Revisiting the Relationship between Eyewall Contraction and Intensification

Daniel P. Stern National Center for Atmospheric Research,* Boulder, Colorado

Search for other papers by Daniel P. Stern in
Current site
Google Scholar
PubMed
Close
,
Jonathan L. Vigh National Center for Atmospheric Research,* Boulder, Colorado

Search for other papers by Jonathan L. Vigh in
Current site
Google Scholar
PubMed
Close
,
David S. Nolan Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

Search for other papers by David S. Nolan in
Current site
Google Scholar
PubMed
Close
, and
Fuqing Zhang The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Fuqing Zhang 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

In the widely accepted convective ring model of tropical cyclone intensification, the intensification of the maximum winds and the contraction of the radius of maximum winds (RMW) occur simultaneously. This study shows that in idealized numerical simulations, contraction and intensification commence at the same time, but that contraction ceases long before peak intensity is achieved. The rate of contraction decreases with increasing initial size, while the rate of intensification does not vary systematically with initial size. Utilizing a diagnostic expression for the rate of contraction, it is shown that contraction is halted in association with a rapid increase in the sharpness of the tangential wind profile near the RMW and is not due to changes in the radial gradient of the tangential wind tendency. It is shown that a number of real storms exhibit a relationship between contraction and intensification that is similar to what is seen in the idealized simulations. In particular, the statistical distribution of intensifying tropical cyclones indicates that, for major hurricanes, most contraction is completed prior to most intensification.

By forcing a linearized vortex model with the diabatic heating and frictional tendencies from a simulation, it is possible to qualitatively reproduce the simulated secondary circulation and separately examine the vortex responses to heating and friction. It is shown that heating and friction both contribute substantially to boundary layer inflow. They also both contribute to the contraction of the RMW, as the positive wind tendency from heating-induced inflow is maximized inside of the RMW, while the net negative wind tendency from friction and frictionally induced inflow is maximized outside of the RMW.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Daniel P. Stern, National Center for Atmospheric Research, 3450 Mitchell Lane, Boulder, CO 80301. E-mail: dstern@ucar.edu

Abstract

In the widely accepted convective ring model of tropical cyclone intensification, the intensification of the maximum winds and the contraction of the radius of maximum winds (RMW) occur simultaneously. This study shows that in idealized numerical simulations, contraction and intensification commence at the same time, but that contraction ceases long before peak intensity is achieved. The rate of contraction decreases with increasing initial size, while the rate of intensification does not vary systematically with initial size. Utilizing a diagnostic expression for the rate of contraction, it is shown that contraction is halted in association with a rapid increase in the sharpness of the tangential wind profile near the RMW and is not due to changes in the radial gradient of the tangential wind tendency. It is shown that a number of real storms exhibit a relationship between contraction and intensification that is similar to what is seen in the idealized simulations. In particular, the statistical distribution of intensifying tropical cyclones indicates that, for major hurricanes, most contraction is completed prior to most intensification.

By forcing a linearized vortex model with the diabatic heating and frictional tendencies from a simulation, it is possible to qualitatively reproduce the simulated secondary circulation and separately examine the vortex responses to heating and friction. It is shown that heating and friction both contribute substantially to boundary layer inflow. They also both contribute to the contraction of the RMW, as the positive wind tendency from heating-induced inflow is maximized inside of the RMW, while the net negative wind tendency from friction and frictionally induced inflow is maximized outside of the RMW.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Daniel P. Stern, National Center for Atmospheric Research, 3450 Mitchell Lane, Boulder, CO 80301. E-mail: dstern@ucar.edu
Save
  • Abarca, S. F., and M. T. Montgomery, 2013: Essential dynamics of secondary eyewall formation. J. Atmos. Sci., 70, 32163230, doi:10.1175/JAS-D-12-0318.1.

    • Search Google Scholar
    • Export Citation
  • Abarca, S. F., and M. T. Montgomery, 2014: Departures from axisymmetric balance dynamics during secondary eyewall formation. J. Atmos. Sci., 71, 37233738, doi:10.1175/JAS-D-14-0018.1.

    • Search Google Scholar
    • Export Citation
  • Black, M. L., J. F. Gamache, F. D. Marks Jr., C. E. Samsury, and H. E. Willoughby, 2002: Eastern Pacific hurricanes Jimena of 1991 and Olivia of 1994: The effect of vertical shear on structure and intensity. Mon. Wea. Rev., 130, 22912312, doi:10.1175/1520-0493(2002)130<2291:EPHJOA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., 2012: Effects of surface exchange coefficients and turbulence length scales on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 140, 11251143, doi:10.1175/MWR-D-11-00231.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and R. Rotunno, 2009: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Mon. Wea. Rev., 137, 17701789, doi:10.1175/2008MWR2709.1.

    • Search Google Scholar
    • Export Citation
  • Bui, H. H., R. K. Smith, M. T. Montgomery, and J. Peng, 2009: Balanced and unbalanced aspects of tropical cyclone intensification. Quart. J. Roy. Meteor. Soc., 135, 17151731, doi:10.1002/qj.502.

    • Search Google Scholar
    • Export Citation
  • Chen, H., D.-L. Zhang, J. Carton, and R. Atlas, 2011: On the rapid intensification of hurricane Wilma (2005). Part I: Model prediction and structural changes. Wea. Forecasting, 26, 885901, doi:10.1175/WAF-D-11-00001.1.

    • Search Google Scholar
    • Export Citation
  • Dunion, J. P., 2011: Rewriting the climatology of the tropical North Atlantic and Caribbean Sea atmosphere. J. Climate, 24, 893908, doi:10.1175/2010JCLI3496.1.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., 1951: Slow thermally or frictionally controlled meridional circulation in a circular vortex. Astrophys. Norv., 5, 1960.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., and M. Lystad, 1977: The Ekman layer of a circular vortex. A numerical and theoretical study. Geophys. Norv., 31, 116.

  • Emanuel, K. A., 1995: The behavior of a simple hurricane model using a convective scheme based on subcloud-layer entropy equilibrium. J. Atmos. Sci., 52, 39603968, doi:10.1175/1520-0469(1995)052<3960:TBOASH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 2012: Self-stratification of tropical cyclone outflow. Part II: Implications for storm intensification. J. Atmos. Sci., 69, 988996, doi:10.1175/JAS-D-11-0177.1.

    • Search Google Scholar
    • Export Citation
  • Evans, C., and R. E. Hart, 2008: Analysis of the wind field evolution associated with the extratropical transition of Bonnie (1998). Mon. Wea. Rev., 136, 20472065, doi:10.1175/2007MWR2051.1.

    • Search Google Scholar
    • Export Citation
  • Hill, K. A., and G. M. Lackmann, 2009: Analysis of idealized tropical cyclone simulations using the Weather Research and Forecasting Model: Sensitivity to turbulence parameterization and grid spacing. Mon. Wea. Rev., 137, 745765, doi:10.1175/2008MWR2220.1.

    • Search Google Scholar
    • Export Citation
  • Hodyss, D., and D. S. Nolan, 2007: Linear anelastic equations for atmospheric vortices. J. Atmos. Sci., 64, 29472959, doi:10.1175/JAS3991.1.

    • Search Google Scholar
    • Export Citation
  • Hogsett, W. A., and S. R. Stewart, 2014: Dynamics of tropical cyclone intensification: Deep convective cyclonic “left movers.” J. Atmos. Sci., 71, 226242, doi:10.1175/JAS-D-12-0284.1.

    • Search Google Scholar
    • Export Citation
  • Holland, G. J., 1997: The maximum potential intensity of tropical cyclones. J. Atmos. Sci., 54, 25192541, doi:10.1175/1520-0469(1997)054<2519:TMPIOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Holland, G. J., and R. T. Merrill, 1984: On the dynamics of tropical cyclone structural changes. Quart. J. Roy. Meteor. Soc., 110, 723745, doi:10.1002/qj.49711046510.

    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 2010: Clouds in tropical cyclones. Mon. Wea. Rev., 138, 293344, doi:10.1175/2009MWR2989.1.

  • Jorgensen, D. P., 1984b: Mesoscale and convective-scale characteristics of mature hurricanes. Part II: Inner core structure of Hurricane Allen (1980). J. Atmos. Sci., 41, 12871311, doi:10.1175/1520-0469(1984)041<1287:MACSCO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Judt, F., and S. S. Chen, 2013: Reply to “Comments on ‘Convectively generated potential vorticity in rainbands and formation of the secondary eyewall in Hurricane Rita of 2005.’” J. Atmos. Sci., 70, 989992, doi:10.1175/JAS-D-12-0151.1.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2013: How does the boundary layer contribute to eyeball replacement cycles in axisymmetric tropical cyclones. J. Atmos. Sci., 70, 28082830, doi:10.1175/JAS-D-13-046.1.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., and Y. Wang, 2001: The dynamics of boundary layer jets within the tropical cyclone core. Part II: Nonlinear enhancement. J. Atmos. Sci., 58, 24852501, doi:10.1175/1520-0469(2001)058<2485:TDOBLJ>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., and D. S. Nolan, 2014: Reply to “Comments on ‘How does the boundary layer contribute to eyewall replacement cycles in axisymmetric tropical cyclones?’” J. Atmos. Sci., 71, 46924704, doi:10.1175/JAS-D-14-0014.1.

    • Search Google Scholar
    • Export Citation
  • Kieu, C. Q., 2012: An investigation into the contraction of the hurricane radius of maximum wind. Meteor. Atmos. Phys., 115, 4756, doi:10.1007/s00703-011-0171-7.

    • Search Google Scholar
    • Export Citation
  • Kimball, S. K., and M. S. Mulekar, 2004: A 15-year climatology of North Atlantic tropical cyclones. Part I: Size parameters. J. Climate, 17, 35553575, doi:10.1175/1520-0442(2004)017<3555:AYCONA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kimball, S. K., and F. C. Dougherty, 2006: The sensitivity of idealized hurricane structure and development to the distribution of vertical levels in MM5. Mon. Wea. Rev., 134, 19872008, doi:10.1175/MWR3171.1.

    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., J. A. Knaff, H. I. Berger, D. C. Herndon, T. A. Cram, C. S. Velden, R. J. Murnane, and J. D. Hawkins, 2007: Estimating hurricane wind structure in the absence of aircraft reconnaissance. Wea. Forecasting, 22, 89101, doi:10.1175/WAF985.1.

    • Search Google Scholar
    • Export Citation
  • Menelaou, K., M. K. Yau, and Y. Martinez, 2014: Some aspects of the problem of secondary eyewall formation in idealized three-dimensional nonlinear simulations. J. Adv. Model. Earth Syst., 6, 491512, doi:10.1002/2014MS000316.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., H. D. Snell, and Z. Yang, 2001: Axisymmetric spindown dynamics of hurricane-like vortices. J. Atmos. Sci., 58, 421435, doi:10.1175/1520-0469(2001)058<0421:ASDOHL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mrowiec, A. A., S. T. Garner, and O. M. Pauluis, 2011: Axisymmetric hurricane in a dry atmosphere: Theoretical framework and numerical experiments. J. Atmos. Sci., 68, 16071619, doi:10.1175/2011JAS3639.1.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., and M. T. Montgomery, 2002: Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part I: Linearized formulation, stability, and evolution. J. Atmos. Sci., 59, 29893020, doi:10.1175/1520-0469(2002)059<2989:NTDPTB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., and L. D. Grasso, 2003: Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part II: Symmetric response and nonlinear simulations. J. Atmos. Sci., 60, 27172745, doi:10.1175/1520-0469(2003)060<2717:NTPTBH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., Y. Moon, and D. P. Stern, 2007: Tropical cyclone intensification from asymmetric convection: Energetics and efficiency. J. Atmos. Sci., 64, 33773405, doi:10.1175/JAS3988.1.

    • Search Google Scholar
    • Export Citation
  • Pu, Z., X. Li, and E. J. Zipser, 2009: Diagnosis of the initial and forecast errors in the numerical simulation of the rapid intensification of Hurricane Emily (2005). Wea. Forecasting, 24, 12361251, doi:10.1175/2009WAF2222195.1.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., and G. H. Bryan, 2012: Effects of parameterized diffusion on simulated hurricanes. J. Atmos. Sci., 69, 22842299, doi:10.1175/JAS-D-11-0204.1.

    • Search Google Scholar
    • Export Citation
  • Rozoff, C. M., W. H. Schubert, and J. P. Kossin, 2008: Some dynamical aspects of tropical cyclone concentric eyewalls. Quart. J. Roy. Meteor. Soc., 134, 583593, doi:10.1002/qj.237.

    • Search Google Scholar
    • Export Citation
  • Rozoff, C. M., D. S. Nolan, J. P. Kossin, F. Zhang, and J. Fang, 2012: The roles of an expanding wind field and inertial stability in tropical cyclone secondary eyewall formation. J. Atmos. Sci., 69, 26212643, doi:10.1175/JAS-D-11-0326.1.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci., 39, 16871697, doi:10.1175/1520-0469(1982)039<1687:ISATCD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and B. D. McNoldy, 2010: Application of the concepts of Rossby length and Rossby depth to tropical cyclone dynamics. J. Adv. Model. Earth Syst., 2, 7, doi:10.3894/JAMES.2010.2.7.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., C. M. Rozoff, J. L. Vigh, B. D. McNoldy, and J. P. Kossin, 2007: On the distribution of subsidence in the hurricane eye. Quart. J. Roy. Meteor. Soc., 133, 595605, doi:10.1002/qj.49.

    • Search Google Scholar
    • Export Citation
  • Schwendike, J., and J. D. Kepert, 2008: The boundary layer winds in Hurricanes Danielle (1998) and Isabel (2003). Mon. Wea. Rev., 136, 31683192, doi:10.1175/2007MWR2296.1.

    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci., 39, 378394, doi:10.1175/1520-0469(1982)039<0378:TROBHT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., 1981: The cyclostrophic adjustment of vortices with application to tropical cyclone modification. J. Atmos. Sci., 38, 20212030, doi:10.1175/1520-0469(1981)038<2021:TCAOVW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., M. T. Montgomery, and N. V. Sang, 2009: Tropical cyclone spin-up revisited. Quart. J. Roy. Meteor. Soc., 135, 13211335, doi:10.1002/qj.428.

    • Search Google Scholar
    • Export Citation
  • Stern, D. P., and D. S. Nolan, 2009: Reexamining the vertical structure of tangential winds in tropical cyclones: Observations and theory. J. Atmos. Sci., 66, 35793600, doi:10.1175/2009JAS2916.1.

    • Search Google Scholar
    • Export Citation
  • Stern, D. P., and D. S. Nolan, 2011: On the vertical decay rate of the maximum tangential winds in tropical cyclones. J. Atmos. Sci., 68, 20732094, doi:10.1175/2011JAS3682.1.

    • Search Google Scholar
    • Export Citation
  • Stern, D. P., J. R. Brisbois, and D. S. Nolan, 2014: An expanded dataset of hurricane eyewall sizes and slopes. J. Atmos. Sci., 71, 27472762, doi:10.1175/JAS-D-13-0302.1.

    • Search Google Scholar
    • Export Citation
  • Van Sang, N., R. K. Smith, and M. T. Montgomery, 2008: Tropical cyclone intensification and predictability in three dimensions. Quart. J. Roy. Meteor. Soc., 134, 563582, doi:10.1002/qj.235.

    • Search Google Scholar
    • Export Citation
  • Vigh, J. L., 2010: Formation of the hurricane eye. Ph.D. dissertation, Colorado State University, 538 pp. [Available online at http://www.ral.ucar.edu/staff/jvigh/documents/vigh2010_dissertation_corrected_color_hyperlinks.pdf.]

  • Vigh, J. L., J. A. Knaff, and W. H. Schubert, 2012: A climatology of hurricane eye formation. Mon. Wea. Rev., 140, 14051426, doi:10.1175/MWR-D-11-00108.1.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2008: Structure and formation of an annular hurricane simulated in a fully compressible, nonhydrostatic model—TCM4. J. Atmos. Sci., 65, 15051527, doi:10.1175/2007JAS2528.1.

    • Search Google Scholar
    • Export Citation
  • Weng, Y., and F. Zhang, 2012: Assimilating airborne Doppler radar observations with an ensemble Kalman filter for convection-permitting hurricane initialization and prediction: Katrina (2005). Mon. Wea. Rev., 140, 841859, doi:10.1175/2011MWR3602.1.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., 1990: Temporal changes in the primary circulation of tropical cyclones. J. Atmos. Sci., 47, 242264, doi:10.1175/1520-0469(1990)047<0242:TCOTPC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., and M. E. Rahn, 2004: Parametric representation of the primary hurricane vortex. Part I: Observations and evaluation of the Holland (1980) model. Mon. Wea. Rev., 132, 30333048, doi:10.1175/MWR2831.1.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., J. A. Clos, and M. G. Shoreibah, 1982: Concentric eye walls, secondary wind maxima, and the evolution of the hurricane vortex. J. Atmos. Sci., 39, 395411, doi:10.1175/1520-0469(1982)039<0395:CEWSWM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., H.-L. Jin, S. J. Lord, and J. M. Piotrowicz, 1984: Hurricane structure and evolution as simulated by an axisymmetric, nonhydrostatic numerical model. J. Atmos. Sci., 41, 11691186, doi:10.1175/1520-0469(1984)041<1169:HSAEAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., R. F. Rogers, D. S. Nolan, and F. D. Marks Jr., 2011: On the characteristic height scales of the hurricane boundary layer. Mon. Wea. Rev., 139, 25232535, doi:10.1175/MWR-D-10-05017.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1561 564 247
PDF Downloads 900 187 17