Journal articles: 'Rankin Vortex'

1

KONDOU, Shuuji, Hiroshi YAMASHITA, Masahisa SHINODA, and Kazuhiro YAMAMOTO. "A Numerical Study on Effect of Vortex Core Radius on Premixed Flame Propagation in Rankin Vortex Flow." Transactions of the Japan Society of Mechanical Engineers Series B 74, no. 747 (2008): 2387–92. http://dx.doi.org/10.1299/kikaib.74.2387.

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2

Wood, Vincent T., and Luther W. White. "A Parametric Wind–Pressure Relationship for Rankine versus Non-Rankine Cyclostrophic Vortices." Journal of Atmospheric and Oceanic Technology 30, no. 12 (December 1, 2013): 2850–67. http://dx.doi.org/10.1175/jtech-d-13-00041.1.

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Abstract A parametric tangential wind profile model is presented for depicting representative pressure deficit profiles corresponding to varying tangential wind profiles of a cyclostrophic, axisymmetric vortex. The model employs five key parameters per wind profile: tangential velocity maximum, radius of the maximum, and three shape parameters that control different portions of the profile. The model coupled with the cyclostrophic balance assumption offers a diagnostic tool for estimating and examining a radial profile of pressure deficit deduced from a theoretical superimposing tangential wind profile in the vortex. Analytical results show that the shape parameters for a given tangential wind maximum of a non-Rankine vortex have an important modulating influence on the behavior of realistic tangential wind and corresponding pressure deficit profiles. The first parameter designed for changing the wind profile from sharply to broadly peaked produces the corresponding central pressure fall. An increase in the second (third) parameter yields the pressure rise by lowering the inner (outer) wind profile inside (outside) the radius of the maximum. Compared to the Rankine vortex, the parametrically constructed non-Rankine vortices have a larger central pressure deficit. It is suggested that the parametric model of non-Rankine vortex tangential winds has good potential for diagnosing the pressure features arising in dust devils, waterspouts, tornadoes, tornado cyclones, and mesocyclones. Finally, presented are two examples in which the parametric model is fitted to a tangential velocity profile, one derived from an idealized numerical simulation and the other derived from high-resolution Doppler radar data collected in a real tornado.

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GORSHKOV, KONSTANTIN A., LEV A. OSTROVSKY, and IRINA A. SOUSTOVA. "Perturbation theory for Rankine vortices." Journal of Fluid Mechanics 404 (February 10, 2000): 1–25. http://dx.doi.org/10.1017/s0022112099007211.

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A perturbation scheme is constructed to describe the evolution of stable, localized Rankine-type hydrodynamic vortices under the action of disturbances such as density stratification. It is based on the elimination of singularities in perturbations by using the necessary orthogonality conditions which determine the vortex motion. Along with the discrete-spectrum modes of the linearized problem which can be kept finite by imposing the orthogonality conditions, the continuous-spectrum perturbations play a crucial role. It is shown that in a stratified fluid, a single (monopole) vortex can be destroyed due to the latter modes before it drifts very far, whereas a vortex pair preserves its stability for a longer time. The motion of the latter is studied in two cases: smooth stratification and a density jump. For the motion of a pair under a small angle to the interface, a complete description is given in the framework of our theory, including the effect of reflection of the pair from a region with slightly larger density.

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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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5

Roy, Anubhab, and Ganesh Subramanian. "Linearized oscillations of a vortex column: the singular eigenfunctions." Journal of Fluid Mechanics 741 (February 20, 2014): 404–60. http://dx.doi.org/10.1017/jfm.2013.666.

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AbstractIn 1880 Lord Kelvin analysed the linearized inviscid oscillations of a Rankine vortex as part of a theory of vortex atoms. These eponymously named neutrally stable modes are, however, exceptional regular oscillations that make up the discrete spectrum of the Rankine vortex. In this paper, we examine the singular oscillations that make up the continuous spectrum (CS) and span the entire base state range of frequencies. In two dimensions, the CS eigenfunctions have a twin-vortex-sheet structure similar to that known from earlier investigations of parallel flows with piecewise linear velocity profiles. The vortex sheets are cylindrical, being threaded by axial lines, with one sheet at the edge of the core and the other at the critical radius in the irrotational exterior; the latter refers to the radial location at which the fluid co-rotates with the eigenmode. In three dimensions, the CS eigenfunctions have core vorticity and may be classified into two families based on the singularity at the critical radius. For the first family, the singularity is a cylindrical vortex sheet threaded by helical vortex lines, while for the second family it has a localized dipole structure with radial vorticity. The presence of perturbation vorticity in the otherwise irrotational exterior implies that the CS modes, unlike the Kelvin modes, offer a modal interpretation for the (linearized) interaction of the Rankine vortex with an external vortical disturbance. It is shown that an arbitrary initial distribution of perturbation vorticity, both in two and three dimensions, may be evolved as a superposition over the discrete and CS modes; this modal representation being equivalent to a solution of the corresponding initial value problem. For the restricted case of an initial axial vorticity distribution in two dimensions, the modal representation may be generalized to a smooth vortex. Finally, for the three-dimensional case, the analogy between rotational flows and stratified shear flows, and the known analytical solution for stratified Couette flow, are used to clarify the singular manner in which the modal superposition for a smooth vortex approaches the Rankine limit.

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6

Jayavel, S., Pratish P. Patil, and Shaligram Tiwari. "Interaction of a skewed Rankine vortex pair." Physics of Fluids 20, no. 8 (August 2008): 083601. http://dx.doi.org/10.1063/1.2969115.

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7

Wang, Lifeng, Ruifeng Hu, Jun Zhang, and Yunpeng Ma. "On the Vortex Detection Method Using Continuous Wavelet Transform with Application to Propeller Wake Analysis." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/242917.

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The method based on the continuous wavelet transformation to detect and characterize two-dimensional vortex is analyzed for a synthetic flow and applied to vortex detection of propeller wake. The characteristics of a vortex, such as center location, core radius, and circulation, are extracted based on the Lamb-Oseen and Rankine vortex models, the latter of which is a novel attempt. The effects of various factors such as the difference scheme, the grid and scale discretization, transform variable, and vortex model on vortex detection have been investigated thoroughly. The method is further applied to identify the tip vortex in a propeller wake.

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8

Gorecki, Piotr, and Rathinam Panneer Selvam. "Rankine combined vortex interaction with a rectangular prism." International Journal of Computational Fluid Dynamics 29, no. 1 (January 2, 2015): 120–32. http://dx.doi.org/10.1080/10618562.2015.1010524.

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9

Ali, Md Shahjahan, Takashi Hosoda, and Ichiro Kimura. "Unsteady RANS and LES Simulation of an Ideal Rankine Vortex Decay." Advances in Civil Engineering 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/523839.

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The 3D numerical simulation was carried out for an idealized Rankine vortex using nonlineark-εmodel (one kind of RANS model) and large eddy simulation (LES) techniques. In this 3D simulation, the vortex flow field was given to rotate with the vertical axis in a free surface rectangular domain. In order to investigate the predictability of standard (linear) and non-lineark-εmodels, the decay of a trailing vortex was simulated and compared with previous DNS data. The governing equations for mean velocities and turbulent flows were discretized with the finite volume method based on a staggered grid system. It was observed that in the growth phase as well as in stabilized phase of turbulence, the decay rate of tangential velocity by RANS model was well comparable with LES simulation as well as previous DNS data. However, in the decay phase of turbulence, RANS model showed slightly faster decay of tangential velocity due to its slower decay of turbulence compared to LES or DNS. The patterns as well as magnitudes of secondary currents predicted by RANS and LES models were well comparable to each other.

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10

Zhou, Kai, and Chao Zhou. "Effects of upstream Rankine vortex on tip leakage vortex breakdown in a subsonic turbine." Aerospace Science and Technology 99 (April 2020): 105776. http://dx.doi.org/10.1016/j.ast.2020.105776.

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11

Hao, Zong Rui, Juan Xu, Hai Yan Bie, and Zhong Hai Zhou. "Numerical Simulation of Three-Dimensional Unsteady Flow Field in the Cyclone." Advanced Materials Research 774-776 (September 2013): 258–61. http://dx.doi.org/10.4028/www.scientific.net/amr.774-776.258.

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Large eddy simulation to describe the turbulent flow of airflow field was used to calculate the unsteady turbulent flow characteristics in the cyclone. It funded that the tangential velocity in the cyclone profile behaved like rankine vortex, with the downward semi-free vortex of the outer layer and the upward forced vortex. With the increasing import gas velocity, the swirling strength of the center increased which reduced collection efficiency by clouding the dust particles in the ash bucket to the center airflow.

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12

Riccardi, G., and D. Durante. "Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles." Journal of Applied Mathematics 2008 (2008): 1–40. http://dx.doi.org/10.1155/2008/586567.

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The velocity induced by a plane, uniform vortex is investigated through the use of an integral relation between Schwarz function of the vortex boundary and conjugate of the velocity. The analysis is restricted to a certain class of vortices, the boundaries of which are described through conformal maps onto the unit circle and the corresponding Schwarz functions possess two poles in the plane of the circle. The dependence of the velocity field on the vortex shape is investigated by comparing velocity and streamfunction with the ones of the equivalent Rankine vortex (which has the same vorticity, area, and center of vorticity). By changing the parameters of the Schwarz function (poles and corresponding residues), rather complicated vortex shapes can be easily analyzed, some of them mimicing an incipient filamentation of the vortex boundary.

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13

Gonzalez, R., and C. D. Vigh. "Study of a Rankine vortex with axial velocity discontinuity in an infinite." Anales AFA 27, no. 4 (January 19, 2017): 121–26. http://dx.doi.org/10.31527/analesafa.2016.27.4.121.

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14

XIE, HuYue, Yun CAO, FengHua QIN, and XiSheng LUO. "The slip effect of micro-droplets in Rankine vortex." SCIENTIA SINICA Physica, Mechanica & Astronomica 47, no. 12 (August 10, 2017): 124702. http://dx.doi.org/10.1360/sspma2017-00075.

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15

Lacaze, Laurent, Anne-Laure Birbaud, and Stéphane Le Dizès. "Elliptic instability in a Rankine vortex with axial flow." Physics of Fluids 17, no. 1 (January 2005): 017101–017101. http://dx.doi.org/10.1063/1.1814987.

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16

Khoo, B. C., K. S. Yeo, and D. F. Lim. "The axisymmetric boundary layer beneath a Rankine-like vortex." Experiments in Fluids 22, no. 4 (February 14, 1997): 300–311. http://dx.doi.org/10.1007/s003480050052.

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17

Mian, Lin, Li Jiachun, and Li Li. "Simulation of typhoon's anomalous track (I)—Rankine vortex model." Applied Mathematics and Mechanics 19, no. 3 (March 1998): 207–11. http://dx.doi.org/10.1007/bf02453384.

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18

Ligneul, P., and R. Latorre. "Study of Nuclei Distribution and Vortex Diffusion Influence on Nuclei Capture by a Tip Vortex and Nuclei Capture Noise." Journal of Fluids Engineering 115, no. 3 (September 1, 1993): 504–7. http://dx.doi.org/10.1115/1.2910167.

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Earlier studies of cavitation nuclei behavior in the presence of a Rankine tip vortex have shown that the nuclei is attracted or captured by the vortex pressure field and during this process noise is produced by the rapid nuclei growth. The present paper extends the study of Ligneul and Latorre (1989). The capture of nuclei by the tip vortex was characterized by an index M which depends on the nuclei radius, initial location, and the vortex circulation. To clarify the nuclei distribution effected by this capture process, the frequency of nuclei capture is derived in terms of the nuclei distribution N(R). The influence of the tip vortex axial diffusion on the nuclei capture process is formulated and number results presented to show how vortex diffusion delays the nuclei capture. The paper closes with a discussion of the numerical simulation of the nuclei capture and noise generation by the tip vortex.

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19

Aboelkassem, Yasser, Georgios H. Vatistas, and Nabil Esmail. "Viscous dissipation of Rankine vortex profile in zero meridional flow." Acta Mechanica Sinica 21, no. 6 (November 21, 2005): 550–56. http://dx.doi.org/10.1007/s10409-005-0073-3.

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20

Zavershinskii, I. P., A. I. Klimov, N. E. Molevich, and D. P. Porfir’ev. "Rankine vortex evolution in a gas with heat release source." Technical Physics Letters 35, no. 4 (April 2009): 344–45. http://dx.doi.org/10.1134/s1063785009040166.

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21

Eloy, Christophe, and Stéphane Le Dizès. "Stability of the Rankine vortex in a multipolar strain field." Physics of Fluids 13, no. 3 (March 2001): 660–76. http://dx.doi.org/10.1063/1.1345716.

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22

Doronina, O. A., P. A. Bakhvalov, and T. K. Kozubskaya. "Numerical study of acoustic radiation dynamics of a Rankine vortex." Acoustical Physics 62, no. 4 (July 2016): 467–77. http://dx.doi.org/10.1134/s1063771016040060.

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23

Lazar, Ayah, A. Stegner, and E. Heifetz. "Inertial instability of intense stratified anticyclones. Part 1. Generalized stability criterion." Journal of Fluid Mechanics 732 (September 6, 2013): 457–84. http://dx.doi.org/10.1017/jfm.2013.412.

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AbstractThe stability of axisymmetric vortices to inertial perturbations is investigated by means of linear stability analysis, taking into account stratification, vertical eddy viscosity, as well as finite depth of the flow. We consider different types of circular barotropic vortices in a linearly stratified shallow layer confined with rigid lids. For the simplest case of the Rankine vortex we develop an asymptotic analytic dispersion relation and a marginal stability criterion, which compares well with numerical results. This is a further generalization to the well-known generalized Rayleigh criterion, which is only valid for non-dissipative and non-stratified eddies. Unlike the Rayleigh criterion, it predicts that intense anticyclones may be stable even with a core region of negative absolute vorticity, and that the dissipation and stratification work together to stabilize the flow. Numerical analysis reveals that the stability diagrams for various types of vortices are almost identical in the Rossby, Burger and Ekman parameter space. This allows extension of our analytical solutions for the Rankine vortex to a wide variety of vortices. Furthermore, we show that a more suitable parameter for the intensity of the vortex is the vortex Rossby number, while for the inviscid case it is the local normalized vorticity. These predictions are in agreement with laboratory experiments presented in part 2 (J. Fluid Mech., vol. 732, 2013, pp. 485–509).

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Burow, Daniel, Hannah V. Herrero, and Kelsey N. Ellis. "Damage Analysis of Three Long-Track Tornadoes Using High-Resolution Satellite Imagery." Atmosphere 11, no. 6 (June 10, 2020): 613. http://dx.doi.org/10.3390/atmos11060613.

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Remote sensing of tornado damage can provide valuable observations for post-event surveys and reconstructions. The tornadoes of 3 March 2019 in the southeastern United States are an ideal opportunity to relate high-resolution satellite imagery of damage with estimated wind speeds from post-event surveys, as well as with the Rankine vortex tornado wind field model. Of the spectral metrics tested, the strongest correlations with survey-estimated wind speeds are found using a Normalized Difference Vegetation Index (NDVI, used as a proxy for vegetation health) difference image and a principal components analysis emphasizing differences in red and blue band reflectance. NDVI-differenced values across the width of the EF-4 Beauregard-Smiths Station, Alabama, tornado path resemble the pattern of maximum ground-relative wind speeds across the width of the Rankine vortex model. Maximum damage sampled using these techniques occurred within 130 m of the tornado vortex center. The findings presented herein establish the utility of widely accessible Sentinel imagery, which is shown to have sufficient spatial resolution to make inferences about the intensity and dynamics of violent tornadoes occurring in vegetated areas.

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25

Zhao, Bowen, Emma Chieusse-Gérard, and Glenn Flierl. "Influence of Bottom Topography on Vortex Stability." Journal of Physical Oceanography 49, no. 12 (December 2019): 3199–219. http://dx.doi.org/10.1175/jpo-d-19-0049.1.

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AbstractThe effects of topography on the linear stability of both barotropic vortices and two-layer, baroclinic vortices are examined by considering cylindrical topography and vortices with stepwise relative vorticity profiles in the quasigeostrophic approximation. Four vortex configurations are considered, classified by the number of relative vorticity steps in the horizontal and the number of layers in the vertical: barotropic one-step vortex (Rankine vortex), barotropic two-step vortex, and their two-layer, baroclinic counterparts with the vorticity steps in the upper layer. In the barotropic calculation, the vortex is destabilized by topography having an oppositely signed potential vorticity jump while stabilized by topography of same-signed jump, that is, anticyclones are destabilized by seamounts while stabilized by depressions. Further, topography of appropriate sign and magnitude can excite a mode-1 instability for a two-step vortex, especially relevant for topographic encounters of an otherwise stable vortex. The baroclinic calculation is in general consistent with the barotropic calculation except that the growth rate weakens and, for a two-step vortex, becomes less sensitive to topography (sign and magnitude) as baroclinicity increases. The smaller growth rate for a baroclinic vortex is consistent with previous findings that vortices with sufficient baroclinic structure could cross the topography relatively easily. Nonlinear contour dynamics simulations are conducted to confirm the linear stability analysis and to describe the subsequent evolution.

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26

Toninelli, Ermes, Reuben S. Aspden, David Phillips, Graham M. Gibson, and Miles J. Padgett. "The transition from a coherent optical vortex to a Rankine vortex: beam contrast dependence on topological charge." Journal of Modern Optics 63, sup3 (September 21, 2016): S51—S56. http://dx.doi.org/10.1080/09500340.2016.1234651.

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27

BALMFORTH, N. J., STEFAN G. LLEWELLYN SMITH, and W. R. YOUNG. "Disturbing vortices." Journal of Fluid Mechanics 426 (January 10, 2001): 95–133. http://dx.doi.org/10.1017/s0022112000002159.

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Inviscid spatially compact vortices (such as the Rankine vortex) have discrete Kelvin modes. For these modes, the critical radius, at which the rotation frequency of the wave matches the angular velocity of the fluid, lies outside the vortex core. When such a vortex is not perfectly compact, but has a weak vorticity distribution beyond the core, these Kelvin disturbances are singular at the critical radius and become ‘quasi-modes’. These are not true eigenmodes but have streamfunction perturbations that decay exponentially with time while the associated vorticity wraps up into a tight spiral without decay. We use a matched asymptotic expansion to derive a simplified description of weakly nonlinear, externally forced quasi-modes.We consider the excitation and subsequent evolution of finite-amplitude quasi- modes excited with azimuthal wavenumber 2. Provided the forcing amplitude is below a certain critical amplitude, the quasi-mode decays and the disturbed vortex returns to axisymmetry. If the amplitude of the forcing is above critical, then nonlinear effects arrest the decay and cat's eye patterns form. Thus the vortex is permanently deformed into a tripolar structure.

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28

Chang, Pao-Liang, Wei-Ting Fang, Pin-Fang Lin, and Ming-Jen Yang. "A Vortex-Based Doppler Velocity Dealiasing Algorithm for Tropical Cyclones." Journal of Atmospheric and Oceanic Technology 36, no. 8 (August 2019): 1521–45. http://dx.doi.org/10.1175/jtech-d-18-0139.1.

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AbstractIn this study, a vortex-based Doppler velocity dealiasing (VDVD) algorithm for tropical cyclones (TCs) is proposed. The algorithm uses a Rankine combined vortex model as a reference field for dealiasing based on an inner–outer iterative procedure. The structure of the reference vortex is adjusted in an inner iterative procedure of VDVD that applies the ground-based velocity track display (GBVTD) technique. The outer loop of the VDVD based on the GBVTD-simplex algorithm is used for center correction. The VDVD is able to recover not only the aliased Doppler velocities from a simulated symmetric vortex but also those superimposed with wavenumber-1 asymmetry, radial wind, or mean flow. For real cases, the VDVD provides dealiased Doppler velocity with 99.4% accuracy for all pixels, based on 472 elevation sweeps from a typhoon without landfall. It is suggested that the VDVD algorithm can improve the quality of downstream applications such as Doppler wind retrievals and radar data assimilations of TCs and other storms, such as tornadoes and mesocyclones, with vortex signatures.

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Prabhu, M., R. Ajith Kumar, T. H. Gopikrishnan, P. J. Deshpande, U. Anandhakrishnan, A. S. Kiran, and R. P. Govindu. "Rankine Vortex Formation during Draining: A New Twin Port Suppression Strategy." Journal of Applied Fluid Mechanics 13, no. 1 (January 1, 2020): 147–60. http://dx.doi.org/10.29252/jafm.13.01.30202.

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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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31

Wood, Vincent T., and Rodger A. Brown. "Simulated Tornadic Vortex Signatures of Tornado-Like Vortices Having One- and Two-Celled Structures." Journal of Applied Meteorology and Climatology 50, no. 11 (November 2011): 2338–42. http://dx.doi.org/10.1175/jamc-d-11-0118.1.

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AbstractA tornadic vortex signature (TVS) is a degraded Doppler velocity signature that occurs when the tangential velocity core region of a tornado is smaller than the effective beamwidth of a sampling Doppler radar. Early Doppler radar simulations, which used a uniform reflectivity distribution across an idealized Rankine vortex, showed that the extreme Doppler velocity peaks of a TVS profile are separated by approximately one beamwidth. The simulations also indicated that neither the size nor the strength of the tornado is recoverable from a TVS. The current study was undertaken to investigate how the TVS might change if vortices having more realistic tangential velocity profiles were considered. The one-celled (axial updraft only) Burgers–Rott vortex model and the two-celled (annular updraft with axial downdraft) Sullivan vortex model were selected. Results of the simulations show that the TVS peaks still are separated by approximately one beamwidth—signifying that the TVS not only is unaffected by the size or strength of a tornado but also is unaffected by whether the tornado structure consists of one or two cells.

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Abrahamson, S., and S. Lonnes. "An Integral Method for Turbulent Boundary Layers on Rotating Disks." Journal of Fluids Engineering 115, no. 4 (December 1, 1993): 614–19. http://dx.doi.org/10.1115/1.2910188.

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An integral method for computing turbulent boundary layers on rotating disks has been developed using a power law profile for the tangential velocity and a new model for the radial profile. A similarity solution results from the formulation. Radial transport, boundary layer growth, and drag on the disk were computed for the case of a forced vortex frees tream flow. The results were compared to previous similarity solutions. The method was extended to a Rankine vortex freestream flow. Differential equations for boundary layer parameters were developed and solved for different Reynolds numbers to look at the net entrainment, boundary layer growth, and drag on the disk.

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Tavares Dias do Rio Vaz, Déborah Aline, Jerson Rogério Pinheiro Vaz, André Luiz Amarante Mesquita, João Tavares Pinho, and Antonio Cesar Pinho Brasil Junior. "Optimum aerodynamic design for wind turbine blade with a Rankine vortex wake." Renewable Energy 55 (July 2013): 296–304. http://dx.doi.org/10.1016/j.renene.2012.12.027.

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34

Wang, Xiaokun, Sinuo Liu, Xiaojuan Ban, Yanrui Xu, Jing Zhou, and Jiří Kosinka. "Robust turbulence simulation for particle-based fluids using the Rankine vortex model." Visual Computer 36, no. 10-12 (August 4, 2020): 2285–98. http://dx.doi.org/10.1007/s00371-020-01914-5.

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35

Lasheras, Juan C., and Kek-Kiong Tio. "Dynamics of a Small Spherical Particle in Steady Two-Dimensional Vortex Flows." Applied Mechanics Reviews 47, no. 6S (June 1, 1994): S61—S69. http://dx.doi.org/10.1115/1.3124442.

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The equation of motion of a small spherical particle in an isolated Rankine vortex is analyzed using an asymptotic scheme valid for the limiting case of small Stokes number St. The effects of particle inertia and added mass, gravity, the acceleration of the fluid, viscous drag, and the Basset history force are taken into consideration. For the case of an isolated Rankine vortex, the analysis shows that in the region where the fluid velocity is large enough, the viscous drag constrains the particle to move with a velocity equal to that of the fluid plus a perturbation of order St. This perturbative term incorporates the effects of gravity, the density difference between the particle and the fluid, and the local acceleration of the fluid. In the region where the fluid velocity is small, the particle moves with a velocity equal to the sum of the fluid velocity and the rising/settling velocity of the particle in still fluid, the effects of particle inertia and fluid acceleration appearing as small perturbations. Throughout the whole region of the flow, the effect of the Basset force always appears at higher order than the other forces acting on the particle and may, consequently, be neglected. The analysis also shows that a particle with a mass density greater than that of the fluid always escapes from the central region of the vortex, but a buoyant particle may be trapped by the equilibrium point located there.

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36

Maicke, Brian A., and Joseph Majdalani. "A constant shear stress core flow model of the bidirectional vortex." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2103 (December 4, 2008): 915–35. http://dx.doi.org/10.1098/rspa.2008.0342.

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In this paper, we discuss the merits of two models for the swirl velocity in the core of a confined bidirectional vortex. The first is piecewise, Rankine-like, based on a combined-vortex representation. It stems from the notion that a uniform shear stress distribution may be assumed in the inner vortex region of a cyclone, especially at high Reynolds numbers. Thereafter, direct integration of the shear stress enables us to retrieve an expression for the swirl velocity that overcomes the inviscid singularity at the centreline. The second model consists of a modified asymptotic solution to the problem obtained directly from the Navier–Stokes equations. Both solutions we present transition smoothly to the outer, free-vortex approximation at some intermediate position in the chamber. This position is deduced from available experimental data to the extent of providing an accurate swirl velocity distribution throughout the chamber. By scaling the constant shear radius to the core layer thickness, the constant of proportionality is readily calculated using the method of least squares. Interestingly, the constant of proportionality is found to be invariant at several vortex Reynolds numbers, thus helping to achieve closure. The combined-vortex representation is validated against a large body of experimental measurements and through comparisons to a laminar core model that is enhanced through the use of an eddy viscosity. Other heuristic schemes are discussed and the two most suitable models to capture realistic flow behaviour at high vortex Reynolds numbers are identified. Our two models are first derived analytically and then anchored on the available experimental measurements.

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Park, Junho, and Paul Billant. "Radiative instability of an anticyclonic vortex in a stratified rotating fluid." Journal of Fluid Mechanics 707 (July 27, 2012): 381–92. http://dx.doi.org/10.1017/jfm.2012.286.

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AbstractIn strongly stratified fluids, an axisymmetric vertical columnar vortex is unstable because of a spontaneous radiation of internal waves. The growth rate of this radiative instability is strongly reduced in the presence of a cyclonic background rotation $f/ 2$ and is smaller than the growth rate of the centrifugal instability for anticyclonic rotation, so it is generally expected to affect vortices in geophysical flows only if the Rossby number $Ro= 2\Omega / f$ is large (where $\Omega $ is the angular velocity of the vortex). However, we show here that an anticyclonic Rankine vortex with low Rossby number in the range $\ensuremath{-} 1\leq Ro\lt 0$, which is centrifugally stable, is unstable to the radiative instability when the azimuthal wavenumber $\vert m\vert $ is larger than 2. Its growth rate for $Ro= \ensuremath{-} 1$ is comparable to the values reported in non-rotating stratified fluids. In the case of continuous vortex profiles, this new radiative instability is shown to occur if the potential vorticity of the base flow has a sufficiently steep radial profile. The most unstable azimuthal wavenumber is inversely proportional to the steepness of the vorticity jump. The properties and mechanism of the instability are explained by asymptotic analyses for large wavenumbers.

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Szantyr, Jan. "Dynamic interaction of the cavitating propeller tip vortex with the rudder." Polish Maritime Research 14, no. 4 (October 1, 2007): 10–14. http://dx.doi.org/10.2478/v10012-007-0033-x.

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Dynamic interaction of the cavitating propeller tip vortex with the rudder The hydrodynamic interaction between the ship propeller and the rudder has many aspects. One of the most interesting is the interaction between the cavitating tip vortex shed from the propeller blades and the rudder. This interaction leads to strongly dynamic behaviour of the cavitating vortex, which in turn generates unusually high pressure pulses in its vicinity. Possibly accurate prediction of these pulses is one of the most important problems in the hydrodynamic design of a new ship. The paper presents a relatively simple computational model of the propeller cavitating tip vortex behaviour close to the rudder leading edge. The model is based on the traditional Rankine vortex and on the potential solution of the dynamics of the cylindrical sections of the cavitating kernel passing through the strongly variable pressure field in the vicinity of the rudder leading edge. The model reproduces numerically the experimentally observed process of initial compression of the vortex kernel in the high pressure region near the stagnation point at the rudder leading edge and subsequent explosive growth of the kernel in the low pressure region further downstream. Numerical simulation of this process enables computation of the additional pressure pulses generated due to this phenomenon and transmitted onto the hull surface. This new numerical model of the cavitating tip vortex is incorporated in the modified unsteady lifting surface program for prediction of propeller cavitation, which has been successfully used in the process of propeller design for several years and which recently has been extended to include the effects of propeller — rudder interaction. The results of calculations are compared with the experimental measurements and they demonstrate reasonable agreement between theory and physical reality.

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OKULOV, V. L., and J. N. SØRENSEN. "Stability of helical tip vortices in a rotor far wake." Journal of Fluid Mechanics 576 (March 28, 2007): 1–25. http://dx.doi.org/10.1017/s0022112006004228.

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As a means of analysing the stability of the wake behind a multi-bladed rotor the stability of a multiplicity of helical vortices embedded in an assigned flow field is addressed. In the model the tip vortices in the far wake are approximated by infinitely long helical vortices with constant pitch and radius. The work is a further development of a model developed in Okulov (J. Fluid Mech., vol. 521, p. 319) in which the linear stability of N equally azimuthally spaced helical vortices was considered. In the present work the analysis is extended to include an assigned vorticity field due to root vortices and the hub of the rotor. Thus the tip vortices are assumed to be embedded in an axisymmetric helical vortex field formed from the circulation of the inner part of the rotor blades and the hub. As examples of inner vortex fields we consider three generic axial columnar helical vortices, corresponding to Rankine, Gaussian and Scully vortices, at radial extents ranging from the core radius of a tip vortex to several rotor radii.The analysis shows that the stability of tip vortices largely depends on the radial extent of the hub vorticity as well as on the type of vorticity distribution. As part of the analysis it is shown that a model in which the vortex system is replaced by N tip vortices of strength Γ and a root vortex of strength − N/Γ is unconditionally unstable.

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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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Francis, J., and D. Parker. "Numerical simulation of observed flow phenomena in the supply and control ports and associated feed channels of a mini-vortex amplifier." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 5 (April 22, 2015): 756–81. http://dx.doi.org/10.1177/0954406215573599.

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The trajectory and reach of jets issuing from tangential control ports at the periphery of a vortex amplifier's swirl chamber depend largely on design geometry, size and pressures applied. Excessive control port pressure causes these jets to extend too far across the face of the radial supply ports, to impact on the opposing supply port wall whereupon, they bifurcate to create back diffusion of control port flow along the supply port channels. Flow through vortex amplifier geometry is simulated using a baseline Reynolds stress turbulence model with Computational Fluid Dynamics (CFX) automatic wall treatment. Anisotropic stress and vortex stretching in the swirl chamber and outlet have not prevented convergence (based on normalised vortex amplifier residuals). Known flow structures are reproduced. This paper is focussed on simulation close to pressures needed for bifurcation. Just before the point on an operating characteristic at which bifurcated tangential flow appears, the recirculation zone crossing most of the radial supply stretches to intermittently cut off the radial flow. The steady state results indicate asymmetry between the four ports, as smoke visualisation tests also imply. The transient results are sufficient to demonstrate time-dependent structures and suggest periodicity of flow structures. The model can be used to inform design and operability studies. Moreover, a curious near-wall structure of spinning flow not previously reported has been predicted close to the axis and hugging the swirl chamber wall opposite the outlet, at radii within the forced part of the Rankine vortex.

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Perrot, Xavier, and Xavier Carton. "Instability of a two-step Rankine vortex in a reduced gravity QG model." Fluid Dynamics Research 46, no. 3 (May 28, 2014): 031417. http://dx.doi.org/10.1088/0169-5983/46/3/031417.

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Gonzalez, Israel, Amaryllis Cotto, and Hugh E. Willoughby. "Synthesis of Vortex Rossby Waves. Part II: Vortex Motion and Waves in the Outer Waveguide." Journal of the Atmospheric Sciences 72, no. 10 (October 1, 2015): 3958–74. http://dx.doi.org/10.1175/jas-d-15-0005.1.

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Abstract Beta, the meridional gradient of planetary vorticity, causes tropical cyclones to propagate poleward and westward at approximately 2 m s−1. In a previous shallow-water linear model, the simulated vortex accelerated without limit, ostensibly because beta forced a free linear mode. In the analogous nonlinear model, wave–wave interaction limited the propagation speed. Subsequent work based upon the asymmetric balance (AB) approximation was unable to replicate the linear result. The present barotropic nondivergent model replicates the linear beta gyres as a streamfunction dipole with a uniform southeasterly ventilation flow across the vortex. The simulated storm accelerates to unphysical, but finite, speeds that are limited by vorticity filamentation. In the analogous nonlinear model, nonlinearly forced wavenumber-1 gyres have opposite phase to the linear gyres so that their ventilation flow counteracts advection by the linear gyres to limit the overall vortex speed to approximately 3 m s−1. A bounded mean vortex with zero circulation at large radius must contain an outer annulus of anticyclonic vorticity to satisfy the circulation theorem. The resulting positive mean vorticity gradient constitutes an outer waveguide that supports downstream-propagating, very-low-frequency vortex Rossby waves. It is confined between an inner critical radius where the waves are absorbed and an outer turning point where they are reflected. Vorticity filamentation at the critical radius limits the beta-drift acceleration. The original unlimited linear acceleration stemmed from too-weak dissipation caused by second-order diffusion applied to velocity components instead of vorticity. Fourth-order diffusion and no outer waveguide in the Rankine-like vortex of the AB simulations plausibly explain the different results.

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Holland, Andrew P., Allen J. Riordan, and E. C. Franklin. "A Simple Model for Simulating Tornado Damage in Forests." Journal of Applied Meteorology and Climatology 45, no. 12 (December 1, 2006): 1597–611. http://dx.doi.org/10.1175/jam2413.1.

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Abstract An analytical model is presented to describe patterns of downed trees produced by tornadic winds. The model uses a combined Rankine vortex of specified tangential and radial components to describe a simple tornado circulation. A total wind field is then computed by adding the forward motion of the vortex. The lateral and vertical forces on modeled tree stands are then computed and are compared with physical characteristics of Scots and loblolly pine. From this model, patterns of windfall are computed and are compared to reveal three basic damage patterns: cross-track symmetric, along-track asymmetric, and crisscross asymmetric. These patterns are shown to depend on forward speed, radial speed, and tree resistance. It is anticipated that this model will prove to be useful in assessing storm characteristics from damage patterns observed in forested areas.

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PRADEEP, D. S., and F. HUSSAIN. "Core dynamics of a strained vortex: instability and transition." Journal of Fluid Mechanics 447 (October 30, 2001): 247–85. http://dx.doi.org/10.1017/s0022112001005869.

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We study the instability of a laminar vortex column (in an external orthogonal strain field) to an axisymmetric core size perturbation, and the resulting transition to fine-scale turbulence. The perturbation, which evolves as a standing wave oscillation (i.e. core dynamics, CD), is inviscidly amplified by the external strain. Analysis of a weakly strained Rankine vortex explains the physical mechanism of instability: resonant interaction between the perturbation – the azimuthal wavenumber m = 0 wave – and m = ±2 waves. The CD instability (CDI) – a type of elliptic instability – experiences the fastest growth when the CD oscillation frequency equals vortex column's fluid angular velocity, such matching occurring only at specific discrete values of the axial wavenumber k. At this resonant frequency, the net effect of the swirl-induced tilting of perturbation vorticity and the CD-induced tilting of base flow vorticity is such that perturbation vorticity is continually aligned with the stretching direction of the external strain. Such strain–vorticity locking occurs for all m; hence all waves are unstable, the instability oscillation frequency being dependent on m. In a viscous Gaussian-like vortex, CDI has low-strain, low-Re and high-k cutoffs – consequences of the competing effects of inviscid amplification and viscous damping. Direct numerical simulation reveals two physical-space mechanisms of transition: (i) formation of a thin annular vortex sheath surrounding a low-enstrophy ‘bubble’ (similar to axisymmetric vortex breakdown) and the sheath's subsequent roll-up into smaller ‘vortexlets’; and (ii) folding and reconnection of core vortex filaments giving rise to additional fine-grained random vorticity within the bubble – both mechanisms caused by CD-induced intense axial flow within the vortex column. The resulting finer tubular vortices (similar to ‘worms’) have in turn their own CD, and thus this transition scenario suggests a physical-space cascade process in developed turbulence (as well as a concomitant anti-cascade process during the bubble's collapse phase). Additionally, we show that bending waves, in spite of their faster growth, effect surprisingly much slower transfer of energy into fine scales than CDI does, and hence are less effective than CDI in vortex transition and in turbulence cascade.

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Potvin, Corey K., Alan Shapiro, Michael I. Biggerstaff, and Joshua M. Wurman. "The VDAC Technique: A Variational Method for Detecting and Characterizing Convective Vortices in Multiple-Doppler Radar Data." Monthly Weather Review 139, no. 8 (August 2011): 2593–613. http://dx.doi.org/10.1175/2011mwr3638.1.

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AbstractThe vortex detection and characterization (VDAC) technique is designed to identify tornadoes, mesocyclones, and other convective vortices in multiple-Doppler radar data and retrieve their size, strength, and translational velocity. The technique consists of fitting radial wind data from two or more radars to a simple analytical model of a vortex and its near environment. The model combines a uniform flow, linear shear flow, linear divergence flow (all of which comprise a broad-scale flow), and modified combined Rankine vortex. The vortex and its environmental flow are allowed to translate. A cost function accounting for the discrepancy between the model and observed radial winds is evaluated over space and time so that observations can be used at the actual times and locations they were acquired. The model parameters are determined by minimizing this cost function.Tests of the technique using analytically generated, numerically simulated, and one observed tornadic wind field were presented by Potvin et al. in an earlier study. In the present study, an improved version of the technique is applied to additional real radar observations of tornadoes and other substorm-scale vortices. The technique exhibits skill in detecting such vortices and characterizing their size and strength. Single-Doppler experiments suggest that the technique may reliably detect and characterize larger (>1-km diameter) vortices even in the absence of overlapping radar coverage.

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Brown, Rodger A., and Vincent T. Wood. "The Tornadic Vortex Signature: An Update." Weather and Forecasting 27, no. 2 (April 1, 2012): 525–30. http://dx.doi.org/10.1175/waf-d-11-00111.1.

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Abstract A tornadic vortex signature (TVS) is a degraded Doppler velocity signature of a tornado that occurs when the core region of a tornado is smaller than the half-power beamwidth of the sampling Doppler radar. Soon after the TVS was discovered in the mid-1970s, simulations were conducted to verify that the signature did indeed represent a tornado. The simulations, which used a uniform reflectivity distribution across a Rankine vortex model, indicated that the extreme positive and negative Doppler velocity values of the signature should be separated by about one half-power beamwidth regardless of tornado size or strength. For a Weather Surveillance Radar-1988 Doppler (WSR-88D) with an effective half-power beamwidth of approximately 1.4° and data collected at 1.0° azimuthal intervals, the two extreme Doppler velocity values should be separated by 1.0°. However, with the recent advent of 0.5° azimuthal sampling (“superresolution”) by WSR-88Ds at lower elevation angles, some of the extreme Doppler velocity values unexpectedly were found to be separated by 0.5° instead of 1.0° azimuthal intervals. To understand this dilemma, the choice of vortex model and reflectivity profile is investigated. It is found that the choice of vortex model does not have a significant effect on the simulation results. However, using a reflectivity profile with a minimum at the vortex center does make a difference. The revised simulations indicate that it is possible for the distance between the peak Doppler velocity values of a TVS to be separated by 0.5° with superresolution data collection.

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Davies-Jones, Robert P., and Vincent T. Wood. "Simulated Doppler Velocity Signatures of Evolving Tornado-Like Vortices." Journal of Atmospheric and Oceanic Technology 23, no. 8 (August 1, 2006): 1029–48. http://dx.doi.org/10.1175/jtech1903.1.

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Abstract Exact solutions of the Navier–Stokes or Euler equations of motion and the continuity equation in cylindrical coordinates for 3D, axisymmetric, inviscid, or laminar flows are utilized to represent evolving vortices that roughly model tornado cyclones or misocyclones contracting to tornadoes. These solutions are unsteady versions of the diffusive Burgers–Rott vortex and the inviscid Rankine-combined vortex. They satisfy the free-slip condition at the ground. Different vortices are obtained by choosing different values of the constant eddy viscosity and uniform horizontal convergence while holding the circulation at infinity constant. A simulated Weather Surveillance Radar-1988 Doppler (WSR-88D) is employed to generate time-varying Doppler velocity signatures in uniform reflectivity of these analytical vortices at ranges of 25 and 50 km from the radar. Mean Doppler velocities are determined by computing 3D integrals over effective resolution volumes. Magnitudes of Doppler vortex signatures at different times in the evolution of the stationary vortices are computed for effective beamwidths of 1.02° and 1.39°, which correspond to azimuthal sampling intervals of 0.5° and 1.0°, respectively. Four tornado predictors—rotational velocity, shear, excess rotational kinetic energy, and circulation—are examined. Results of the simulations show that for smaller effective beamwidths, Doppler vortex signatures are stronger and exceed fixed threshold values of rotational velocity and shear earlier. With finer azimuthal resolution, tornado cyclone, misocyclone, or tornado signatures switch to tornadic vortex signatures later. Circulations of the vortex signatures give good estimates of the circulations of the simulated tornadoes and tornado cyclones with relative insensitivity to range, effective beamwidth, and stage of evolution. High circulation and convergence values of a rotation signature reveal the potential for a tornado earlier than all the other predictors, which increase significantly during tornadogenesis.

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Coleman, Colin S. "The Stability of Swirling Jets." Publications of the Astronomical Society of Australia 8, no. 1 (1989): 38–40. http://dx.doi.org/10.1017/s1323358000022864.

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AbstractThe stability of a swirling cylindrical jet of compressible fluid is examined by performing a normal mode analysis and numerically solving the eigenvalue problem. Perturbations of the form f(r)exp[i(ωt-mϕ-kz)] are considered, where f is any fluid variable. Instabilities which are characteristic of both a non-swirling (top-hat) jet and a Rankine vortex are investigated for a particular axial wavenumber.The vortex instabilities are weak, and are found to remain weak when axial flow is present. The jet instabilities are much stronger, but axial flow is a stabilizing influence. The positive helicity (km > 0) non-axisymmetric modes (m ≠ 0) are stabilized by a small component of azimuthal flow. The axisymmetric mode (m = 0) and the negative helicity non-axisymmetric modes persist in rapidly swirling jets, but with a greatly reduced growth rate.

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Harvey, Benjamin J., Maarten H. P. Ambaum, and Xavier J. Carton. "Instability of Shielded Surface Temperature Vortices." Journal of the Atmospheric Sciences 68, no. 5 (May 1, 2011): 964–71. http://dx.doi.org/10.1175/2010jas3669.1.

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Abstract The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.

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Journal articles on the topic 'Rankin Vortex'

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