A Parametric Wind–Pressure Relationship for Rankine versus Non-Rankine Cyclostrophic Vortices

Vincent T. Wood NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

Search for other papers by Vincent T. Wood in
Current site
Google Scholar
PubMed
Close
and
Luther W. White Department of Mathematics, University of Oklahoma, Norman, Oklahoma

Search for other papers by Luther W. White in
Current site
Google Scholar
PubMed
Close
Restricted access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

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.

Corresponding author address: Vincent T. Wood, NOAA/OAR/NSSL, 120 David L. Boren Blvd., Room 3921, Norman, OK 73072-7323. E-mail: vincent.wood@noaa.gov

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.

Corresponding author address: Vincent T. Wood, NOAA/OAR/NSSL, 120 David L. Boren Blvd., Room 3921, Norman, OK 73072-7323. E-mail: vincent.wood@noaa.gov
Save
  • Alekseenko, S. V., Kuibin P. A. , and Okulov V. L. , 2007: Theory of Concentrated Vortices.Springer-Verlag, 494 pp.

  • Blair, S. F., Deroche D. R. , and Pietrycha A. E. , 2008: In situ observations of the 21 April 2007 Tulia, Texas tornado. Electron. J. Severe Storms Meteor., 3 (3). [Available online at http://www.ejssm.org/ojs/index.php/ejssm/issue/view/14.]

    • Search Google Scholar
    • Export Citation
  • Bluestein, H. B., Weiss C. C. , and Pazmany A. L. , 2004: Doppler radar observations of dust devils in Texas. Mon. Wea. Rev., 132, 209224.

    • Search Google Scholar
    • Export Citation
  • Burgers, J. M., 1948: A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech., 1, 197199.

  • Cantor, B. A., Kanak K. M. , and Edgett K. S. , 2006: Mars Orbiter Camera observations of Martian dust devils and their tracks (September 1997 to January 2006) and evaluation of theoretical vortex models. J. Geophys. Res., 111, E12002, doi:10.1029/2006JE002700.

    • Search Google Scholar
    • Export Citation
  • Carbone, R. E., Carpenter M. J. , and Burghart C. D. , 1985: Doppler radar sampling limitations in convective storms. J. Atmos. Oceanic Technol., 2, 357361.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R. P., 1986: Tornado dynamics. Thunderstorm Morphology and Dynamics, 2nd ed. E. Kessler, Ed., University of Oklahoma Press, 197–236.

  • Dowell, D. C., Alexander C. R. , Wurman J. M. , and Wicker L. J. , 2005: Centrifuging of hydrometeors and debris in tornadoes: Radar-reflectivity patterns and wind-measurement errors. Mon. Wea. Rev., 133, 15011524.

    • Search Google Scholar
    • Export Citation
  • Fiedler, B. H., 1994: The thermodynamic speed limit and its violation in axisymmetric numerical simulations of tornado-like vortices. Atmos.–Ocean, 32, 335359.

    • Search Google Scholar
    • Export Citation
  • Fiedler, B. H., and Rotunno R. , 1986: A theory for the maximum windspeeds in tornado-like vortices. J. Atmos. Sci., 43, 23282340.

  • Fujita, T. T., 1981: Tornadoes and downbursts in the context of generalized planetary scales. J. Atmos. Sci., 38, 15111534.

  • Hoecker, W. H., Jr., 1961: Three-dimensional pressure pattern of the Dallas tornado and some resultant implications. Mon. Wea. Rev., 89, 533542.

    • Search Google Scholar
    • Export Citation
  • Holland, G. J., 1980: An analytic model of the wind and pressure profiles in hurricanes. Mon. Wea. Rev., 108, 12121218.

  • Houston, S. H., and Powell M. D. , 1994: Observed and modeled wind and water-level response from Tropical Storm Marco (1990). Wea. Forecasting, 9, 427439.

    • Search Google Scholar
    • Export Citation
  • Inoue, H. Y., and Coauthors, 2011: Finescale Doppler radar observations of a tornado and low-level misocyclones within a winter storm in the Japan Sea coastal region. Mon. Wea. Rev., 139, 351369.

    • Search Google Scholar
    • Export Citation
  • Jelesnianski, C. P., 1966: Numerical computation of storm surges without bottom stress. Mon. Wea. Rev., 94, 379394.

  • Karstens, C. D., Samaras T. M. , Lee B. D. , Gallus W. A. Jr., and Finley C. A. , 2010: Near-ground pressure and wind measurements in tornadoes. Mon. Wea. Rev., 138, 25702588.

    • Search Google Scholar
    • Export Citation
  • Knaff, J. A., Sampson C. R. , Fitzpatrick P. J. , Jin Y. , and Hill C. M. , 2011: Simple diagnosis of tropical cyclone structure via pressure gradients. Wea. Forecasting, 26, 10201031.

    • Search Google Scholar
    • Export Citation
  • Lee, J. J., Samaras T. M. , and Young C. R. , 2004: Pressure measurements at the ground in an F-4 tornado. Preprints, 22nd Conf. on Severe Local Storms, Hyannis, MA, Amer. Meteor. Soc., 15.3. [Available online at https://ams.confex.com/ams/11aram22sls/techprogram/paper_81700.htm.]

  • Lee, W.-C., and Wurman J. , 2005: Diagnosed three-dimensional axisymmetric structure of the Mulhall tornado on 3 May 1999. J. Atmos. Sci., 62, 23732393.

    • Search Google Scholar
    • Export Citation
  • Lee, W.-C., Jou B. J.-D. , Chang P.-L. , and Deng S.-M. , 1999: Tropical cyclone kinematic structure retrieved from single-Doppler radar observations. Part I: Doppler velocity patterns and the GBVTD technique. Mon. Wea. Rev., 127, 24192439.

    • Search Google Scholar
    • Export Citation
  • Levenberg, K., 1944: A method for the solution of certain problems in least squares. Quart. Appl. Math., 2, 164168.

  • Leverson, V. H., Sinclair P. C. , and Golden J. H. , 1977: Waterspout wind, temperature, and pressure structure deduced from aircraft measurements. Mon. Wea. Rev., 105, 715733.

    • Search Google Scholar
    • Export Citation
  • Lewellen, W. S., Lewellen D. C. , and Sykes R. I. , 1997: Large-eddy simulation of a tornado's interaction with the surface. J. Atmos. Sci., 54, 581605.

    • Search Google Scholar
    • Export Citation
  • Markowski, P., and Richardson Y. , 2010: Mesoscale Meteorology in Midlatitudes.1st ed. John Wiley and Sons, Ltd., 407 pp.

  • Marquardt, D., 1963: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math., 11, 431441.

  • NCDC, 1999: Storm Data.Vol. 37, No. 5, 372 pp.

  • Ooyama, K., 1969: Numerical simulation of the life cycle of tropical cyclones. J. Atmos. Sci., 26, 340.

  • Press, W. H., Teukolsky S. A. , Vetterling W. T. , and Flannery B. P. , 1992: Numerical Recipes in Fortran 77: The Art of Scientific Computing. 2nd ed. Cambridge University Press, 933 pp.

  • Rankine, W. J. M., 1882: A Manual of Applied Physics.10th ed. Charles Griff and Co., 663 pp.

  • Rott, N., 1958: On the viscous core of a line vortex. Z. Angew. Math. Phys., 9, 543553.

  • Rotunno, R., 2013: The fluid dynamics of tornadoes. Annu. Rev. Fluid Mech., 45, 5984.

  • Sinclair, P. C., 1973: The lower structure of dust devils. J. Atmos. Sci., 30, 15991619.

  • Snow, J. T., and Lund D. E. , 1989: Inertial motions in analytical vortex models. J. Atmos. Sci., 46, 36053610.

  • Sullivan, R. D., 1959: A two-cell vortex solution of the Navier–Stokes equations. J. Aerosp. Sci., 26, 767768.

  • Tanamachi, R. L., Bluestein H. B. , Lee W.-C. , Bell M. , and 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. Wea. Rev., 135, 783800.

    • Search Google Scholar
    • Export Citation
  • Tanamachi, R. L., Bluestein H. B. , Xue M. , Lee W.-C. , Orzel K. A. , Frasier S. J. , and Wakimoto R. M. , 2013: Near-surface vortex structure in a tornado and in a sub-tornado-strength, convective-storm vortex observed by a mobile, W-band radar during VORTEX2. Mon. Wea. Rev., 141, 36613690.

    • Search Google Scholar
    • Export Citation
  • Wakimoto, R. M., and Wilson J. W. , 1989: Non-supercell tornadoes. Mon. Wea. Rev., 117, 11131140.

  • Weatherford, C. L., and Gray W. M. , 1988: Typhoon structure as revealed by aircraft reconnaissance. Part I: Data analysis and climatology. Mon. Wea. Rev., 116, 10321043.

    • Search Google Scholar
    • Export Citation
  • Winn, W. P., Hunyady S. J. , and Aulich G. D. , 1999: Pressure at the ground in a large tornado. J. Geophys. Res., 104 (D18), 22 06722 082.

    • Search Google Scholar
    • Export Citation
  • Wood, V. T., and White L. W. , 2011: A new parametric model of vortex tangential-wind profiles: Development, testing, and verification. J. Atmos. Sci., 68, 9901006.

    • Search Google Scholar
    • Export Citation
  • Wood, V. T., White L. W. , Willoughby H. E. , and Jorgensen D. P. , 2013: A new parametric tropical cyclone tangential wind profile model. Mon. Wea. Rev., 141, 18841909.

    • Search Google Scholar
    • Export Citation
  • Wurman, J., 2002: The multiple-vortex structure of a tornado. Wea. Forecasting, 17, 473505.

  • Wurman, J., and Gill S. , 2000: Finescale radar observations of the Dimmitt, Texas (2 June 1995), tornado. Mon. Wea. Rev., 128, 21352164.

    • Search Google Scholar
    • Export Citation
  • Wurman, J., and Samaras T. , 2004: Comparison of in-situ pressure and DOW Doppler winds in a tornado and RHI vertical slices through 4 tornadoes during 1996-2004. Preprints, 22nd Conf. on Severe Local Storms, Hyannis, MA, Amer. Meteor. Soc., 15.4. [Available online at https://ams.confex.com/ams/11aram22sls/techprogram/paper_82352.htm.]

  • Wurman, J., and Alexander C. R. , 2005: The 30 May 1998 Spencer, South Dakota, storm. Part II: Comparison of observed damage and radar-derived winds in the tornadoes. Mon. Wea. Rev., 133, 97119.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1034 350 143
PDF Downloads 602 104 5