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1
Koshel, Konstantin V., and Eugene A. Ryzhov. "Parametric resonance in the dynamics of an elliptic vortex in a periodically strained environment." Nonlinear Processes in Geophysics 24, no. 1 (January 12, 2017): 1–8. http://dx.doi.org/10.5194/npg-24-1-2017.
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Abstract. The model of an elliptic vortex evolving in a periodically strained background flow is studied in order to establish the possible unbounded regimes. Depending on the parameters of the exterior flow, there are three classical regimes of the elliptic vortex motion under constant linear deformation: (i) rotation, (ii) nutation, and (iii) infinite elongation. The phase portrait for the vortex dynamics features critical points which correspond to the stationary vortex not changing its form and orientation. We demonstrate that, given superimposed periodic oscillations to the exterior deformation, the phase space region corresponding to the elliptic critical point experiences parametric instability leading to locally unbounded dynamics of the vortex. This dynamics manifests itself as the vortex nutates along the strain axis while continuously elongating. This motion continues until nonlinear effects intervene near the region associated with the steady-state separatrix. Next, we show that, for specific values of the perturbation parameters, the parametric instability is effectively suppressed by nonlinearity in the primal parametric instability zone. The secondary zone of the parametric instability, on the contrary, produces an effective growth of the vortex's aspect ratio.
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MacKay, R. S. "Instability of vortex streets." Dynamics and Stability of Systems 2, no. 1 (January 1987): 55–71. http://dx.doi.org/10.1080/02681118708806027.
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Acheson, D. J. "Instability of vortex leapfrogging." European Journal of Physics 21, no. 3 (May 1, 2000): 269–73. http://dx.doi.org/10.1088/0143-0807/21/3/310.
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Marxen, Olaf, Matthias Lang, and Ulrich Rist. "Vortex formation and vortex breakup in a laminar separation bubble." Journal of Fluid Mechanics 728 (July 1, 2013): 58–90. http://dx.doi.org/10.1017/jfm.2013.222.
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AbstractThe convective primary amplification of a forced two-dimensional perturbation initiates the formation of essentially two-dimensional large-scale vortices in a laminar separation bubble. These vortices are then shed from the bubble with the forcing frequency. Immediately downstream of their formation, the vortices get distorted in the spanwise direction and quickly disintegrate into small-scale turbulence. The laminar–turbulent transition in a forced laminar separation bubble is dominated by this vortex formation and breakup process. Using numerical and experimental data, we give an in-depth characterization of this process in physical space as well as in Fourier space, exploiting the largely periodic character of the flow in time as well as in the spanwise direction. We present evidence that a combination of more than one secondary instability mechanism is active during this process. The first instability mechanism is the elliptic instability of vortex cores, leading to a spanwise deformation of the cores with a spanwise wavelength of the order of the size of the vortex. Another mechanism, potentially an instability of flow in between two consecutive vortices, is responsible for three-dimensionality in the braid region. The corresponding disturbances possess a much smaller spanwise wavelength as compared to those amplified through elliptic instability. The secondary instability mechanisms occur for both fundamental and subharmonic frequency, respectively, even in the absence of continuous forcing, indicative of temporal amplification in the region of vortex formation.
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SCHAEFFER, NATHANAËL, and STÉPHANE LE DIZÈS. "Nonlinear dynamics of the elliptic instability." Journal of Fluid Mechanics 646 (March 8, 2010): 471–80. http://dx.doi.org/10.1017/s002211200999351x.
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In this paper, we analyse by numerical simulations the nonlinear dynamics of the elliptic instability in the configurations of a single strained vortex and a system of two counter-rotating vortices. We show that although a weakly nonlinear regime associated with a limit cycle is possible, the nonlinear evolution far from the instability threshold is, in general, much more catastrophic for the vortex. In both configurations, we put forward some evidence of a universal nonlinear transition involving shear layer formation and vortex loop ejection, leading to a strong alteration and attenuation of the vortex, and a rapid growth of the vortex core size.
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LEWEKE, T., and C. H. K. WILLIAMSON. "Cooperative elliptic instability of a vortex pair." Journal of Fluid Mechanics 360 (April 10, 1998): 85–119. http://dx.doi.org/10.1017/s0022112097008331.
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In this paper, we investigate the three-dimensional instability of a counter-rotating vortex pair to short waves, which are of the order of the vortex core size, and less than the inter-vortex spacing. Our experiments involve detailed visualizations and velocimetry to reveal the spatial structure of the instability for a vortex pair, which is generated underwater by two rotating plates. We discover, in this work, a symmetry-breaking phase relationship between the two vortices, which we show to be consistent with a kinematic matching condition for the disturbances evolving on each vortex. In this sense, the instabilities in each vortex evolve in a coupled, or ‘cooperative’, manner. Further results demonstrate that this instability is a manifestation of an elliptic instability of the vortex cores, which is here identified clearly for the first time in a real open flow. We establish a relationship between elliptic instability and other theoretical instability studies involving Kelvin modes. In particular, we note that the perturbation shape near the vortex centres is unaffected by the finite size of the cores. We find that the long-term evolution of the flow involves the inception of secondary transverse vortex pairs, which develop near the leading stagnation point of the pair. The interaction of these short-wavelength structures with the long-wavelength Crow instability is studied, and we observe significant modifications in the longevity of large vortical structures.
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Barnes, C. J., M. R. Visbal, and P. G. Huang. "On the effects of vertical offset and core structure in streamwise-oriented vortex–wing interactions." Journal of Fluid Mechanics 799 (June 21, 2016): 128–58. http://dx.doi.org/10.1017/jfm.2016.320.
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This article explores the three-dimensional flow structure of a streamwise-oriented vortex incident on a finite aspect-ratio wing. The vertical positioning of the incident vortex relative to the wing is shown to have a significant impact on the unsteady flow structure. A direct impingement of the streamwise vortex produces a spiralling instability in the vortex just upstream of the leading edge, reminiscent of the helical instability modes of a Batchelor vortex. A small negative vertical offset develops a more pronounced instability while a positive vertical offset removes the instability altogether. These differences in vertical position are a consequence of the upstream influence of pressure gradients provided by the wing. Direct impingement or a negative vertical offset subject the vortex to an adverse pressure gradient that leads to a reduced axial velocity and diminished swirl conducive to hydrodynamic instability. Conversely, a positive vertical offset removes instability by placing the streamwise vortex in line with a favourable pressure gradient, thereby enhancing swirl and inhibiting the growth of unstable modes. In every case, the helical instability only occurs when the properties of the incident vortex fall within the instability threshold predicted by linear stability theory. The influence of pressure gradients associated with separation and stall downstream also have the potential to introduce suction-side instabilities for a positive vertical offset. The influence of the wing is more severe for larger vortices and diminishes with vortex size due to weaker interaction and increased viscous stability. Helical instability is not the only possible outcome in a direct impingement. Jet-like vortices and a higher swirl ratio in wake-like vortices can retain stability upon impact, resulting in the laminar vortex splitting over either side of the wing.
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Mounce, A. M., S. Oh, S. Mukhopadhyay, W. P. Halperin, A. P. Reyes, P. L. Kuhns, K. Fujita, M. Ishikado, and S. Uchida. "Charge-induced vortex lattice instability." Nature Physics 7, no. 2 (November 28, 2010): 125–28. http://dx.doi.org/10.1038/nphys1835.
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Tophøj, Laust, and Hassan Aref. "Instability of vortex pair leapfrogging." Physics of Fluids 25, no. 1 (January 2013): 014107. http://dx.doi.org/10.1063/1.4774333.
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Sukhanovskii, A., A. Evgrafova, and E. Popova. "Instability of cyclonic convective vortex." IOP Conference Series: Materials Science and Engineering 208 (June 2017): 012040. http://dx.doi.org/10.1088/1757-899x/208/1/012040.
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Blanco-Rodríguez, Francisco J., and Stéphane Le Dizès. "Curvature instability of a curved Batchelor vortex." Journal of Fluid Mechanics 814 (February 6, 2017): 397–415. http://dx.doi.org/10.1017/jfm.2017.34.
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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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Cariteau, B., and J. B. Flór. "An experimental investigation on elliptical instability of a strongly asymmetric vortex pair in a stable density stratification." Nonlinear Processes in Geophysics 13, no. 6 (November 20, 2006): 641–49. http://dx.doi.org/10.5194/npg-13-641-2006.
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Abstract. We investigate the elliptical instability of a strongly asymmetric vortex pair in a stratified fluid, generated by the acceleration and deceleration of the rotation of a single flap. The dominant parameter is the Froude number, Fr=U/(NR), based on the maximum azimuthal velocity, U, and corresponding radius, R, of the strongest vortex, i.e. the principal vortex, and buoyancy frequency N. For Fr>1, both vortices are elliptically unstable while the instability is suppressed for Fr<1. In an asymmetric vortex pair, the principal vortex is less – and the secondary vortex more – elliptical than the vortices in an equivalent symmetric dipolar vortex. The far more unstable secondary vortex interacts with the principal vortex and increases the strain on the latter, thus increasing its ellipticity and its instability growth rate. The nonlinear interactions render the elliptical instability more relevant. An asymmetric dipole can be more unstable than an equivalent symmetric dipole. Further, the wavelength of the instability is shown to be a function of the Froude number for strong stratifications corresponding to small Froude numbers, whereas it remains constant in the limit of a homogenous fluid.
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Blanco-Rodríguez, Francisco J., and Stéphane Le Dizès. "Elliptic instability of a curved Batchelor vortex." Journal of Fluid Mechanics 804 (September 9, 2016): 224–47. http://dx.doi.org/10.1017/jfm.2016.533.
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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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Posa, A., and R. Broglia. "Influence by the hub vortex on the instability of the tip vortices shed by propellers with and without winglets." Physics of Fluids 34, no. 11 (November 2022): 115115. http://dx.doi.org/10.1063/5.0122751.
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Large-eddy simulations on a cylindrical grid consisting of 5 × 109 points are reported on both conventional and winglets propellers with and without a downstream shaft. Comparisons are focused on the influence by the hub vortex on the process of instability of the tip vortices. They demonstrate that in straight ahead conditions, this influence is actually quite limited for both propellers. The presence of the hub vortex at the wake core results in only a slight upstream shift of the instability of the tip vortices. Meanwhile, the development of the instability of the hub vortex is always delayed, compared to that of the tip vortices, and the former keeps coherent further downstream of their breakup. The results of this study highlight that the hub vortex is not a major source of instability of the tip vortices. Therefore, simplified configurations with no hub vortex, often adopted in the literature, can also provide a good approximation of the process of instability of the tip vortices shed by actual propellers. In contrast, the instability of the tip vortices could be the trigger of that of the hub vortex, whose development is slower. Therefore, experimental and computational studies aimed at analyzing the dynamics of the hub vortex should be designed accordingly, extending to further downstream distances.
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Miyazaki, Takeshi, and Hideshi Hanazaki. "Baroclinic instability of Kirchhoff's elliptic vortex." Journal of Fluid Mechanics 261 (February 25, 1994): 253–71. http://dx.doi.org/10.1017/s0022112094000339.
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The linear instability of Kirchhoff's elliptic vortex in a vertically stratified rotating fluid is investigated using the quasi-geostrophic, f-plane approximation. Any elliptic vortex is shown to be unstable to baroclinic disturbances of azimuthal wavenumber m = 1 (bending mode) and m = 2 (elliptical deformation). The axial wavenumber of the unstable bending mode approaches Λc = 1.7046 in the limit of small ellipticity, indicating that it is a short-wave baroclinic instability. The instability occurs when the bending wave rotates around the vortex axis with angular velocity identical to the rotation rate of the undisturbed elliptic vortex. On the other hand, the wavenumber of the elliptical deformation mode approaches zero in the same limit, showing that it is a long-wave sideband instability.
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ALLEN, J. J., and B. AUVITY. "Interaction of a vortex ring with a piston vortex." Journal of Fluid Mechanics 465 (August 25, 2002): 353–78. http://dx.doi.org/10.1017/s0022112002001118.
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Recent studies on vortex ring generation, e.g. Rosenfeld et al. (1998), have highlighted the subtle effect of generation geometry on the final properties of rings. Experimental generation of vortex rings often involves moving a piston through a tube, resulting in a vortex ring being generated at the tube exit. A generation geometry that has been cited as a standard consists of the tube exit mounted flush with a wall, with the piston stroke ending at the tube exit, Glezer (1988). We employ this geometry to investigate the effect of the vortex that forms in front of the advancing piston (piston vortex) on the primary vortex ring that is formed at the tube exit. It is shown that when the piston finishes its stroke flush with the wall, and hence forms an uninterrupted plane, the piston vortex is convected through the primary ring and then ingested into the primary vortex. The ingestion of the piston vortex results in an increased ring impulse and an altered trajectory, when compared to the case when the piston motion finishes inside the tube. As the Reynolds number of the experiments, based on the piston speed and piston diameter, is the order of 3000, transition to turbulence is observed during the self-induced translation phase of the ring motion. Compared to the case when the piston is stopped inside the tube, the vortex ring which has ingested the piston vortex transitions to turbulence at a significantly reduced distance from the orifice exit and suggests the transition map suggested by Glezer (1988) is under question. A secondary instability characterized by vorticity filaments with components in the axial and radial directions, is observed forming on the piston vortex. The structure of the instability appears to be similar to the streamwise vortex filaments that form in the braid regions of shear layers. This instability is subsequently ingested into the primary ring during the translation phase and may act to accelerate the growth of the Tsai–Widnall instability. It is suggested that the origin of the instability is Görtler in nature and the result of the unsteady wall jet nature of the boundary layer separating on the piston face.
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Ryan, Kris, Christopher J. Butler, and Gregory J. Sheard. "Stability characteristics of a counter-rotating unequal-strength Batchelor vortex pair." Journal of Fluid Mechanics 696 (March 6, 2012): 374–401. http://dx.doi.org/10.1017/jfm.2012.55.
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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.
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GAUTAM, SANDEEP. "CROW INSTABILITY IN UNITARY FERMI GAS." Modern Physics Letters B 27, no. 14 (May 16, 2013): 1350097. http://dx.doi.org/10.1142/s0217984913500978.
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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.
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Liu, Zhi Rong, Jun Wei Wang, and Rui Zhu. "Fluid Experimental Research on Dual-Vortex Interaction Instability." Advanced Materials Research 459 (January 2012): 195–98. http://dx.doi.org/10.4028/www.scientific.net/amr.459.195.
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A series of dual-vortex fulid visualization and interaction instability experiments are undertaken with PIV (Particle Image Velocimetry) system under various experimental parameters sets. The motion characteristics and the circulation-time curves of the dual-vortex are presented through PIV processing and analysis. The dual-vortex distance b=50mm, main wingtip angle α1=10° & side wingtip angle α2=8° are optimum experimental parameters for vortices dissipation, the most vortex strength is reduced by 30%-40%
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Ford, Rupert. "The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water." Journal of Fluid Mechanics 280 (December 10, 1994): 303–34. http://dx.doi.org/10.1017/s0022112094002946.
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The stability of an axisymmetric vortex with a single radial discontinuity in potential vorticity is investigated in rotating shallow water. It is shown analytically that the vortex is always unstable, using the WKBJ method for instabilities with large azimuthal mode number. The analysis reveals that the instability is of mixed type, involving the interaction of a Rossby wave on the boundary of the vortex and a gravity wave beyond the sonic radius. Numerically, it is demonstrated that the growth rate of the instability is generally small, except when the potential vorticity in the vortex is the opposite sign to the background value, in which case it is shown that inertial instability is likely to be stronger than the present instability.
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BILLANT, P., A. DELONCLE, J. M. CHOMAZ, and P. OTHEGUY. "Zigzag instability of vortex pairs in stratified and rotating fluids. Part 2. Analytical and numerical analyses." Journal of Fluid Mechanics 660 (July 21, 2010): 396–429. http://dx.doi.org/10.1017/s002211201000282x.
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The three-dimensional stability of vertical vortex pairs in stratified and rotating fluids is investigated using the analytical approach established in Part 1 and the predictions are compared to the results of previous direct numerical stability analyses for pairs of co-rotating equal-strength Lamb–Oseen vortices and to new numerical analyses for equal-strength counter-rotating vortex pairs. A very good agreement between theoretical and numerical results is generally found, thereby providing a comprehensive description of the zigzag instability. Co-rotating and counter-rotating vortex pairs are most unstable to the zigzag instability when the Froude number Fh = Γ/(2πR2N) (where Γ is the vortex circulation, R the vortex radius and N the Brunt–Väisälä frequency) is lower than unity independently of the Rossby number Ro = Γ/(4πR2Ωb) (Ωb is the planetary rotation rate). In this range, the maximum growth rate is proportional to the strain Γ/(2πb2) (b is the separation distance between the vortices) and is almost independent of Fh and Ro. The most amplified wavelength scales like Fhb when the Rossby number is large and like Fhb/|Ro| when |Ro| ≪ 1, in agreement with previous results. While the zigzag instability always bends equal-strength co-rotating vortex pairs in a symmetric way, the instability is only quasi-antisymmetric for finite Ro for equal-strength counter-rotating vortex pairs because the cyclonic vortex is less bent than the anticyclonic vortex. The theory is less accurate for co-rotating vortex pairs around Ro ≈ −2 because the bending waves rotate very slowly for long wavelength. The discrepancy can be fully resolved by taking into account higher-order three-dimensional effects.When Fh is increased above unity, the growth rate of the zigzag instability is strongly reduced because the bending waves of each vortex are damped by a critical layer at the radius where the angular velocity of the vortex is equal to the Brunt–Väisälä frequency. The zigzag instability, however, continues to exist and is dominant up to a critical Froude number, which mostly depends on the Rossby number. Above this threshold, equal-strength co-rotating vortex pairs are stable with respect to long-wavelength bending disturbances whereas equal-strength counter-rotating vortex pairs become unstable to a quasi-symmetric instability resembling the Crow instability in homogeneous fluids. However, its growth rate is lower than in homogeneous fluids because of the damping by the critical layer. The structure of the critical layer obtained in the computations is in excellent agreement with the theoretical solution.Physically, the different stability properties of vortex pairs in stratified and rotating fluids compared to homogeneous fluids are shown to come from the reversal of the direction of the self-induced motion of bent vortices.
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LIN, H. C., and W. M. YANG. "LOWEST STABILITY BOUNDARY ON FLOW OF CONCENTRIC ROTATING CYLINDERS." International Journal of Bifurcation and Chaos 20, no. 05 (May 2010): 1527–32. http://dx.doi.org/10.1142/s0218127410026678.
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In this study, we numerically investigate the lowest instability boundary of nonaxisymmetric Taylor vortex flow (TVF) for different axial wavenumbers. The variation in the axial wavenumber of a supercritical TVF can affect the instability of the flow, because the wavelength of a Taylor vortex is constant only when the flow is axisymmetrical. When the nonaxisymmetric TVF is transformed to a wavy vortex flow (WVF), the instability boundary is changed with the variation in the axial wavenumber. We carry out an instability analysis of the nonaxisymmetric TVF between two concentric rotating cylinders, which have a radius ratio of 0.88.
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Kennan, Sean C., and Pierre J. Flament. "Observations of a Tropical Instability Vortex*." Journal of Physical Oceanography 30, no. 9 (September 2000): 2277–301. http://dx.doi.org/10.1175/1520-0485(2000)030<2277:ooativ>2.0.co;2.
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Wang, Hongyun. "Short Wave Instability on Vortex Filaments." Physical Review Letters 80, no. 21 (May 25, 1998): 4665–68. http://dx.doi.org/10.1103/physrevlett.80.4665.
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Meunier, Patrice, and Thomas Leweke. "Three-dimensional instability during vortex merging." Physics of Fluids 13, no. 10 (October 2001): 2747–50. http://dx.doi.org/10.1063/1.1399033.
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FLORYAN, J. M. "Vortex instability in a divergingconverging channel." Journal of Fluid Mechanics 482 (May 10, 2003): 17–50. http://dx.doi.org/10.1017/s0022112003003987.
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FUKUMOTO, YASUHIDE, and YUJI HATTORI. "Curvature instability of a vortex ring." Journal of Fluid Mechanics 526 (March 10, 2005): 77–115. http://dx.doi.org/10.1017/s0022112004002678.
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Gitterman, M., B. Ya Shapiro, I. Shapiro, B. Kalisky, A. Shaulov, and Y. Yeshurun. "Oscillating flux instability in vortex matter." Physica C: Superconductivity 460-462 (September 2007): 1247–48. http://dx.doi.org/10.1016/j.physc.2007.04.191.
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Pozrikidis, C. "The nonlinear instability of Hill's vortex." Journal of Fluid Mechanics 168, no. -1 (July 1986): 337. http://dx.doi.org/10.1017/s002211208600040x.
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Richardson, G. "Instability of a superconducting line vortex." Physica D: Nonlinear Phenomena 110, no. 1-2 (December 1997): 139–53. http://dx.doi.org/10.1016/s0167-2789(97)00119-x.
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Janu, Z., R. Tichy, and V. Plechacek. "Instability in vortex system in HTSC." IEEE Transactions on Magnetics 30, no. 2 (March 1994): 1226–28. http://dx.doi.org/10.1109/20.312223.
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Asselin, Daniel J., and C. H. K. Williamson. "Influence of a wall on the three-dimensional dynamics of a vortex pair." Journal of Fluid Mechanics 817 (March 20, 2017): 339–73. http://dx.doi.org/10.1017/jfm.2017.114.
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In this paper, we are interested in perturbed vortices under the influence of a wall or ground plane. Such flows have relevance to aircraft wakes in ground effect, to ship hull junction flows, to fundamental studies of turbulent structures close to a ground plane and to vortex generator flows, among others. In particular, we study the vortex dynamics of a descending vortex pair, which is unstable to a long-wave instability (Crow, AIAA J., vol. 8 (12), 1970, pp. 2172–2179), as it interacts with a horizontal ground plane. Flow separation on the wall generates opposite-sign secondary vortices which in turn induce the ‘rebound’ effect, whereby the primary vortices rise up away from the wall. Even small perturbations in the vortices can cause significant topological changes in the flow, ultimately generating an array of vortex rings which rise up from the wall in a three-dimensional ‘rebound’ effect. The resulting vortex dynamics is almost unrecognizable when compared with the classical Crow instability. If the vortices are generated below a critical height over a horizontal ground plane, the long-wave instability is inhibited by the wall. We then observe two modes of vortex–wall interaction. For small initial heights, the primary vortices are close together, enabling the secondary vortices to interact with each other, forming vertically oriented vortex rings in what we call a ‘vertical rings mode’. In the ‘horizontal rings mode’, for larger initial heights, the Crow instability develops further before wall interaction; the peak locations are farther apart and the troughs closer together upon reaching the wall. The proximity of the troughs to each other and the wall increases vorticity cancellation, leading to a strong axial pressure gradient and axial flow. Ultimately, we find a series of small horizontal vortex rings which ‘rebound’ from the wall. Both modes comprise two small vortex rings in each instability wavelength, distinct from Crow instability vortex rings, only one of which is formed per wavelength. The phenomena observed here are not limited to the above perturbed vortex pairs. For example, remarkably similar phenomena are found where vortex rings impinge obliquely with a wall.
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CANALS, MIGUEL, and GENO PAWLAK. "Three-dimensional vortex dynamics in oscillatory flow separation." Journal of Fluid Mechanics 674 (March 23, 2011): 408–32. http://dx.doi.org/10.1017/s0022112011000012.
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The dynamics of coherent columnar vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is on the low Keulegan–Carpenter number range (0.2 < KC < 2), where KC is the ratio between the fluid particle excursion during half an oscillation cycle and the obstacle size, and for moderate Reynolds numbers (700 < Rev < 7500). For this parameter range, a periodic unidirectional vortex pair ejection regime is observed, in which the direction of vortex propagation is set by the initial conditions of the oscillations. These vortex pairs provide a direct mechanism for the transfer of momentum and enstrophy to the outer region of rough oscillating boundary layers. Vortices are observed to be short-lived relative to the oscillation time scale, which limits their propagation distance from the boundary. The instability mechanisms leading to vortex decay are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Dye visualizations reveal complex three-dimensional vortex interactions resulting in rapid vortex destruction. These visualizations suggest that one of the instabilities affecting the spanwise vortices is an elliptical instability of the strained vortex cores. This is supported by DPIV measurements which identify the spatial structure of the perturbations associated with the elliptical instability in the divergence field. We also identify regions in the periphery of the vortex cores which are unstable to the centrifugal instability. Vortex longevity is quantified via a vortex decay time scale, and the results indicate that vortex pair lifetimes are of the order of an oscillation period T.
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Olsthoorn, Jason, and Stuart B. Dalziel. "Three-dimensional visualization of the interaction of a vortex ring with a stratified interface." Journal of Fluid Mechanics 820 (May 10, 2017): 549–79. http://dx.doi.org/10.1017/jfm.2017.215.
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The study of vortex-ring-induced stratified mixing has long played a key role in understanding externally forced stratified turbulent mixing. While several studies have investigated the dynamical evolution of such a system, this study presents an experimental investigation of the mechanical evolution of these vortex rings, including the stratification-modified three-dimensional instability. The aim of this paper is to understand how vortex rings induce mixing of the density field. We begin with a discussion of the Reynolds and Richardson number dependence of the vortex-ring interaction using two-dimensional particle image velocimetry measurements. Then, through the use of modern imaging techniques, we reconstruct from an experiment the full three-dimensional time-resolved velocity field of a vortex ring interacting with a stratified interface. This work agrees with many of the previous two-dimensional experimental studies, while providing insight into the three-dimensional instabilities of the system. Observations indicate that the three-dimensional instability has a similar wavenumber to that found for the unstratified vortex-ring instability at later times. We determine that the time scale associated with this instability growth has an inverse Richardson number dependence. Thus, the time scale associated with the instability is different from the time scale of interface recovery, possibly explaining the significant drop in mixing efficiency at low Richardson numbers. The structure of the underlying instability is a simple displacement mode of the vorticity field.
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BOULANGER, NICOLAS, PATRICE MEUNIER, and STÉPHANE LE DIZÈS. "Tilt-induced instability of a stratified vortex." Journal of Fluid Mechanics 596 (January 17, 2008): 1–20. http://dx.doi.org/10.1017/s0022112007009263.
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This experimental and theoretical study considers the dynamics and the instability of a Lamb–Oseen vortex in a stably stratified fluid. In a companion paper, it was shown that tilting the vortex axis with respect to the direction of stratification induces the formation of a rim of strong axial flow near a critical radius when the Froude number of the vortex is larger than one.Here, we demonstrate that this tilt-induced flow is responsible for a three-dimensional instability. We show that the instability results from a shear instability of the basic axial flow in the critical-layer region. The theoretical predictions for the wavelength and the growth rate obtained by a local stability analysis of the theoretical critical-layer profile are compared to experimental measurements and a good agreement is observed. The late stages of the instability are also analysed experimentally. In particular, we show that the tilt-induced instability does not lead to the destruction of the vortex, but to a sudden decrease of its Froude number, through the turbulent diffusion of its core size, when the initial Froude number is close to 1. A movie is available with the online version of the paper.
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ORLANDI, P., and G. F. CARNEVALE. "Evolution of isolated vortices in a rotating fluid of finite depth." Journal of Fluid Mechanics 381 (February 25, 1999): 239–69. http://dx.doi.org/10.1017/s0022112098003693.
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Laboratory experiments have shown that monopolar isolated vortices in a rotating flow undergo instabilities that result in the formation of multipolar vortex states such as dipoles and tripoles. In some cases the instability is entirely two-dimensional, with the vortices taking the form of vortex columns aligned along the direction of the ambient rotation at all times. In other cases, the vortex first passes through a highly turbulent three-dimensional state before eventually reorganizing into vortex columns. Through a series of three-dimensional numerical simulations, the roles that centrifugal instability, barotropic instability, and the bottom Ekman boundary layer play in these instabilities are investigated. Evidence is presented that the centrifugal instability can trigger the barotropic instabilities by the enhancement of vorticity gradients. It is shown that the bottom Ekman layer is not essential to these instabilities but can strongly modify their evolution.
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Maslowe, Sherwin A. "Linear instability of a perturbed Lamb–Oseen vortex." Fluid Dynamics Research 54, no. 1 (February 1, 2022): 015513. http://dx.doi.org/10.1088/1873-7005/ac522d.
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Abstract This paper presents an investigation of the stability of a vortex with azimuthal velocity profile V ˉ = 1 − 1 − ε r 2 e − r 2 / r . When ε = 0, the Lamb–Oseen vortex model is recovered. Although the Lamb–Oseen vortex supports propagating waves known as Kelvin waves, the flow is stable according to Rayleigh’s circulation criterion. In this paper, on the other hand, the modified vortex profile admits linearly unstable disturbances for ε > 0 and we investigate their characteristics. These may be either axisymmetric or non-axisymmetric, but we find that the axisymmetric perturbations have the largest growth rates. When their growth rates are small, it becomes very difficult to solve the linear equation governing the axisymmetric perturbations because the eigenfunctions have a rapid exponential growth as one moves outward radially from the vortex center. To deal with such cases, a modified Riccati transformation was employed and found to be effective in solving the associated eigenvalue problem.
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Quaranta, Hugo Umberto, Hadrien Bolnot, and Thomas Leweke. "Long-wave instability of a helical vortex." Journal of Fluid Mechanics 780 (September 9, 2015): 687–716. http://dx.doi.org/10.1017/jfm.2015.479.
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We investigate the instability of a single helical vortex filament of small pitch with respect to displacement perturbations whose wavelength is large compared to the vortex core size. We first revisit previous theoretical analyses concerning infinite Rankine vortices, and consider in addition the more realistic case of vortices with Gausssian vorticity distributions and axial core flow. We show that the various instability modes are related to the local pairing of successive helix turns through mutual induction, and that the growth rate curve can be qualitatively and quantitatively predicted from the classical pairing of an array of point vortices. We then present results from an experimental study of a helical vortex filament generated in a water channel by a single-bladed rotor under carefully controlled conditions. Various modes of displacement perturbations could be triggered by suitable modulation of the blade rotation. Dye visualisations and particle image velocimetry allowed a detailed characterisation of the vortex geometry and the determination of the growth rate of the long-wave instability modes, showing good agreement with theoretical predictions for the experimental base flow. The long-term (downstream) development of the pairing instability leads to a grouping and swapping of helix loops. Despite the resulting complicated three-dimensional structure, the vortex filaments surprisingly remain mostly intact in our observation interval. The characteristic distance of evolution of the helical wake behind the rotor decreases with increasing initial amplitude of the perturbations; this can be predicted from the linear stability theory.
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Abdullah, M. Z., Z. Husain, and S. M. Fraser. "Application of Deswirl Device in Cyclone Dust Separator." ASEAN Journal on Science and Technology for Development 20, no. 3&4 (December 27, 2017): 203–16. http://dx.doi.org/10.29037/ajstd.354.
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The experimental investigations of the vortex flow inside the vortex finder (outlet duct) of the cyclone dust separator have been carried out. Preliminary study from the visualization experiment has been performed and discovered vortex instability inside the conventional vortex finder. In order to minimize the instabilities, the streamlined entry shape was inserted at the vortex finder entrance and the results showed remarkable improvement of the vortex flow instability inside the vortex finder. The velocity measurements of two main components of velocity were performed using a laser-Doppler anemometry at the cyclone vortex finder outlet. The experiments were conducted at a constant flow rate of 0.0246m3/s with the vortex finder diameter of 64mm and with several types of entrance configuration in order to improve the cyclone performance and to reduce the losses. The use of deswirl devices inside the vortex finder significantly reduced pressure drop and energy losses.
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Men, Hongyuan, Xinliang Li, and Hongwei Liu. "Direct numerical simulations of hypersonic boundary layer transition over a hypersonic transition research vehicle model lifting body at different angles of attack." Physics of Fluids 35, no. 4 (April 2023): 044111. http://dx.doi.org/10.1063/5.0146651.
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This paper performs direct numerical simulations of hypersonic boundary layer transition over a Hypersonic Transition Research Vehicle (HyTRV) model lifting body designed by the China Aerodynamic Research and Development Center. Transitions are simulated at four angles of attack: 0°, 3°, 5°, and 7°. The free-stream Mach number is 6, and the unit Reynolds number is 107 m−1. Four distinct transitional regions are identified: the shoulder cross-flow and vortex region and the shoulder vortex region on the leeward side, the windward vortex region and the windward cross-flow region on the windward side. As the angle of attack increases, the transition locations on the leeward side generally move forward and the transition ranges expand, while the transition locations generally move backward and the transition ranges decrease on the windward side. Moreover, the shoulder vortex region moves toward the centerline of the leeward side. At large angles of attack (5° and 7°), the streamwise vortex on the shoulder cross-flow and vortex region will enable the transition region to be divided into the cross-flow instability region on both sides and the streamwise vortex instability region in the middle. In addition, the streamwise vortex also leads to a significant increase in cross-flow instability in their upper region, which can generate a new streamwise vortex instability region between the two transition regions on the leeward side. Furthermore, since the decrease in the intensity and the range for the cross-flow on the windward side, the windward cross-flow region tends to become narrow and ultimately disappears.
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Zhao, Wu, Wei Tao Jia, Quan Bin Zhang, and Zhan Qi Hu. "Stable Equilibrium Analysis and Simulation Considering Effect of Cutting Fluid Inside and Outside BTA Boring Bar." Advanced Materials Research 902 (February 2014): 129–34. http://dx.doi.org/10.4028/www.scientific.net/amr.902.129.
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This paper is proposed to reveal the stable equilibrium on the boring bar during heavy-duty deep-hole boring trepanning processing environment, including three conditions considering vortex instability caused by outside cutting fluid, perturbation instability caused by inside cutting fluid and synthesized instability accompanied both inner and outer cutting fluid, respectively. Every position of stable equilibrium and formula of rotation speed in instability are obtained. It is shown that the system instability induced by no matter how different situations, is resulted from half frequency vortex and perturbation, through case calculation and simulation on system stability.
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Kunchur, Milind N., and James M. Knight. "Hot-Electron Instability in Superconductors." Modern Physics Letters B 17, no. 10n12 (May 20, 2003): 549–58. http://dx.doi.org/10.1142/s0217984903005573.
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High flux velocities in a superconductor can distort the quasiparticle distribution function and elevate the electronic temperature. Close to T c , a non-thermal distribution function shrinks the vortex core producing the well-known Larkin-Ovchinnikov flux instability. In the present work we consider the opposite limit of low temperatures, where electron-electron scattering is more rapid than electron-phonon, resulting in an electronic temperature rise with a thermal-like distribution function. This produces a different kind of flux instability, due to a reduction in condensate and expansion of the vortex core. Measurements in YBCO films confirm the distinct predictions ofthis mechanism.
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CROUCH, J. D. "Instability and transient growth for two trailing-vortex pairs." Journal of Fluid Mechanics 350 (November 10, 1997): 311–30. http://dx.doi.org/10.1017/s0022112097007040.
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The stability of two vortex pairs is analysed as a model for the vortex system generated by an aircraft in flaps-down configuration. The co-rotating vortices on the starboard and port sides tumble about one another as they propagate downward. This results in a time-periodic basic state for the stability analysis. The dynamics and instability of the trailing vortices are modelled using thin vortex filaments. Stability equations are derived by matching the induced velocities from Biot–Savart integrals with kinematic equations obtained by temporal differentiation of the vortex position vectors. The stability equations are solved analytically as an eigenvalue problem, using Floquet theory, and numerically as an initial value problem. The instabilities are periodic along the axes of the vortices with wavelengths that are large compared to the size of the vortex cores. The results show symmetric instabilities that are linked to the long-wavelength Crow instability. In addition, new symmetric and antisymmetric instabilities are observed at shorter wavelengths. These instabilities have growth rates 60–100% greater than the Crow instability. The system of two vortex pairs also exhibits transient growth which can lead to growth factors of 10 or 15 in one-fifth of the time required for the same growth due to instability.
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Pozrikidis, C., and J. J. L. Higdon. "Nonlinear Kelvin–Helmholtz instability of a finite vortex layer." Journal of Fluid Mechanics 157 (August 1985): 225–63. http://dx.doi.org/10.1017/s0022112085002361.
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The nonlinear growth of periodic disturbances on a finite vortex layer is examined. Under the assumption of constant vorticity, the evolution of the layer may be analysed by following the contour of the vortex region. A numerical procedure is introduced which leads to higher-order accuracy than previous methods with negligible increase in computational effort. The response of the vortex layer is studied as a function of layer thickness and the amplitude and form of the initial disturbance. For small initial disturbances, all unstable layers form a large rotating vortex core of nearly elliptical shape. The growth rate of the disturbances is strongly affected by the layer thickness; however, the final amplitude of the disturbance is relatively insensitive to the thickness and reaches a maximum value of approximately 20% of the wavelength. In the fully developed layers, the amplitude shows a small oscillation owing to the rotation of the vortex core. For finite-amplitude initial disturbances, the evolution of the layer is a function of the initial amplitude. For thin layers with thickness less than 3% of the wavelength, three different patterns were observed in the vortex-core region: a compact elliptic core, an elongated S-shaped core and a bifurcation into two orbiting cores. For thicker layers, stationary elliptic cores may develop if the thickness exceeds 15% of the wavelength. The spacing and eccentricity of these cores is in good agreement with previously discovered steady-state solutions. The growth rate of interfacial area (or length of the vortex contour) is calculated and is found to approach a constant value in well-developed vortex layers.
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Thomas, P. J., and D. Auerbach. "The observation of the simultaneous development of a long- and a short-wave instability mode on a vortex pair." Journal of Fluid Mechanics 265 (April 25, 1994): 289–302. http://dx.doi.org/10.1017/s0022112094000844.
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Experiments on the stability of vortex pairs are described. The vortices (ratio of length to core diameter L/c of up to 300) were generated at the edge of a flat plate rotating about a horizontal axis in water. The vortex pairs were found to be unstable, displaying two distinct modes of instability. For the first time, as far as it is known to the authors, a long-wave as well as a short-wave mode of instability were observed to develop simultaneously on such a vortex pair. Experiments involving single vortices show that these do not develop any instability whatsoever. The wavelengths of the developing instability modes on the investigated vortex pairs are compared to theoretical predictions. Observed long wavelengths are in good agreement with the classic symmetric long-wave bending mode identified by Crow (1970). The developing short waves, on the other hand, appear to be less accurately described by the theoretical results predicted, for example, by Windnall, Bliss & Tsai (1974).
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KLOOSTERZIEL, R. C., G. F. CARNEVALE, and P. ORLANDI. "Inertial instability in rotating and stratified fluids: barotropic vortices." Journal of Fluid Mechanics 583 (July 4, 2007): 379–412. http://dx.doi.org/10.1017/s0022112007006325.
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The unfolding of inertial instability in intially barotropic vortices in a uniformly rotating and stratified fluid is studied through numerical simulations. The vortex dynamics during the instability is examined in detail. We demonstrate that the instability is stabilized via redistribution of angular momentum in a way that produces a new equilibrated barotropic vortex with a stable velocity profile. Based on extrapolations from the results of a series of simulations in which the Reynolds number and strength of stratification are varied, we arrive at a construction based on angular momentum mixing that predicts the infinite-Reynolds-number form of the equilibrated vortex toward which inertial instability drives an unstable vortex. The essential constraint is conservation of total absolute angular momentum. The construction can be used to predict the total energy loss during the equilibration process. It also shows that the equilibration process can result in anticyclones that are more susceptible to horizontal shear instabilities than they were initially, a phenomenon previously observed in laboratory and numerical studies.
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ALLEN, J. J., and T. NAITOH. "Scaling and instability of a junction vortex." Journal of Fluid Mechanics 574 (February 15, 2007): 1–23. http://dx.doi.org/10.1017/s0022112006003879.
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This paper details experiments in the region where an impulsively started moving wall slides under a stationary wall. The experiments were conducted over a Reynolds number range of ReΓ=5×102–5×105. The length scale for the Reynolds number is defined as the distance the wall has moved from rest and increases during an experiment. Experiments show that for ReΓ>103 a vortex forms close to the junction where the moving wall meets the stationary one. The data shows that while the vortical structure is small, in relation to the fixed-apparatus length scale, the size of the vortex normalized with respect to the wall speed and viscosity scales in a universal fashion with respect to ReΓ. The scaling rate is proportional to t5/6 when the Reynolds number is large. The kinematic behaviour of the vortex is related to the impulse that the moving wall applies to the fluid and results in a prediction that the transient structure should grow as t5/6 and the velocity field should scale as t−1/6. The spatial-growth prediction is in good agreement with the experimental results and the velocity scaling is moderately successful in collapsing the experimental data.For ReΓ>2×104 three-dimensional instabilities appear on the perimeter of the vortical structure and the flow transitions from an unsteady two-dimensional flow to a strongly three-dimensional vortical structure at ReΓ≃ 4 × 104. The instability mechanism is centrifugal. The formation and growth of these instability structures and their ingestion into the primary vortex core causes the three-dimensional breakdown of the primary vortex. Two movies are available with the online version of the paper.
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Yim, Eunok, and Paul Billant. "Analogies and differences between the stability of an isolated pancake vortex and a columnar vortex in stratified fluid." Journal of Fluid Mechanics 796 (May 11, 2016): 732–66. http://dx.doi.org/10.1017/jfm.2016.248.
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In order to understand the dynamics of pancake shaped vortices in stably stratified fluids, we perform a linear stability analysis of an axisymmetric vortex with Gaussian angular velocity in both the radial and axial directions with an aspect ratio of ${\it\alpha}$. The results are compared to those for a columnar vortex (${\it\alpha}=\infty$) in order to identify the instabilities. Centrifugal instability occurs when $\mathscr{R}>c(m)$ where $\mathscr{R}=ReF_{h}^{2}$ is the buoyancy Reynolds number, $F_{h}$ the Froude number, $Re$ the Reynolds number and $c(m)$ a constant which differs for the three unstable azimuthal wavenumbers $m=0,1,2$. The maximum growth rate depends mostly on $\mathscr{R}$ and is almost independent of the aspect ratio ${\it\alpha}$. For sufficiently large buoyancy Reynolds number, the axisymmetric mode is the most unstable centrifugal mode whereas for moderate $\mathscr{R}$, the mode $m=1$ is the most unstable. Shear instability for $m=2$ develops only when $F_{h}\leqslant 0.5{\it\alpha}$. By considering the characteristics of shear instability for a columnar vortex with the same parameters, this condition is shown to be such that the vortex is taller than the minimum wavelength of shear instability in the columnar case. For larger Froude number $F_{h}\geqslant 1.5{\it\alpha}$, the isopycnals overturn and gravitational instability can operate. Just below this threshold, the azimuthal wavenumbers $m=1,2,3$ are unstable to baroclinic instability. A simple model shows that baroclinic instability develops only above a critical vertical Froude number $F_{h}/{\it\alpha}$ because of confinement effects.
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Stout, Eric, and Fazle Hussain. "External turbulence-induced axial flow and instability in a vortex." Journal of Fluid Mechanics 793 (March 16, 2016): 353–79. http://dx.doi.org/10.1017/jfm.2016.123.
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External turbulence-induced axial flow in an incompressible, normal-mode stable Lamb–Oseen (two-dimensional) vortex column is studied via direct numerical simulations of the Navier–Stokes equations. Azimuthally oriented vorticity filaments, formed from external turbulence, advect radially towards or away from the vortex axis (depending on the filament’s swirl direction), resulting in a net induced axial flow in the vortex core; axial flow increases with increasing vortex Reynolds number ($Re=$ vortex circulation/viscosity). This contrasts the viscous mechanism for axial flow generation downstream of a lifting body, wherein an axial pressure gradient is produced by viscous diffusion of the swirl (Batchelor, J. Fluid Mech., vol. 20, 1964, pp. 645–658). Analysis of the self-induced motion of an arbitrarily curved external filament shows that any non-axisymmetric filament undergoes radial advection. We then studied the evolution of a vortex column starting with an imposed optimal transient growth perturbation. For a range of Re values, axial flow develops and initially grows as (time)$^{5/2}$ before decreasing after two turnover times; for $Re=10\,000$ – the highest computationally achievable – axial flow at late times becomes sufficiently strong to induce vortex instability. Contrary to a prior claim of a parent–offspring mechanism at the outer edge of the core, vorticity tilting within the core by axial flow is the underlying mechanism producing energy growth. Thus, external perturbations in practical flows (at $Re\sim 10^{7}$) produce destabilizing axial flow, possibly leading to the sought-after vortex breakup.
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Shcherbakov, S. "A COMPLETE DESCRIPTION OF THE MECHANICS OF TURBULENCE IN A MOVING FLUID." PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS 2020, no. 3 (September 26, 2020): 97–109. http://dx.doi.org/10.55176/2414-1038-2020-3-97-109.
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The conditions and mechanisms of events in a moving fluid are analyzed, leading to the apparent disorder of unsteady flow, known as turbulence. The method of analysis is the use of different forms of equations of motion and transfer of characteristics, the selection of stable formations in the flow structure and a description of the interaction between them. The non-trivial results of previous works are used. The transfer and transformation of disturbances of a vortex distributed in the flow is analyzed, the conditions under which insulated tubes with a helical flow appear inside the shear flow. An important condition is the short duration of vortex disturbances. Equations are obtained that describe the interaction of the main shear flow and the vortex tube, the features of which lead to flow instability. The existence of two mechanisms for the development of turbulence is shown - the autogeneration of local decelerations and the instability of stretching of vortex tubes. The self-generation mechanism is the transfer of kinetic energy from the main flow to an annular vortex with the generation of a new annular vortex. This is the main mechanism that ensures the propagation of instability downstream, arises first when the Re number increases. The tensile instability leads to the splitting of the vortex tube into independent sections, the generation of many annular vortices that fill the space and drift in it. The vortex multiplication factor in each generation increases with the Re number and can reach many thousands. The role of ordered unsteady flows in the initiation of turbulence is shown.