Long-Term Effect of Barotropic Instability across the Moat in Double-Eyewall Tropical Cyclone–Like Vortices in Forced and Unforced Shallow-Water Models

Tsz-Kin Lai aDepartment of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Eric A. Hendricks bNational Center for Atmospheric Research, Boulder, Colorado

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M. K. Yau aDepartment of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Abstract

Secondary eyewall formation and the ensuing eyewall replacement cycles may take place in mature tropical cyclones (TCs) during part of their lifetime. A better understanding of the underlying dynamics is beneficial to improving the prediction of TC intensity and structure. Previous studies suggested that the barotropic instability (BI) across the moat (aka type-2 BI) can make a substantial contribution to the inner-eyewall decay through the associated eddy radial transport of absolute angular momentum (AAM). Simultaneously, the type-2 BI can also increase the AAM of the outer eyewall. While the previous studies focused on the early stage of the type-2 BI, this paper explores the long-term effect of the type-2 BI and the underlying processes in forced and unforced shallow-water experiments. Under the long-term effect, it will be shown that the inner eyewalls repeatedly weaken and strengthen (while the order is reversed for the outer eyewalls). Sensitivity tests are conducted to examine the sensitivity of the long-term effect of the type-2 BI to different vortex parameters and the strength of the parameterized diabatic heating. Implication of the long-term effect for the intensity changes of the inner and outer eyewalls of real TCs are also discussed.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tsz-Kin Lai, eric.lai@mail.mcgill.ca

Abstract

Secondary eyewall formation and the ensuing eyewall replacement cycles may take place in mature tropical cyclones (TCs) during part of their lifetime. A better understanding of the underlying dynamics is beneficial to improving the prediction of TC intensity and structure. Previous studies suggested that the barotropic instability (BI) across the moat (aka type-2 BI) can make a substantial contribution to the inner-eyewall decay through the associated eddy radial transport of absolute angular momentum (AAM). Simultaneously, the type-2 BI can also increase the AAM of the outer eyewall. While the previous studies focused on the early stage of the type-2 BI, this paper explores the long-term effect of the type-2 BI and the underlying processes in forced and unforced shallow-water experiments. Under the long-term effect, it will be shown that the inner eyewalls repeatedly weaken and strengthen (while the order is reversed for the outer eyewalls). Sensitivity tests are conducted to examine the sensitivity of the long-term effect of the type-2 BI to different vortex parameters and the strength of the parameterized diabatic heating. Implication of the long-term effect for the intensity changes of the inner and outer eyewalls of real TCs are also discussed.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tsz-Kin Lai, eric.lai@mail.mcgill.ca
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  • Abarca, S. F., and M. T. Montgomery, 2015: Are eyewall replacement cycles governed largely by axisymmetric balance dynamics?. J. Atmos. Sci., 72, 8287, https://doi.org/10.1175/JAS-D-14-0151.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., 1983: A finite-amplitude Eliassen-Palm theorem in isentropic coordinates. J. Atmos. Sci., 40, 18771883, https://doi.org/10.1175/1520-0469(1983)040<1877:AFAEPT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA general circulation model. Methods Comput. Phys., 17, 173265, https://doi.org/10.1016/B978-0-12-460817-7.50009-4.

    • Search Google Scholar
    • Export Citation
  • Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100, 487490, https://doi.org/10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Black, M. L., and H. E. Willoughby, 1992: The concentric eyewall cycle of Hurricane Gilbert. Mon. Wea. Rev., 120, 947957, https://doi.org/10.1175/1520-0493(1992)120<0947:TCECOH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Didlake, A. C. Jr., and R. A. Houze Jr., 2011: Kinematics of the secondary eyewall observed in Hurricane Rita (2005). J. Atmos. Sci., 68, 16201636, https://doi.org/10.1175/2011JAS3715.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Didlake, A. C. Jr., G. M. Heymsfield, P. D. Reasor, and S. R. Guimond, 2017: Concentric eyewall asymmetries in Hurricane Gonzalo (2014) observed by airborne radar. Mon. Wea. Rev., 145, 729749, https://doi.org/10.1175/MWR-D-16-0175.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fischer, M. S., R. F. Rogers, and P. D. Reasor, 2020: The rapid intensification and eyewall replacement cycles of Hurricane Irma (2017). Mon. Wea. Rev., 148, 9811004, https://doi.org/10.1175/MWR-D-19-0185.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fortner, L. E. Jr., 1958: Typhoon Sarah, 1956. Bull. Amer. Meteor. Soc., 39, 633639, https://doi.org/10.1175/1520-0477-39.12.633.

  • Hendricks, E. A., and W. H. Schubert, 2010: Adiabatic rearrangement of hollow PV towers. J. Adv. Model. Earth Syst., 2 (4), https://doi.org/10.3894/JAMES.2010.2.8.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hendricks, E. A., W. H. Schubert, Y.-H. Chen, H.-C. Kuo, and M. S. Peng, 2014: Hurricane eyewall evolution in a forced shallow-water model. J. Atmos. Sci., 71, 16231643, https://doi.org/10.1175/JAS-D-13-0303.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houze, R. A. Jr., S. S. Chen, B. F. Smull, W.-C. Lee, and M. M. Bell, 2007: Hurricane intensity and eyewall replacement. Science, 315, 12351239, https://doi.org/10.1126/science.1135650.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, Y.-H., M. T. Montgomery, and C.-C. Wu, 2012: Concentric eyewall formation in Typhoon Sinlaku (2008). Part II: Axisymmetric dynamical processes. J. Atmos. Sci., 69, 662674, https://doi.org/10.1175/JAS-D-11-0114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical cyclones in the North Atlantic basin. Wea. Forecasting, 18, 10931108, https://doi.org/10.1175/1520-0434(2003)018<1093:LCORIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaplan, J., M. DeMaria, and J. A. Knaff, 2010: A revised tropical cyclone rapid intensification index for the Atlantic and eastern North Pacific basins. Wea. Forecasting, 25, 220241, https://doi.org/10.1175/2009WAF2222280.1.

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

    • Crossref
    • 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, https://doi.org/10.1175/JAS-D-14-0014.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., and W. H. Schubert, 2001: Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-like vortices. J. Atmos. Sci., 58, 21962209, https://doi.org/10.1175/1520-0469(2001)058<2196:MPFPAR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., and W. H. Schubert, 2004: Mesovortices in Hurricane Isabel (2003). Bull. Amer. Meteor. Soc., 85, 151153, https://doi.org/10.1175/BAMS-85-2-151.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., and M. Sitkowski, 2009: An objective model for identifying secondary eyewall formation in hurricanes. Mon. Wea. Rev., 137, 876892, https://doi.org/10.1175/2008MWR2701.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., W. H. Schubert, and M. T. Montgomery, 2000: Unstable interactions between a hurricane’s primary eyewall and a secondary ring of enhanced vorticity. J. Atmos. Sci., 57, 38933917, https://doi.org/10.1175/1520-0469(2001)058<3893:UIBAHS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., B. D. McNoldy, and W. H. Schubert, 2002: Vortical swirls in hurricane eye clouds. Mon. Wea. Rev., 130, 31443149, https://doi.org/10.1175/1520-0493(2002)130<3144:VSIHEC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuo, H.-C., C.-P. Chang, Y.-T. Yang, and H.-J. Jiang, 2009: Western North Pacific typhoons with concentric eyewalls. Mon. Wea. Rev., 137, 37583770, https://doi.org/10.1175/2009MWR2850.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lai, T.-K., K. Menelaou, and M. K. Yau, 2019: Barotropic instability across the moat and inner eyewall dissipation: A numerical study of Hurricane Wilma (2005). J. Atmos. Sci., 76, 9891013, https://doi.org/10.1175/JAS-D-18-0191.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lai, T. -K., E. A. Hendricks, K. Menelaou, and M. K. Yau, 2021a: Roles of barotropic instability across the moat in inner eyewall decay and outer eyewall intensification: Three-dimensional numerical experiments. J. Atmos. Sci., 78, 473496, https://doi.org/10.1175/JAS-D-20-0168.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lai, T. -K., E. A. Hendricks, M. K. Yau, and K. Menelaou, 2021b: Roles of barotropic instability across the moat in inner eyewall decay and outer eyewall intensification: Essential dynamics. J. Atmos. Sci., 78, 14111428, https://doi.org/10.1175/JAS-D-20-0169.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McNoldy, B. D., 2004: Triple eyewall in Hurricane Juliette. Bull. Amer. Meteor. Soc., 85, 16631666, https://doi.org/10.1175/BAMS-85-11-1663.

  • McNoldy, B. D., 2021: Tropical cyclone radar loops. University of Miami Rosenstiel School of Marine and Atmospheric Science, https://bmcnoldy.rsmas.miami.edu/tropics/maria17/Maria_19-20Sep17_TJUA.gif.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., L. P. Graves, and M. T. Montgomery, 2003: A formal theory for vortex Rossby waves and vortex evolution. Geophys. Astrophys. Fluid Dyn., 97, 275309, https://doi.org/10.1080/0309192031000108698.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Molinari, J., J. A. Zhang, R. F. Rogers, and D. Vollaro, 2019: Repeated eyewall replacement cycles in Hurricane Frances (2004). Mon. Wea. Rev., 147, 20092022, https://doi.org/10.1175/MWR-D-18-0345.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and R. J. Kallenbach, 1997: A theory for vortex Rossby-waves and its application to spiral bands and intensity changes in hurricanes. Quart. J. Roy. Meteor. Soc., 123, 435465, https://doi.org/10.1002/qj.49712353810.

    • Crossref
    • 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, https://doi.org/10.1175/1520-0469(2001)058<0421:ASDOHL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., S. F. Abarca, R. K. Smith, C.-C. Wu, and Y.-H. Huang, 2014: Comments on “How does the boundary layer contribute to eyewall replacement cycles in axisymmetric tropical cyclones?”. J. Atmos. Sci., 71, 46824691, https://doi.org/10.1175/JAS-D-13-0286.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., 1990: Boundary layer structure and dynamics in outer hurricane rainbands. Part II: Downdraft modification and mixed layer recovery. Mon. Wea. Rev., 118, 918938, https://doi.org/10.1175/1520-0493(1990)118<0918:BLSADI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reasor, P. D., M. T. Montgomery, F. D. Marks Jr., and J. F. Gamache, 2000: Low-wavenumber structure and evolution of the hurricane inner core observed by airborne dual-Doppler radar. Mon. Wea. Rev., 128, 16531680, https://doi.org/10.1175/1520-0493(2000)128<1653:LWSAEO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Robert, A. J., 1966: The integration of a low order spectral form of the primitive meteorological equations. J. Meteor. Soc. Japan, 44, 237245, https://doi.org/10.2151/jmsj1965.44.5_237.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rodgers, E. B., W. S. Olson, V. M. Karyampudi, and H. F. Pierce, 1998: Satellite-derived latent heating distribution and environmental influences in Hurricane Opal (1995). Mon. Wea. Rev., 126, 12291247, https://doi.org/10.1175/1520-0493(1998)126<1229:SDLHDA>2.0.CO;2.

    • Crossref
    • 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, https://doi.org/10.1002/qj.237.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rozoff, C. M., J. P. Kossin, W. H. Schubert, and P. Mulero, 2009: Internal control of hurricane intensity variability: The dual nature of potential vorticity mixing. J. Atmos. Sci., 66, 133147, https://doi.org/10.1175/2008JAS2717.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Samsury, C. E., and E. J. Zipser, 1995: Secondary wind maxima in hurricanes: Airflow and relationship to rainband. Mon. Wea. Rev., 123, 35023517, https://doi.org/10.1175/1520-0493(1995)123<3502:SWMIHA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schecter, D. A., and K. Menelaou, 2017: Note on analyzing perturbation growth in tropical cyclone–like vortices radiating inertia–gravity waves. J. Atmos. Sci., 74, 15611571, https://doi.org/10.1175/JAS-D-16-0289.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., M. T. Montgomery, R. K. Taft, T. A. Gunn, S. R. Fulton, J. P. Kossin, and J. P. Edwards, 1999: Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes. J. Atmos. Sci., 56, 11971223, https://doi.org/10.1175/1520-0469(1999)056<1197:PEAECA>2.0.CO;2.

    • Crossref
    • 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, https://doi.org/10.1175/1520-0469(1982)039<0378:TROBHT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sheets, R. C., and N. E. LaSeur, 1979: Project STORMFURY: Present status–future plans. WMO Bull., 28, 1723.

  • Tsujino, S., K. Tsuboki, and H.-C. Kuo, 2017: Structure and maintenance mechanism of long-lived concentric eyewalls associated with simulated Typhoon Bolaven (2012). J. Atmos. Sci., 74, 36093634, https://doi.org/10.1175/JAS-D-16-0236.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tsujino, S., T. Horinouchi, T. Tsukada, H.-C. Kuo, H. Yamada, and K. Tsuboki, 2021: Inner-core wind field in a concentric eyewall replacement of Typhoon Trami (2018): A quantitative analysis based on the Himawari-8 satellite. J. Geophys. Res. Atmos., 126, e2020JD034434, https://doi.org/10.1029/2020JD034434.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tung, K. K., 1986: Nongeostrophic theory of zonally averaged circulation. Part I: Formulation. J. Atmos. Sci., 43, 26002618, https://doi.org/10.1175/1520-0469(1986)043<2600:NTOZAC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., 1988: The dynamics of the tropical cyclone core. Aust. Meteor. Mag., 36, 183191.

  • 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, https://doi.org/10.1175/1520-0469(1982)039<0395:CEWSWM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., D. P. Jorgensen, R. A. Black, and S. L. Rosenthal, 1985: Project STORMFURY: A scientific chronicle 1962–1983. Bull. Amer. Meteor. Soc., 66, 505514, https://doi.org/10.1175/1520-0477(1985)066<0505:PSASC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wood, K. M., and E. A. Ritchie, 2015: A definition for rapid weakening of North Atlantic and eastern North Pacific tropical cyclones. Geophys. Res. Lett., 42, 10 09110 097, https://doi.org/10.1002/2015GL066697.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, C.-C., H.-J. Cheng, Y. Wang, and K.-H. Chou, 2009: A numerical investigation of the eyewall evolution in a landfalling typhoon. Mon. Wea. Rev., 137, 2140, https://doi.org/10.1175/2008MWR2516.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, C.-C., S.-N. Wu, and H.-H. Wei, 2016: The role of convective heating in tropical cyclone eyewall ring evolution. J. Atmos. Sci., 73, 319330, https://doi.org/10.1175/JAS-D-15-0085.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, Y.-T., H.-C. Kuo, E. A. Hendricks, and M. S. Peng, 2013: Structural and intensity changes of concentric eyewall typhoons in the western North Pacific basin. Mon. Wea. Rev., 141, 26322648, https://doi.org/10.1175/MWR-D-12-00251.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., and W. Perrie, 2018: Effects of asymmetric secondary eyewall on tropical cyclone evolution in Hurricane Ike (2008). Geophys. Res. Lett., 45, 16761683, https://doi.org/10.1002/2017GL076988.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, K., Q. Lin, W.-C. Lee, Y. Q. Sun, and F. Zhang, 2016: Doppler radar analysis of triple eyewalls in Typhoon Usagi (2013). Bull. Amer. Meteor. Soc., 97, 2530, https://doi.org/10.1175/BAMS-D-15-00029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhou, X., and B. Wang, 2011: Mechanism of concentric eyewall replacement cycles and associated intensity change. J. Atmos. Sci., 68, 972988, https://doi.org/10.1175/2011JAS3575.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhu, Z., and P. Zhu, 2014: The role of outer rainband convection in governing the eyewall replacement cycle in numerical simulations of tropical cyclones. J. Geophys. Res. Atmos., 119, 80498072, https://doi.org/10.1002/2014JD021899.

    • Crossref
    • Search Google Scholar
    • Export Citation
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