance and mobility of the patients were improved, while preoperative complaints were reduced. The gap at the graft donor site was bridged with new bone in all cases.
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subtalar arthrodesis with the combined Batchelor grice technique
Foot and Ankle Surgery, 2004Co-Authors: M Vlachou, D Demetriades, I HagerAbstract:Abstract Eight patients (13ft) with progressive neuromuscular planovalgus foot deformity, underwent an extraarticular subtalar arthrodesis with the combined Batchelor–Grice procedure. All patients were ambulant and received conservative treatment with braces and special orthopaedic shoes prior to operation. Postoperatively the feet were immobilized in short casts for six weeks. Evaluation was based on the appearance of the feet, the clinical symptoms and X-ray measurements. Solid fusion and sustained correction, took place in all feet. Foot appearance and mobility of the patients were improved, while preoperative complaints were reduced. The gap at the graft donor site was bridged with new bone in all cases.
Tomas Teitelbaum - One of the best experts on this subject based on the ideXlab platform.
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Decay of Batchelor and Saffman rotating turbulence.
Physical Review E, 2012Co-Authors: Tomas Teitelbaum, Pablo D. MininniAbstract:The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two canonical self-preserving solutions of the von K\'arm\'an--Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra $\ensuremath{\sim}{k}^{4}$ (Batchelor turbulence) and $\ensuremath{\sim}{k}^{2}$ (Saffman turbulence) and show that, while a self-similar decay can not be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two- and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von K\'arm\'an--Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.
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Decay of Batchelor and Saffman rotating turbulence.
Physical review. E Statistical nonlinear and soft matter physics, 2012Co-Authors: Tomas Teitelbaum, Pablo D. MininniAbstract:The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two canonical self-preserving solutions of the von Kármán-Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra ∼k^{4} (Batchelor turbulence) and ∼k^{2} (Saffman turbulence) and show that, while a self-similar decay can not be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two- and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von Kármán-Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.