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Three-dimensional instabilities in tornado-like vortices with secondary circulations

Published online by Cambridge University Press:  19 September 2012

David S. Nolan
David S. Nolan*
Affiliation:
Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL, USA
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Abstract

Tornadoes and other intense atmospheric vortices are known to occasionally transition to a flow structure with multiple vortices within their larger circulations. This phenomenon has long been ascribed to fluid dynamical instability of the inner-core circulation, and many previous studies have diagnosed low-wavenumber unstable modes in tornado-like vortices that resemble the observed structures. However, relatively few of these studies have incorporated the strong vertical motions of the inner-core circulation into the stability analysis, and no stability analyses have been performed using a complete, frictionally driven secondary circulation with strong radial inflow near the surface. Stability analyses are presented using the complete circulations generated from idealized simulations of tornado-like vortices. Fast-growing unstable modes are found that are consistent with the asymmetric structures present in these simulations. Attempts to correlate the structures and locations of these modes with instability conditions for vortices with axial jets derived by Howard & Gupta and by Leibovich & Stewartson produce only mixed results. Analyses of perturbation energy growth show that interactions between eddy fluxes and the radial shear of the azimuthal wind contribute very little to the growth of the dominant modes. Rather, the radial shear of the vertical wind and the vertical shear of the vertical wind (corresponding to deformation in the axial direction) are the primary energy sources for perturbation growth. Relatively weak axisymmetric instabilities are also identified that have some similarity to symmetric oscillations that have been observed in tornadoes.

JFM classification

Vortex Flows: Vortex breakdown Vortex Flows: Vortex dynamics Vortex Flows: Vortex instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 711 , 25 November 2012 , pp. 61 - 100
Copyright
Copyright © Cambridge University Press 2012

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References

1. Agee, E. M., Snow, J. T., Nickerson, F. S., Clare, P. R., Church, C. R. & Schaal, L. A. 1977 An observational study of the West Lafayatte, Indiana, tornado of 20 March 1976. Mon. Weath. Rev. 103, 318–333.2.0.CO;2>CrossRefGoogle Scholar
2. Bluestein, H. B., French, M. M., Tanamachi, R. L., Frasier, S., Hardwick, K., Junyet, F. & Pazmany, A. L. 2007a Close-range observations of tornadoes in supercells made with a dual-polarization, X-band, mobile Doppler radar. Mon. Weath. Rev. 135, 1522–1543.CrossRefGoogle Scholar
3. Bluestein, H. B., Lee, W.-C., Bell, M., Weiss, C. C. & Pazmany, A. L. 2003 Mobile Doppler radar observations of a tornado in a supervell near Bassett. Nebraska, on 5 June 1999. Part II. Tornado-vortex structure. Mon. Weath. Rev. 131, 2968–2984.2.0.CO;2>CrossRefGoogle Scholar
4. Bluestein, H. B. & Pazmany, A. L. 2000 Observations of tornadoes and other convective phenomena with a mobile, 3-mm wavelength, Doppler radar: the spring 1999 field experiment. Bull. Am. Meteorol. Soc. 81, 2939–2951.2.3.CO;2>CrossRefGoogle Scholar
5. Bluestein, H. B., Weiss, C. C., French, M. M., Holthaus, E. M. & Tanamchi, R. L. 2007b The structure of tornadoes near Attica, Kansas on 12 May 2004: High-resolution, mobile, Doppler radar observations. Mon. Weath. Rev. 135, 475–506.CrossRefGoogle Scholar
6. Bluestein, H. B., Weiss, C. C. & Pazmany, A. L. 2004 Doppler radar observations of dust devils in Texas. Mon. Weath. Rev. 132, 209–224.2.0.CO;2>CrossRefGoogle Scholar
7. Church, C. R. & Snow, J. T. 1993 Laboratory models of tornadoes. In The Tornado: Its Structure, Dynamics, Prediction, and Hazards (ed. Church, C. et al. ). American Geophysical Union.CrossRefGoogle Scholar
8. Church, C. R., Snow, J. T., Baker, G. L. & Agee, E. M. 1979 Characteristics of tornado-like vortices as a function of swirl ratio: a laboratory investigation. J. Atmos. Sci. 36, 1755–1776.2.0.CO;2>CrossRefGoogle Scholar
9. Davies-Jones, R. P. 1973 The dependence of core radius on swirl ratio in a tornado simulator. J. Atmos. Sci. 30, 1427–1430.2.0.CO;2>CrossRefGoogle Scholar
10. Emanuel, K. A. 1984 A note on the stability of columnar vortices. J. Fluid Mech. 145, 235–238.CrossRefGoogle Scholar
11. Escudier, M. P. 1984 Observations of the flow produced in a cylindrical container by a rotating end wall. Exp. Fluids 2, 189–196.CrossRefGoogle Scholar
12. Fiedler, B. H. 1989 Conditions for laminar flow in geophysical vortices. J. Atmos. Sci. 46, 252–260.2.0.CO;2>CrossRefGoogle Scholar
13. Fiedler, B. H. 1993 Numerical simulation of axisymmetric tornado genesis in forced convection. In The Tornado: Its Structure, Dynamics, Prediction, and Hazards (ed. Church, C. et al. ), American Geophysical Union.Google Scholar
14. Fiedler, B. H. 1994 The thermodynamic speed limit and its violation in axisymmetric numerical simulations of tornado-like vortices. Atmos.-Ocean 32, 335–359.CrossRefGoogle Scholar
15. Fiedler, B. H. 1998 Wind-speed limits in numerical simulated tornadoes with suction vortices. Q. J. Meteorol. Soc. 124, 2377–2392.Google Scholar
16. Fiedler, B. H. 2009 Suction vortices and spiral breakdown in numerical simulations of tornado-like vortices. Atmos. Sci. Lett. 10, 109–114.CrossRefGoogle Scholar
17. Fiedler, B. H. & Rotunno, R. 1986 A theory for the maximum windspeeds in tornado-like vortices. J. Atmos. Sci. 43, 2328–2340.2.0.CO;2>CrossRefGoogle Scholar
18. Fujita, T. T. 1970 The Lubbock tornadoes: a study of suction spots. Weatherwise 23, 160–173.Google Scholar
19. Gall, R. L. 1983 A linear analysis of the multiple vortex phenomenon in simulated tornadoes. J. Atmos. Sci. 40, 2010–2024.2.0.CO;2>CrossRefGoogle Scholar
20. Gall, R. L. 1985 Linear dynamics of the multiple-vortex phenomenon in tornadoes. J. Atmos. Sci. 42, 761–772.2.0.CO;2>CrossRefGoogle Scholar
21. Gallare, F. & Chomaz, J.-M. 2003 Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223–253.CrossRefGoogle Scholar
22. Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4, 195–218.CrossRefGoogle Scholar
23. Hall, N. M. J. & Sardeshmukh, P. D. 1998 Is the time-mean northern hemisphere flow baroclinically unstable? J. Atmos. Sci. 55, 41–56.2.0.CO;2>CrossRefGoogle Scholar
24. Howard, L. N. & Gupta, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows. J. Fluid Mech. 14, 463–476.CrossRefGoogle Scholar
25. Howells, P. C., Rotunno, R. & Smith, R. K. 1988 A comparative study of atmospheric and laboratory analogue numerical tornado-vortex models. Q. J. R. Meteorol. Soc. 114, 801–822.CrossRefGoogle Scholar
26. Lee, W.-C. & Wurman, J. 2005 Diagnosed three-dimensional axisymmetric structure of the Mulhall tornado on 3 May 1999. J. Atmos. Sci. 62, 2373–2393.CrossRefGoogle Scholar
27. Leibovich, S. 1984 Vortex stability and breakdown: survey and extension. AIAA J. 22, 1192–1205.CrossRefGoogle Scholar
28. Leibovich, S. & Stewartson, K. 1983 A sufficient condition for the instability of columnar vortices. J. Fluid Mech. 126, 335–356.CrossRefGoogle Scholar
29. Lewellen, D. C. & Lewellen, W. S. 2007a Near-surface intensification of tornado vortices. J. Atmos. Sci. 64, 2176–2194.CrossRefGoogle Scholar
30. Lewellen, D. C. & Lewellen, W. S. 2007b Near-surface vortex intensification through corner flow collapse. J. Atmos. Sci. 64, 2195–2209.CrossRefGoogle Scholar
31. Lewellen, W. S., Lewellen, D. C. & Sykes, R. I. 1997 Large-eddy simulation of a tornado’s interaction with the surface. J. Atmos. Sci. 54, 581–605.2.0.CO;2>CrossRefGoogle Scholar
32. Lewellen, D. C., Lewellen, W. S. & Xia, J. 2000 The influence of a local swirl ratio on tornado intensification near the surface. J. Atmos. Sci. 57, 527–544.2.0.CO;2>CrossRefGoogle Scholar
33. Lilly, D. K. 1969 Tornado dynamics. NCAR Manuscript 69-117, 39 pp. [Available from NCAR, P. O. Box 3000, Boulder, CO 80307].Google Scholar
34. Lugt, H. J. 1989 Vortex breakdown in atmospheric columnar vortices. Bull. Am. Meteorol. Soc. 70, 1526–1537.2.0.CO;2>CrossRefGoogle Scholar
35. Markowski, P. & Richardson, Y. 2010 Mesoscale Meteorology in Mid-latitudes. Wiley-Blackwell.CrossRefGoogle Scholar
36. Maxworthy, T. 1973 Vorticity source for large-scale dust devils and other comments on naturally occurring vortices. J. Atmos. Sci. 30, 1717–1720.2.0.CO;2>CrossRefGoogle Scholar
37. Michaelke, A. & Timme, A. 1967 On the inviscid instability of certain two-dimensional vortex-type flows. J. Fluid Mech. 29, 647–666.CrossRefGoogle Scholar
38. Nolan, D. S. 2001 The stabilizing effects of axial stretching on vortex dynamics. Phys. Fluids 13, 1724–1738.CrossRefGoogle Scholar
39. Nolan, D. S. 2005a Instabilities in hurricane-like boundary layers. Dyn. Atmos. Oceans 40, 209–236.CrossRefGoogle Scholar
40. Nolan, D. S. 2005b A new scaling for tornado-like vortices. J. Atmos. Sci. 62, 2639–2645.CrossRefGoogle Scholar
41. Nolan, D. S. & Farrell, B. F. 1999a Generalized stability analyses of asymmetric disturbances in one- and two-celled vortices maintained by radial inflow. J. Atmos. Sci. 56, 1282–1307.2.0.CO;2>CrossRefGoogle Scholar
42. Nolan, D. S. & Farrell, B. F. 1999b The structure and dynamics of tornado-like vortices. J. Atmos. Sci. 56, 2908–2936.2.0.CO;2>CrossRefGoogle Scholar
43. Nolan, D. S. & Grasso, L. D. 2003 Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part II. Symmetric response and nonlinear simulations. J. Atmos. Sci. 60, 2717–2745.2.0.CO;2>CrossRefGoogle Scholar
44. Nolan, D. S. & Montgomery, M. T. 2002 a Three-dimensional stability analyses of tornado-like vortices with secondary circulations. Preprints, 21st Conf. on Severe Local Storms, San Antonio, TX, pp. 477–480. Am. Meteor. Soc..Google Scholar
45. Nolan, D. S. & Montgomery, M. T. 2002b Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part I. Linearized formulation, stability, and evolution. J. Atmos. Sci. 59, 2989–3020.2.0.CO;2>CrossRefGoogle Scholar
46. Oberleithner, K., Sieber, M., Nayeri, C. N., Paschereit, C. O., Petz, C., Hege, H.-C., Noack, B. R. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383–414.CrossRefGoogle Scholar
47. Pauley, R. L. & Snow, J. T. 1988 On the kinematics and dynamics of the 18 July 1986 Minneapolis Tornado. Mon. Weath. Rev. 116, 2731–2736.Google Scholar
48. Rotunno, R. 1978 A note on the stability of a cylindrical vortex sheet. J. Fluid Mech. 87, 761–771.CrossRefGoogle Scholar
49. Rotunno, R. 1979 A study in tornado-like vortex dynamics. J. Atmos. Sci. 36, 140–155.2.0.CO;2>CrossRefGoogle Scholar
50. Rotunno, R. 1984 An investigation of a three-dimensional asymmetric vortex. J. Atmos. Sci. 41, 283–298.2.0.CO;2>CrossRefGoogle Scholar
51. Schubert, W. H., Montgomery, M. T., Taft, R. K., Guinn, T. A., Fulton, S. R., Kossin, J. P. & Edwards, J. P 1999 Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes. J. Atmos. Sci. 56, 1197–1223.2.0.CO;2>CrossRefGoogle Scholar
52. Serre, E. & Bontoux, P. 2002 Vortex breakdown in a three-dimensional swirling flow. J. Fluid Mech. 459, 347–370.CrossRefGoogle Scholar
53. Shtern, V. & Hussain, F. 1999 Collapse, symmetry breaking, and hysteresis in swirling flows. Annu. Rev. Fluid Mech. 31, 537–566.Google Scholar
54. Snow, J. T. 1982 A review of recent advances in tornado vortex dynamics. Rev. Geophys. 20, 953–964.CrossRefGoogle Scholar
55. Staley, D. O. & Gall, R. L. 1979 Barotropic instability in a tornado vortex. J. Atmos. Sci. 36, 973–981.Google Scholar
56. Steffens, J. L. 1988 The effect of vorticity-profile shape on the instability of a two-dimensional vortex. J. Atmos. Sci. 45, 254–260.2.0.CO;2>CrossRefGoogle Scholar
57. Tanamachi, R. L., Bluestein, H. B., Lee, W.-C., Bell, M. & Pazmany, A. 2007 Ground-based velocity-track display (GBVTD) analysis of W-band Doppler radar data in a tornado near Stockton, Kansas, on 15 May 1999. Mon. Weath. Rev. 135, 783–800.CrossRefGoogle Scholar
58. Terwey, W. D. & Montgomery, M. T. 2002 Wavenumber-2 and wavenumber-m vortex Rossby wave instabilities in a generalized three-region model. J. Atmos. Sci. 59, 2421–2427.2.0.CO;2>CrossRefGoogle Scholar
59. Wakimoto, R. M., Atkins, N. T. & Wurman, J. 2011 The LaGrange tornado during VORTEX2. Part I. Photogrammetric analysis of tornado combined with single-Doppler radar. Mon. Weath. Rev. 139, 2233–2258.CrossRefGoogle Scholar
60. Walko, R. & Gall, R. 1984 A two-dimensional linear stability analysis of the multiple vortex phenomenon. J. Atmos. Sci. 41, 3456–3471.2.0.CO;2>CrossRefGoogle Scholar
61. Ward, N. B. 1972 The exploration of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci. 29, 1194–1204.2.0.CO;2>CrossRefGoogle Scholar
62. Wurman, J. 2002 The multiple-vortex structure of a tornado. Wea. Forecasting 17, 473–505.2.0.CO;2>CrossRefGoogle Scholar
63. Wurman, J., Straka, J. M. & Rasmussen, E. N. 1996 Fine-scale Doppler radar observations of tornadoes. Science 272, 1774–1777.CrossRefGoogle ScholarPubMed
64. Zhang, W. & Sarkar, P. P. 2012 Near-ground tornado-like vortex structure resolved by particle image velocimetry (PIV). Exp. Fluids 52, 479–493.CrossRefGoogle Scholar