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Scott, R. K., and D. G. Dritschel. "Vortex–Vortex Interactions in the Winter Stratosphere." Journal of the Atmospheric Sciences 63, no. 2 (February 1, 2006): 726–40. http://dx.doi.org/10.1175/jas3632.1.
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Abstract This paper examines the interaction of oppositely signed vortices in the compressible (non-Boussinesq) quasigeostrophic system, with a view to understanding vortex interactions in the polar winter stratosphere. A series of simplifying approximations leads to a two-vortex system whose dynamical properties are determined principally by two parameters: the ratio of the circulation of the vortices and the vertical separation of their centroids. For each point in this two-dimensional parameter space a family of equilibrium solutions exists, further parameterized by the horizontal separation of the vortex centroids, which are stable for horizontal separations greater than a critical value. The stable equilibria are characterized by vortex deformations that generally involve stronger deformations of the larger and/or lower of the two vortices. For smaller horizontal separations, the equilibria are unstable and a strongly nonlinear, time-dependent interaction takes place, typically involving the shedding of material from the larger vortex while the smaller vortex remains coherent. Qualitatively, the interactions resemble previous observations of certain stratospheric sudden warmings that involved the interaction of a growing anticyclonic circulation with the cyclonic polar vortex.
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ISHIKAWA, Hitoshi, Seiichiro IZAWA, Osamu MOCHIZUKI, and Masaru KIYA. "Vortex Ring-Vortex Tube Interactions." Transactions of the Japan Society of Mechanical Engineers Series B 68, no. 674 (2002): 2688–94. http://dx.doi.org/10.1299/kikaib.68.2688.
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Peng, Di, and James W. Gregory. "Vortex dynamics during blade-vortex interactions." Physics of Fluids 27, no. 5 (May 2015): 053104. http://dx.doi.org/10.1063/1.4921449.
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Rockwell, Donald. "VORTEX-BODY INTERACTIONS." Annual Review of Fluid Mechanics 30, no. 1 (January 1998): 199–229. http://dx.doi.org/10.1146/annurev.fluid.30.1.199.
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FRITTS, DAVID C., STEVE ARENDT, and ØYVIND ANDREASSEN. "Vorticity dynamics in a breaking internal gravity wave. Part 2. Vortex interactions and transition to turbulence." Journal of Fluid Mechanics 367 (July 25, 1998): 47–65. http://dx.doi.org/10.1017/s0022112098001633.
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A companion paper (Part 1) employed a three-dimensional numerical simulation to examine the vorticity dynamics of the initial instabilities of a breaking internal gravity wave in a stratified, sheared, compressible fluid. The present paper describes the vorticity dynamics that drive this flow to smaller-scale, increasingly isotropic motions at later times. Following the initial formation of discrete and intertwined vortex loops, the most important interactions are the self-interactions of single vortex tubes and the mutual interactions of multiple vortex tubes in close proximity. The initial formation of vortex tubes from the roll-up of localized vortex sheets gives the vortex tubes axial variations with both axisymmetric and azimuthal-wavenumber-2 components. The axisymmetric variations excite axisymmetric twist waves or Kelvin vortex waves which propagate along the tubes, drive axial flows, deplete the tubes' cores, and fragment the tubes. The azimuthal-wavenumber-2 variations excite m=2 twist waves on the vortex tubes, which undergo strong amplification and unravel single vortex tubes into pairs of intertwined helical tubes; the vortex tubes then burst or fragment. Reconnection often occurs among the remnants of such vortex fragmentation. A common mutual interaction is that of orthogonal vortex tubes, which causes mutual stretching and leads to long-lived structures. Such an interaction also sometimes creates an m=1 twist wave having an approximately steady helical form as well as a preferred sense of helicity. Interactions among parallel vortex tubes are less common, but include vortex pairing. Finally, the intensification and roll-up of weaker vortex sheets into new tubes occurs throughout the evolution. All of these vortex interactions result in a rapid cascade of energy and enstrophy toward smaller scales of motion.
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Verzicco, R., and P. Orlandi. "Wall/Vortex-Ring Interactions." Applied Mechanics Reviews 49, no. 10 (October 1, 1996): 447–61. http://dx.doi.org/10.1115/1.3101985.
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This review article presents a state-of-the-art review of the ring and wall interactions in the case of normal and oblique collisions. The different approaches used to study this flow and the results obtained are described and discussed. These techniques span from flow visualizations to LDV measurements, direct numerical simulations, particle-in-cell vortex methods and viscous and inviscid interactions. The relevance of these basic flows to the comprehension of wall-turbulence is also described. Finally, further developments, such as interaction with a grooved surface and with a deformable wall, and in Non-Newtonian fluids, are suggested.
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BAMBREY, ROSS R., JEAN N. REINAUD, and DAVID G. DRITSCHEL. "Strong interactions between two corotating quasi-geostrophic vortices." Journal of Fluid Mechanics 592 (November 14, 2007): 117–33. http://dx.doi.org/10.1017/s0022112007008373.
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In this paper we investigate the interaction between two corotating quasi-geostrophic vortices. The initially ellipsoidal vortices are separated horizontally by a distance corresponding to the margin of stability, as determined from an ellipsoidal analysis. The subsequent interaction depends on four parameters: the vortex volume ratio, the vertical centroid separation, and the height-to-width aspect ratios of each vortex. The most commonly observed strong interaction is partial merger, where only part of the weaker vortex is incorporated into the stronger one or cast into filamentary debris. Despite the proliferation of small-scale filamentary structure during many vortex interactions, on average the self-induced vortex energy exhibits an ‘inverse cascade’ to larger scales, broadly consistent with spectral theories of turbulence. Curiously, we observe that a range of intermediate-scale vortices are preferentially sheared out during the interactions, leaving two main populations of large and small vortices.
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TANG, S. K., and N. W. M. KO. "Sound sources in the interactions of two inviscid two-dimensional vortex pairs." Journal of Fluid Mechanics 419 (September 25, 2000): 177–201. http://dx.doi.org/10.1017/s0022112000001294.
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The sources of sound during the interactions of two identical two-dimensional inviscid vortex pairs are investigated numerically by using the vortex sound theory and the method of contour dynamics. The sound sources are identified and then separated into two independent components, which represent the contributions from the vortex centroid dynamics and the microscopic vortex core dynamics. Results show that the sound generation mechanism of the latter is independent of the type of vortex pair interaction, while that of the former depends on the jerks, accelerations and vortex forces on the vortex pairs. The power developed by the vortex forces is found to be important in the generation of sound when the vortex cores are severely deformed and their centroids are close to each other. The isolated source terms also explain the appearance of wavy oscillations on the time variations of the sound source strengths in the vortex ring and the two-dimensional vortex interaction systems.
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Kivshar, Yuri S., Alexander Nepomnyashchy, Vladimir Tikhonenko, Jason Christou, and Barry Luther-Davies. "Vortex-stripe soliton interactions." Optics Letters 25, no. 2 (January 15, 2000): 123. http://dx.doi.org/10.1364/ol.25.000123.
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Doligalski, T. L., C. R. Smith, and J. D. A. Walker. "Vortex Interactions with Walls." Annual Review of Fluid Mechanics 26, no. 1 (January 1994): 573–616. http://dx.doi.org/10.1146/annurev.fl.26.010194.003041.
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Roenby, Johan, and Hassan Aref. "Chaos in body–vortex interactions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (February 24, 2010): 1871–91. http://dx.doi.org/10.1098/rspa.2009.0619.
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The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.
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KUO, ALLEN C., and LORENZO M. POLVANI. "Wave–vortex interaction in rotating shallow water. Part 1. One space dimension." Journal of Fluid Mechanics 394 (September 10, 1999): 1–27. http://dx.doi.org/10.1017/s0022112099005534.
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Using a physical space (i.e. non-modal) approach, we investigate interactions between fast inertio-gravity (IG) waves and slow balanced flows in a shallow rotating fluid. Specifically, we consider a train of IG waves impinging on a steady, exactly balanced vortex. For simplicity, the one-dimensional problem is studied first; the limitations of one-dimensionality are offset by the ability to define balance in an exact way. An asymptotic analysis of the problem in the small-amplitude limit is performed to demonstrate the existence of interactions. It is shown that these interactions are not confined to the modification of the wave field by the vortex but, more importantly, that the waves are able to alter in a non-trivial way the potential vorticity associated with that vortex. Interestingly, in this one-dimensional problem, once the waves have traversed the vortex region and have propagated away, the vortex exactly recovers its initial shape and thus bears no signature of the interaction. Furthermore, we prove this last result in the case of arbitrary vortex and wave amplitudes. Numerical integrations of the full one-dimensional shallow-water equations in strongly nonlinear regimes are also performed: they confirm that time-dependent interactions exist and increase with wave amplitude, while at the final state the vortex bears no sign of the interaction. In addition, they reveal that cyclonic vortices interact more strongly with the wave field than anticyclonic ones.
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Nair, Aditya G., and Kunihiko Taira. "Network-theoretic approach to sparsified discrete vortex dynamics." Journal of Fluid Mechanics 768 (March 10, 2015): 549–71. http://dx.doi.org/10.1017/jfm.2015.97.
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We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters interacting amongst themselves. We also evaluate the performance of sparsification with increasing number of point vortices. The sparsified-dynamics model developed with spectral graph theory requires a reduced number of vortex-to-vortex interactions but agrees well with the full nonlinear dynamics. Furthermore, the sparsified model derived from the sparse graphs conserves the invariants of discrete vortex dynamics. We highlight the similarities and differences between the present sparsified-dynamics model and reduced-order models.
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Dritschel, David G. "A general theory for two-dimensional vortex interactions." Journal of Fluid Mechanics 293 (June 25, 1995): 269–303. http://dx.doi.org/10.1017/s0022112095001716.
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A general theory for two-dimensional vortex interactions is developed from the observation that, under slowly changing external influences, an individual vortex evolves through a series of equilibrium states until such a state proves unstable. Once an unstable equilibrium state is reached, a relatively fast unsteady evolution ensues, typically involving another nearby vortex. During this fast unsteady evolution, a fraction of the original coherent circulation is lost to filamentary debris, and, remarkably, the flow reorganizes into a set of quasi-steady stable vortices.The simplifying feature of the proposed theory is its use of adiabatic steadiness and marginal stability to determine the shapes and separation distance of vortices on the brink of an inelastic interaction. As a result, the parameter space for the inelastic interaction of nearby vortices is greatly reduced. In the case of two vortex patches, which is the focus of the present work, inelastic interactions depend only on a single parameter: the area ratio of the two vortices (taking the vorticity magnitude inside each to be equal). Without invoking adiabatic steadiness and marginal stability, one would have to contend with the additional parameters of vortex separation and shape, and the latter is actually an infinitude of parameters.
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Cenedese, Claudia, Robert E. Todd, Glen G. Gawarkiewicz, W. Brechner Owens, and Andrey Y. Shcherbina. "Offshore Transport of Shelf Waters through Interaction of Vortices with a Shelfbreak Current." Journal of Physical Oceanography 43, no. 5 (May 1, 2013): 905–19. http://dx.doi.org/10.1175/jpo-d-12-0150.1.
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Abstract Interactions between vortices and a shelfbreak current are investigated, with particular attention to the exchange of waters between the continental shelf and slope. The nonlinear, three-dimensional interaction between an anticyclonic vortex and the shelfbreak current is studied in the laboratory while varying the ratio ε of the maximum azimuthal velocity in the vortex to the maximum alongshelf velocity in the shelfbreak current. Strong interactions between the shelfbreak current and the vortex are observed when ε > 1; weak interactions are found when ε < 1. When the anticyclonic vortex comes in contact with the shelfbreak front during a strong interaction, a streamer of shelf water is drawn offshore and wraps anticyclonically around the vortex. Measurements of the offshore transport and identification of the particle trajectories in the shelfbreak current drawn offshore from the vortex allow quantification of the fraction of the shelfbreak current that is deflected onto the slope; this fraction increases for increasing values of ε. Experimental results in the laboratory are strikingly similar to results obtained from observations in the Middle Atlantic Bight (MAB); after proper scaling, measurements of offshore transport and offshore displacement of shelf water for vortices in the MAB that span a range of values of ε agree well with laboratory predictions.
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Kuo, Hung-Chi, Wayne H. Schubert, Chia-Ling Tsai, and Yu-Fen Kuo. "Vortex Interactions and Barotropic Aspects of Concentric Eyewall Formation." Monthly Weather Review 136, no. 12 (December 1, 2008): 5183–98. http://dx.doi.org/10.1175/2008mwr2378.1.
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Abstract Concentric eyewall formation can be idealized as the interaction of a tropical cyclone core with nearby weaker vorticity of various spatial scales. This paper considers barotropic aspects of concentric eyewall formation from modified Rankine vortices. In this framework, the following parameters are found to be important in concentric eyewall formation: vorticity strength ratio, separation distance, companion vortex size, and core vortex skirt parameter. A vorticity skirt on the core vortex affects the filamentation dynamics in two important ways. First, the vorticity skirt lengthens the filamentation time, and therefore slows moat formation in the region just outside the radius of maximum wind. Second, at large radii, a skirted core vortex induces higher strain rates than a corresponding Rankine vortex and is thus more capable of straining out the vorticity field far from the core. Calculations suggest that concentric structures result from binary interactions when the small vortex is at least 4–6 times as strong as the larger companion vortex. An additional requirement is that the separation distance between the edges of the two vortices be less than 6–7 times the smaller vortex radius. Broad moats form when the initial companion vortex is small, the vorticity skirt outside the radius of maximum wind is small, and the strength ratio is large. In concentric cases, an outer vorticity ring develops when the initial companion vortex is large, the vorticity skirt outside the radius of maximum wind is small, and the strength ratio is not too large. In general, when the companion vortex is 3 times as strong as the core vortex and the separation distance is 4–6 times the radius of the smaller vortex, a core vortex with a vorticity skirt produces concentric structures. In contrast, a Rankine vortex produces elastic interaction in this region of parameter space. Thus, a Rankine vortex of sufficient strength favors the formation of a concentric structure closer to the core vortex, while a skirted vortex of sufficient strength favors the formation of concentric structures farther from the core vortex. This may explain satellite microwave observations that suggest a wide range of radii for concentric eyewalls.
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Chernodub, M. "Vortex profiles and vortex interactions at the electroweak crossover." Nuclear Physics B - Proceedings Supplements 83-84, no. 1-3 (March 2000): 571–73. http://dx.doi.org/10.1016/s0920-5632(00)00318-2.
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Chernodub, M. N., E. M. Ilgenfritz, and A. Schiller. "Vortex profiles and vortex interactions at the electroweak crossover." Nuclear Physics B - Proceedings Supplements 83-84 (April 2000): 571–73. http://dx.doi.org/10.1016/s0920-5632(00)91741-9.
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Gemmell, Brad J., Kevin T. Du Clos, Sean P. Colin, Kelly R. Sutherland, and John H. Costello. "The most efficient metazoan swimmer creates a ‘virtual wall’ to enhance performance." Proceedings of the Royal Society B: Biological Sciences 288, no. 1942 (January 6, 2021): 20202494. http://dx.doi.org/10.1098/rspb.2020.2494.
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It has been well documented that animals (and machines) swimming or flying near a solid boundary get a boost in performance. This ground effect is often modelled as an interaction between a mirrored pair of vortices represented by a true vortex and an opposite sign ‘virtual vortex’ on the other side of the wall. However, most animals do not swim near solid surfaces and thus near body vortex–vortex interactions in open-water swimmers have been poorly investigated. In this study, we examine the most energetically efficient metazoan swimmer known to date, the jellyfish Aurelia aurita , to elucidate the role that vortex interactions can play in animals that swim away from solid boundaries. We used high-speed video tracking, laser-based digital particle image velocimetry (dPIV) and an algorithm for extracting pressure fields from flow velocity vectors to quantify swimming performance and the effect of near body vortex–vortex interactions. Here, we show that a vortex ring (stopping vortex), created underneath the animal during the previous swim cycle, is critical for increasing propulsive performance. This well-positioned stopping vortex acts in the same way as a virtual vortex during wall-effect performance enhancement, by helping converge fluid at the underside of the propulsive surface and generating significantly higher pressures which result in greater thrust. These findings advocate that jellyfish can generate a wall-effect boost in open water by creating what amounts to a ‘virtual wall’ between two real, opposite sign vortex rings. This explains the significant propulsive advantage jellyfish possess over other metazoans and represents important implications for bio-engineered propulsion systems.
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Zhang, Yu, Joseph Pedlosky, and Glenn R. Flierl. "Shelf Circulation and Cross-Shelf Transport out of a Bay Driven by Eddies from an Open-Ocean Current. Part I: Interaction between a Barotropic Vortex and a Steplike Topography." Journal of Physical Oceanography 41, no. 5 (May 1, 2011): 889–910. http://dx.doi.org/10.1175/2010jpo4496.1.
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Abstract This paper examines interaction between a barotropic point vortex and a steplike topography with a bay-shaped shelf. The interaction is governed by two mechanisms: propagation of topographic Rossby waves and advection by the forcing vortex. Topographic waves are supported by the potential vorticity (PV) jump across the topography and propagate along the step only in one direction, having higher PV on the right. Near one side boundary of the bay, which is in the wave propagation direction and has a narrow shelf, waves are blocked by the boundary, inducing strong out-of-bay transport in the form of detached crests. The wave–boundary interaction as well as out-of-bay transport is strengthened as the minimum shelf width is decreased. The two control mechanisms are related differently in anticyclone- and cyclone-induced interactions. In anticyclone-induced interactions, the PV front deformations are moved in opposite directions by the point vortex and topographic waves; a topographic cyclone forms out of the balance between the two opposing mechanisms and is advected by the forcing vortex into the deep ocean. In cyclone-induced interactions, the PV front deformations are moved in the same direction by the two mechanisms; a topographic cyclone forms out of the wave–boundary interaction but is confined to the coast. Therefore, anticyclonic vortices are more capable of driving water off the topography. The anticyclone-induced transport is enhanced for smaller vortex–step distance or smaller topography when the vortex advection is relatively strong compared to the wave propagation mechanism.
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Nguyen, Van Luc, Tomohiro Degawa, and Tomomi Uchiyama. "Numerical simulation of the interaction between a vortex ring and a bubble plume." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 9 (September 2, 2019): 3192–224. http://dx.doi.org/10.1108/hff-12-2018-0734.
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Purpose This paper aims to provide discussions of a numerical method for bubbly flows and the interaction between a vortex ring and a bubble plume. Design/methodology/approach Small bubbles are released into quiescent water from a cylinder tip. They rise under the buoyant force, forming a plume. A vortex ring is launched vertically upward into the bubble plume. The interactions between the vortex ring and the bubble plume are numerically simulated using a semi-Lagrangian–Lagrangian approach composed of a vortex-in-cell method for the fluid phase and a Lagrangian description of the gas phase. Findings A vortex ring can transport the bubbles surrounding it over a distance significantly depending on the correlative initial position between the bubbles and the core center. The motion of some bubbles is nearly periodic and gradually extinguishes with time. These bubble trajectories are similar to two-dimensional-helix shapes. The vortex is fragmented into multiple regions with high values of Q, the second invariant of velocity gradient tensor, settling at these regional centers. The entrained bubbles excite a growth rate of the vortex ring's azimuthal instability with a formation of the second- and third-harmonic oscillations of modes of 16 and 24, respectively. Originality/value A semi-Lagrangian–Lagrangian approach is applied to simulate the interactions between a vortex ring and a bubble plume. The simulations provide the detail features of the interactions.
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Renard, P. H., D. Thévenin, J. C. Rolon, and S. Candel. "Dynamics of flame/vortex interactions." Progress in Energy and Combustion Science 26, no. 3 (June 2000): 225–82. http://dx.doi.org/10.1016/s0360-1285(00)00002-2.
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Cutler, A. D., and P. Bradshaw. "Strong vortex/boundary layer interactions." Experiments in Fluids 14, no. 5 (April 1993): 321–32. http://dx.doi.org/10.1007/bf00189490.
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Cutler, A. D., and P. Bradshaw. "Strong vortex/boundary layer interactions." Experiments in Fluids 14, no. 6 (May 1993): 393–401. http://dx.doi.org/10.1007/bf00190193.
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Chorin, Alexandre Joel. "Hairpin removal in vortex interactions." Journal of Computational Physics 91, no. 1 (November 1990): 1–21. http://dx.doi.org/10.1016/0021-9991(90)90001-h.
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Chorin, Alexander J. "Hairpin removal in vortex interactions." Journal of Computational Physics 87, no. 2 (April 1990): 496. http://dx.doi.org/10.1016/0021-9991(90)90272-3.
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Rutland, Christopher J., and Joel H. Ferziger. "Simulations of flame-vortex interactions." Combustion and Flame 84, no. 3-4 (April 1991): 343–60. http://dx.doi.org/10.1016/0010-2180(91)90011-y.
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Forster, Kyle J., Sammy Diasinos, Graham Doig, and Tracie J. Barber. "Large eddy simulation of transient upstream/downstream vortex interactions." Journal of Fluid Mechanics 862 (January 9, 2019): 227–60. http://dx.doi.org/10.1017/jfm.2018.949.
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Experimentally validated large eddy simulations were performed on two NACA0012 vanes at various lateral offsets to observe the transient effects of the near field interactions between two streamwise vortices. The vanes were separated in the streamwise direction, allowing the upstream vortex to impact on the downstream geometry. These vanes were evaluated at an angle of incidence of $8^{\circ }$ and a Reynolds number of 70 000, with rear vane angle reversed to create a co-rotating or counter-rotating vortex pair. The downstream vortex merged with the upstream in the co-rotating condition, driven by the suppression of one of the tip vortices of the downstream vane. At close proximity to the pressure side, the vane elongated the upstream vortex, resulting in it being the weakened and merging into the downstream vortex. This produced a transient production of bifurcated vortices in the wake region. The downstream vortex of the co-rotating pair experienced faster meandering growth, with position oscillations equalising between the vortices. The position oscillation was determined to be responsible for statistical variance in the merging location, with variation in vortex separation causing the vortices at a single plane to merge and separate in a time-dependent manner. In the counter-rotating condition position oscillations were found to be larger, with higher growth, but less uniform periodicity. It was found that the circulation transfer between the vortices was linked to the magnitude of their separation, with high separation fluctuations weakening the upstream vortex and strengthening the downstream vortex. In the case of upstream vortex impingement on the downstream vane, the upstream vortex was found to bifurcate, with a four vortex system being formed by interactions with the shear layer. This eventually resulted in a single dominant vortex, which did not magnify its oscillation amplitudes as it travelled downstream due to the destruction of the interacting vortices.
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Folz, Patrick J. R., and Keiko K. Nomura. "A quantitative assessment of viscous asymmetric vortex pair interactions." Journal of Fluid Mechanics 829 (September 14, 2017): 1–30. http://dx.doi.org/10.1017/jfm.2017.527.
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The interactions of two like-signed vortices in viscous fluid are investigated using two-dimensional numerical simulations performed across a range of vortex strength ratios, $\unicode[STIX]{x1D6EC}=\unicode[STIX]{x1D6E4}_{1}/\unicode[STIX]{x1D6E4}_{2}\leqslant 1$, corresponding to vortices of circulation, $\unicode[STIX]{x1D6E4}_{i}$, with differing initial size and/or peak vorticity. In all cases, the vortices evolve by viscous diffusion before undergoing a primary convective interaction, which ultimately results in a single vortex. The post-interaction vortex is quantitatively evaluated in terms of an enhancement factor, $\unicode[STIX]{x1D700}=\unicode[STIX]{x1D6E4}_{end}/\unicode[STIX]{x1D6E4}_{2,start}$, which compares its circulation, $\unicode[STIX]{x1D6E4}_{end}$, to that of the stronger starting vortex, $\unicode[STIX]{x1D6E4}_{2,start}$. Results are effectively characterized by a mutuality parameter, $MP\equiv (S/\unicode[STIX]{x1D714})_{1}/(S/\unicode[STIX]{x1D714})_{2}$, where the ratio of induced strain rate, $S$, to peak vorticity, $\unicode[STIX]{x1D714}$, for each vortex, $(S/\unicode[STIX]{x1D714})_{i}$, is found to have a critical value, $(S/\unicode[STIX]{x1D714})_{cr}\approx 0.135$, above which core detrainment occurs. If $MP$ is sufficiently close to unity, both vortices detrain and a two-way mutual entrainment process leads to $\unicode[STIX]{x1D700}>1$, i.e. merger. In asymmetric interactions and mergers, generally one vortex dominates; the weak/no/strong vortex winner regimes correspond to $MP<,=,>1$, respectively. As $MP$ deviates from unity, $\unicode[STIX]{x1D700}$ decreases until a critical value, $MP_{cr}$ is reached, beyond which there is only a one-way interaction; one vortex detrains and is destroyed by the other, which dominates and survives. There is no entrainment and $\unicode[STIX]{x1D700}\sim 1$, i.e. only a straining out occurs. Although $(S/\unicode[STIX]{x1D714})_{cr}$ appears to be independent of Reynolds number, $MP_{cr}$ shows a dependence. Comparisons are made with available experimental data from Meunier (2001, PhD thesis, Université de Provence-Aix-Marseille I).
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Horner, M. B., E. Saliveros, and R. A. McD Galbraith. "An experimental investigation of the oblique blade-vortex interaction." Aeronautical Journal 96, no. 955 (May 1992): 184–91. http://dx.doi.org/10.1017/s0001924000024830.
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AbstractThe experimental results of an oblique Blade-Vortex Interaction (BVI) study are presented. The quality of all pressure data reflects improvements in the Glasgow University BVI facility and in the method of reducing and presenting data. The data collected during oblique interactions is found qualitatively and quantitatively similar to that collected in corresponding parallel interactions, for interactions within ± 30° of parallel. Details of the pressure data are examined in the light of understanding gained from parallel BVI experimentation. The study highlights the effects of three dimensional flow interactions not accounted for in the nondimensionalisation traditionally utilised in the analysis of parallel blade-vortex interactions.
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KALKHORAN, I. M., M. K. SMART, and F. Y. WANG. "Supersonic vortex breakdown during vortex/cylinder interaction." Journal of Fluid Mechanics 369 (August 25, 1998): 351–80. http://dx.doi.org/10.1017/s0022112098001566.
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The head-one interaction of a supersonic streamwise vortex with a circular cylinder reveals a vortex breakdown similar in many ways to that of incompressible vortex breakdown. In particular, the dramatic flow reorganization observed during the interaction resembles the conical vortex breakdown reported by Sarpkaya (1995) at high Reynolds number. In the present study, vortex breakdown is brought about when moderate and strong streamwise vortices encounter the bow shock in front of a circular cylinder at Mach 2.49. The main features of the vortex/cylinder interaction are the formation of a blunt-nosed conical shock with apex far upstream of the undisturbed shock stand-off distance, and a vortex core which responds to passage through the apex of the conical shock by expanding into a turbulent conical flow structure. The geometry of the expanding vortex core as well as the location of the conical shock apex are seen to be strong functions of the incoming vortex strength and the cylinder diameter. A salient feature of the supersonic vortex breakdown is the formation of an entropy-shear layer, which separates an interior subsonic zone containing the burst vortex from the surrounding supersonic flow. In keeping with the well-established characteristics of the low-speed vortex breakdown, a region of reversed flow is observed inside the turbulent subsonic zone. The steady vortex/cylinder interaction flow fields generated in the current study exhibit many characteristics of the unsteady vortex distortion patterns previously observed during normal shock wave/vortex interactions. This similarity of the instantaneous flow structure indicates that the phenomenon previously called vortex distortion by Kalkhoran et al. (1996) is a form of supersonic vortex breakdown.
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Garmann, D. J., and M. R. Visbal. "Interactions of a streamwise-oriented vortex with a finite wing." Journal of Fluid Mechanics 767 (February 24, 2015): 782–810. http://dx.doi.org/10.1017/jfm.2015.51.
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AbstractA canonical study is developed to investigate the unsteady interactions of a streamwise-oriented vortex impinging upon a finite surface using high-fidelity simulation. As a model problem, an analytically defined vortex superimposed on a free stream is convected towards an aspect-ratio-six ($\mathit{AR}=6$) plate oriented at an angle of ${\it\alpha}=4^{\circ }$ and Reynolds number of $\mathit{Re}=20\,000$ in order to characterize the unsteady modes of interaction resulting from different spanwise positions of the incoming vortex. Outboard, tip-aligned and inboard positioning are shown to produce three distinct flow regimes: when the vortex is positioned outboard of, but in close proximity to, the wingtip, it pairs with the tip vortex to form a dipole that propels itself away from the plate through mutual induction, and also leads to an enhancement of the tip vortex. When the incoming vortex is aligned with the wingtip, the tip vortex is initially strengthened by the proximity of the incident vortex, but both structures attenuate into the wake as instabilities arise in the pair’s feeding sheets from the entrainment of opposite-signed vorticity into either structure. Finally, when the incident vortex is positioned inboard of the wingtip, the vortex bifurcates in the time-mean sense with portions convecting above and below the wing, and the tip vortex is mostly suppressed. The time-mean bifurcation is actually a result of an unsteady spiralling instability in the vortex core that reorients the vortex as it impacts the leading edge, pinches off, and alternately attaches to either side of the wing. The increased effective angle of attack inboard of impingement enhances the three-dimensional recirculation region created by the separated boundary layer off the leading edge which draws fluid from the incident vortex inboard and diminishes its impact on the outboard section of the wing. The slight but remaining downwash present outboard of impingement reduces the effective angle of attack in that region, resulting in a small separation bubble on either side of the wing in the time-mean solution, effectively unloading the tip outboard of impingement and suppressing the tip vortex. All incident vortex positions provide substantial increases in the wing’s lift-to-drag ratio; however, significant sustained rolling moments also result. As the vortex is brought inboard, the rolling moment diminishes and eventually switches sign as the reduced outboard loading balances the augmented sectional lift inboard of impingement.
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HULSHOFF, S. J., A. HIRSCHBERG, and G. C. J. HOFMANS. "Sound production of vortex–nozzle interactions." Journal of Fluid Mechanics 439 (July 23, 2001): 335–52. http://dx.doi.org/10.1017/s0022112001004554.
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The factors which affect the sound production of a vortex as it passes through a nozzle are investigated at both low and high Mach numbers using time-accurate inviscid-flow computations. Vortex circulation, initial position, and mean-flow Mach number are shown to be the primary factors which influence the amplitude and phase of the sound produced. Nozzle geometry and distribution of vorticity are also shown to play significant roles in determining the detailed form of the signal. Additionally, it is shown that solution bifurcations are possible at sufficiently large values of vortex circulation. Comparisons are made between sound signals computed directly using a numerical method for the Euler equations and predictions obtained using a compressible vortex-sound analogy coupled with a compact-source assumption for the computation of vorticity dynamics. The results confirm that the latter approach is accurate for a range of problems with low mean-flow Mach numbers. At higher Mach numbers, however, the non-compactness of the source becomes apparent, resulting in significant changes to the character of the signal which cannot be predicted using the analogy-based approach. Implications for the construction of simplified models of vortex sound in solid-rocket nozzles are discussed.
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Sakajo, Takashi, and Yuuki Shimizu. "Point vortex interactions on a toroidal surface." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (July 2016): 20160271. http://dx.doi.org/10.1098/rspa.2016.0271.
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Owing to non-constant curvature and a handle structure, it is not easy to imagine intuitively how flows with vortex structures evolve on a toroidal surface compared with those in a plane, on a sphere and a flat torus. In order to cultivate an insight into vortex interactions on this manifold, we derive the evolution equation for N -point vortices from Green's function associated with the Laplace–Beltrami operator there, and we then formulate it as a Hamiltonian dynamical system with the help of the symplectic geometry and the uniformization theorem. Based on this Hamiltonian formulation, we show that the 2-vortex problem is integrable. We also investigate the point vortex equilibria and the motion of two-point vortices with the strengths of the same magnitude as one of the fundamental vortex interactions. As a result, we find some characteristic interactions between point vortices on the torus. In particular, two identical point vortices can be locally repulsive under a certain circumstance.
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LE DIZÈS, STÉPHANE, and ALBERTO VERGA. "Viscous interactions of two co-rotating vortices before merging." Journal of Fluid Mechanics 467 (September 24, 2002): 389–410. http://dx.doi.org/10.1017/s0022112002001532.
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The viscous evolution of two co-rotating vortices is analysed using direct two-dimensional numerical simulations of the Navier–Stokes equations. The article focuses on vortex interaction regimes before merging. Two parameters are varied: a steepness parameter n which measures the steepness of the initial vorticity profiles in a given family of profiles, and the Reynolds number Re (between 500 and 16 000). Two distinct relaxation processes are identified. The first one is non-viscous and corresponds to a rapid adaptation of each vortex to the external (strain) field generated by the other vortex. This adaptation process, which is profile dependent, is described and explained using the damped Kelvin modes of each vortex. The second relaxation process is a slow diffusion phenomenon. It is similar to the relaxation of any non-Gaussian axisymmetrical vortex towards the Gaussian. The quasi-stationary solution evolves on a viscous-time scale toward a single attractive solution which corresponds to the evolution from two initially Gaussian vortices. The attractive solution is analysed in detail up to the merging threshold a/b ≈ 0.22 where a and b are the vortex radius and the separation distance respectively. The vortex core deformations are quantified and compared to those induced by a single vortex in a rotating strain field. A good agreement with the asymptotic predictions is demonstrated for the eccentricity of vortex core streamlines. A weak anomalous Reynolds number dependence of the solution is also identified. This dependence is attributed to the advection–diffusion of vorticity towards the hyperbolic points of the system and across the separatrix connecting these points. A Re1/3 scaling for the vorticity at the central hyperbolic point is obtained. These findings are discussed in the context of a vortex merging criterion.
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Lentink, David, GertJan F. Van Heijst, Florian T. Muijres, and Johan L. Van Leeuwen. "Vortex interactions with flapping wings and fins can be unpredictable." Biology Letters 6, no. 3 (February 3, 2010): 394–97. http://dx.doi.org/10.1098/rsbl.2009.0806.
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As they fly or swim, many animals generate a wake of vortices with their flapping fins and wings that reveals the dynamics of their locomotion. Previous studies have shown that the dynamic interaction of vortices in the wake with fins and wings can increase propulsive force. Here, we explore whether the dynamics of the vortex interactions could affect the predictability of propulsive forces. We studied the dynamics of the interactions between a symmetrically and periodically pitching and heaving foil and the vortices in its wake, in a soap-film tunnel. The phase-locked movie sequences reveal that abundant chaotic vortex-wake interactions occur at high Strouhal numbers. These high numbers are representative for the fins and wings of near-hovering animals. The chaotic wake limits the forecast horizon of the corresponding force and moment integrals. By contrast, we find periodic vortex wakes with an unlimited forecast horizon for the lower Strouhal numbers (0.2–0.4) at which many animals cruise. These findings suggest that swimming and flying animals could control the predictability of vortex-wake interactions, and the corresponding propulsive forces with their fins and wings.
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Voropayev, S. I., and Ya D. Afanasyev. "Two-dimensional vortex-dipole interactions in a stratified fluid." Journal of Fluid Mechanics 236 (March 1992): 665–89. http://dx.doi.org/10.1017/s0022112092001575.
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Planar motion produced when a viscous fluid is forced from an initial state of rest is studied. We consider a vortex dipole produced by the action of a point force (Cantwell 1986), and a vortex quadrupole produced by the action of two equal forces of opposite direction. We also present results from an experimental investigation into the dynamics of the interactions between vortex dipoles as well as between vortex dipoles and a vertical wall in a stratified fluid. Theoretical consideration reveals that the dynamics of two-dimensional vortex-dipole interactions are determined by two main governing parameters: the dipolar intensity of the vorticity distribution (momentum) and the quadrupolar intensity of the vorticity distribution of the flow. We document details of different basic types of interactions and present a physical interpretation of the results obtained in terms of vortex multipoles: dipoles, quadrupoles and their combinations.
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Zheng, Z. C., and W. Li. "Dependence of radiated sound frequency on vortex core dynamics in multiple vortex interactions." Aeronautical Journal 113, no. 1142 (April 2009): 233–42. http://dx.doi.org/10.1017/s0001924000002906.
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Abstract With both theoretical analysis and measurement data, it has been identified previously that there exists a robust sound emission from a pair of counter-rotating aircraft wake vortices at the frequency of unsteady vortex core rotation. In a vortex system with multiple vortices, the sound emission frequency can be subjected to change because of interactions among the vortices. The behaviour of the influence, indicated by the ratio between the core size and the distance of the vortices and the underlining vortex core dynamic mechanisms, is investigated in this study. A vortex particle method is used to simulate the vortex core dynamics in two-dimensional, inviscid and incompressible flow. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula. Cases of co-rotating vortices and a multiple-vortex system composed of two counter-rotating vortex pairs are studied for applications to aircraft wake vortex sound. The study shows, without vortex merging, individual frequencies can be clearly identified that are due each to core rotation (self induction) and co-rotating motion of a vortex centre around the other (mutual induction). The ratio of the core size and the distance between vortices does not seem to significantly influence the frequency of vortex core rotation. With vortex merging, a single frequency due to the merged vortex core is generated.
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Carlson, Bailey, Al Habib Ullah, and Jordi Estevadeordal. "Experimental Investigation of Vortex-Tube Streamwise-Vorticity Characteristics and Interaction Effects with a Finite-Aspect-Ratio Wing." Fluids 5, no. 3 (July 24, 2020): 122. http://dx.doi.org/10.3390/fluids5030122.
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An experimental study is conducted to analyze a streamwise-oriented vortex and investigate the unsteady interaction with a finite-aspect-ratio wing. A pressurized vortex tube is used to generate streamwise vortices in a wind tunnel and the resulting flow behavior is analyzed. The vortex tube, operated at various pressures, yields flows that evolve downstream under several freestream wind tunnel speeds. Flow measurements are performed using two- and three- dimensional (2D and 3D) particle image velocimetry to observe vortices and their freestream interactions from which velocity and vorticity data are comparatively analyzed. Results indicate that vortex velocity greater than freestream flow velocity is a primary factor in maintaining vortex structures further downstream, while increased supply pressure and reduced freestream velocity also reduce vortex dissipation rate. The generated streamwise-oriented vortex is also impinged on a finite-aspect-ratio airfoil wing with a cross-section of standard NACA0012 airfoil. The wingtip-aligned vortex is shown to investigate the interaction of the streamwise vortex and the wingtip vortex region. The results indicate that the vorticity at the high vortex-tube pressure has a significant effect on the boundary layer of airfoil.
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Koshel, Konstantin, Eugene Ryzhov, and Xavier Carton. "Vortex Interactions Subjected to Deformation Flows: A Review." Fluids 4, no. 1 (January 18, 2019): 14. http://dx.doi.org/10.3390/fluids4010014.
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Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.
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Masson, C. A., R. B. Green, R. A. McD Galbraith, and F. N. Coton. "Experimental investigation of a loaded rotor blade's interaction with a single vortex." Aeronautical Journal 102, no. 1018 (December 1998): 451–57. http://dx.doi.org/10.1017/s000192400002769x.
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AbstractPresented in this paper are the preliminary results from a blade-vortex interaction (BVI) test series conducted in the University of Glasgow's 1·61m x 2·13m closed-return, low-speed windtunnel, in which a single vortex interaction with a rigid, loaded rotor blade was studied. This work is an extension of that by Horner and Galbraith, which describes the flow phenomena present during single vortex interaction with an unloaded blade. The paper presents blade surface pressure data recorded by 72 pressure transducers located in the outer regions of the blade during these interactions. Integrated Cn and Cm1/4 data are also presented to provide a detailed history of a BVI event. In addition, a method of isolating the bound circulation and vortex induced effects is presented, from which it is concluded that for a BVI event the vortex-induced effects are (to a first approximation) independent of rotor pitch setting.
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Adhikari, Prabal, and Jaehong Choi. "Magnetic vortices in the Abelian Higgs model with derivative interactions." International Journal of Modern Physics A 33, no. 36 (December 30, 2018): 1850215. http://dx.doi.org/10.1142/s0217751x18502159.
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We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the [Formula: see text] gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external magnetic field: since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum-dependent terms. We find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of “successive approximations,” which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).
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Jaworski, J. W. "Sound from aeroelastic vortex–fibre interactions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2159 (October 14, 2019): 20190071. http://dx.doi.org/10.1098/rsta.2019.0071.
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The motion of a line vortex moving past a one-dimensional flexible fibre is examined theoretically. A Schwarz–Christoffel conformal mapping enables the analytical solution of the potential flow field and its hydrodynamic moment on the flexible fibre, which is composed of a rigid segment constrained to angular motions on a wedge. The hydroelastic coupling of the vortex path and fibre motion affects the noise signature, which is evaluated for the special case of acoustically compact fibres embedded in a half plane. Results from this analysis attempt to address how the coupled interactions between vortical sources and flexible barbules on the upper surface of owl wings may contribute to their acoustic stealth. The analytical formulation is also amenable to application to vortex sound prediction from flexible trailing edges provided that an appropriate acoustic Green's function can be determined. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.
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Smith, G. B., and T. Wei. "Small-scale structure in colliding off-axis vortex rings." Journal of Fluid Mechanics 259 (January 25, 1994): 281–90. http://dx.doi.org/10.1017/s0022112094000133.
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Off-axis collisions of equal-strength vortex rings were experimentally examined. Two equal-strength vortices were generated which moved toward each other along parallel, but offset, trajectories. Two colour laser-induced fluorescence visualization techniques were used to observe these phenomena and gain insight into their importance in vortex interactions. The most prominent features of this interaction were rapid growth and rotation of the rings and formation of evenly spaced ringlets around the cores of the original rings. Large-scale motions are described using simple vortex induction arguments. The small scales are caused by nonlinear amplification of instabilities during the asymmetric interaction.
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ILIE, Marcel, and Augustin SEMENESCU. "AERODYNAMIC STUDIES OF AIRCRAFT ENGINE TURBINE STAGE." ANNALS OF THE ACADEMY OF ROMANIAN SCIENTISTS Series on ENGINEERING SCIENCES 14, no. 2 (2022): 5–18. http://dx.doi.org/10.56082/annalsarscieng.2022.2.5.
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The present research concerns the aerodynamic computational studies of stator-rotor turbine stage. The computational studies are carried out using the large-eddy simulation approach. In the aircraft engine compressor/turbine stage blade-vortex interactions occur. The present study aims at the understanding the blade-vortex interaction mechanism and its impact on the aerodynamics of rotor-stator compressor/turbine stages. The computational studies are carried out in a rotating frame of reference, for high-Reynolds number flow, Re = 1.3x105. The analysis reveals that the blade-vortex interaction causes the flow separation on the stator stage and a time-varying lift and drag.
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Mishra, Prasad, Renganathan Sudharshan, and Kumar Ezhil. "Numerical study of flame/vortex interactions in 2-D Trapped Vortex Combustor." Thermal Science 18, no. 4 (2014): 1373–87. http://dx.doi.org/10.2298/tsci111006162m.
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The interactions between flame and vortex in a 2-D Trapped Vortex Combustor are investigated by simulating the Reynolds Averaged Navier Stokes (RANS) equations, for the following five cases namely (i) non-reacting (base) case, (ii) post-vortex ignition without premixing, (iii) post-vortex ignition with premixing, (iv) pre-vortex ignition without premixing and (v) pre-vortex ignition with premixing. For the post-vortex ignition without premixing case, the reactants are mixed well in the cavity resulting in a stable ?C? shaped flame along the vortex edge. Further, there is insignificant change in the vorticity due to chemical reactions. In contrast, for the pre-vortex ignition case (no premixing); the flame gets stabilized at the interface of two counter rotating vortices resulting in reduced reaction rates. There is a noticeable change in the location and size of the primary vortex as compared to case (ii). When the mainstream air is premixed with fuel, there is a further reduction in the reaction rates and thus structure of cavity flame gets altered significantly for case (v). Pilot flame established for cases (ii) and (iii) are well shielded from main flow and hence the flame structure and reaction rates do not change appreciably. Hence, it is expected that cases (ii) and (iii) can perform well over a wide range of operating conditions.
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George, A. R., and A. S. Lyrintzis. "Acoustics of transonic blade-vortex interactions." AIAA Journal 26, no. 7 (July 1988): 769–76. http://dx.doi.org/10.2514/3.9968.
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Ferrell, Richard A., and Bumsoo Kyung. "Roton-vortex interactions in superfluid helium." Physical Review Letters 67, no. 8 (August 19, 1991): 1003–6. http://dx.doi.org/10.1103/physrevlett.67.1003.
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Koumoutsakos, Petros. "Active control of vortex–wall interactions." Physics of Fluids 9, no. 12 (December 1997): 3808–16. http://dx.doi.org/10.1063/1.869515.
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Zhang, M. M., L. Cheng, and Y. Zhou. "Closed-loop controlled vortex-airfoil interactions." Physics of Fluids 18, no. 4 (April 2006): 046102. http://dx.doi.org/10.1063/1.2189287.
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