On the structure and stability of the hurricane eyewall

References

• Anthes, R. A. 1974. The dynamics and energetics of mature tropical cyclones. Rev. Geophys. 12, 495–522.
   Web of Science ®Google Scholar
• Black, M. L. and Willoughby, H. E. 1992. The concentric eyewall cycle of hurricane Gilbert. Mon. Wea. Rev. 120, 947–957. doi:10.1175/1520-0493(1992)120<0947:TCECOH>2.0.CO;2.
   Web of Science ®Google Scholar
• Bryan, G. H., and Rotunno, R. 2009. Evaluation of an analytical model for the maximum intensity of hurricanes. J. Atmos. Sci. 66, 3042–3060. doi:10.1175/2009JAS3038.1.
   Web of Science ®Google Scholar
• Buizza, R. 1994. Sensitivity of optimal unstable structures. Quart. J. Roy. Meteorol Soc. 120, 429–451. doi:10.1002/qj.49712051609.
   Web of Science ®Google Scholar
• Carrier, G. F., Hammond, A. L., and George, O. D. 1971. A model of the mature hurricane. J. Fluid Mech. 47, 145–170. doi:10.1017/S0022112071000983.
   Web of Science ®Google Scholar
• Chandrasekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability. Dover Publications Inc., 652 p.
   Google Scholar
• Depperman, C. E. 1947. Notes on the origin and structures of Philippine typhoons. Bull. Amer. Meteor. Soc. 28, 399–404.
   Google Scholar
• Elliott, L. 1973. Stability of a viscous fluid between rotating cylinders with axial flow and pressure gradient round the cylinders. Phys. Fluids 16, 577–580. doi:10.1063/1.1694390.
   Web of Science ®Google Scholar
• Emanuel, K. A. 1986. An air-sea interaction theory for hurricanes. Part I: steady state maintenance. J. Atmos. Sci. 43, 585–605. doi:10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.
   Web of Science ®Google Scholar
• Emanuel, K. A. 1988. The maximum intensity of hurricanes. J. Atmos. Sci. 45, 1143–1155. doi:10.1175/1520-0469(1988)045<1143:TMIOH>2.0.CO;2.
   Web of Science ®Google Scholar
• Emanuel, K. A. 1995. Sensitivity of hurricanes to surface exchange coefficients and a revised steady-state model incorporating eye dynamics. J. Atmos. Sci. 52, 3969–3976. doi:10.1175/1520-0469(1995)052<3969:SOTCTS>2.0.CO;2.
   Web of Science ®Google Scholar
• Hakim, G. J. 2011. The mean state of axisymmetric hurricanes in statistical equilibrium. J. Atmos. Sci. 68, 1364–1376. doi:10.1175/2010JAS3644.1.
   Web of Science ®Google Scholar
• Haltiner, G. J., and Williams, R. T. 1980. Numerical Prediction and Dynamic Meteorology. 2nd ed. Wiley Publisher, 496 pp.
   Google Scholar
• Hazelton, A. T., Rogers, R., and Hart, R. E. 2015. Shear-relative asymmetries in tropical cyclone eyewall slope. Mon. Wea. Rev. 143, 883–903. doi:10.1175/MWR-D-14-00122.1.
   Web of Science ®Google Scholar
• Holland, G. 1980. An analytic model of the wind and pressureprofiles in hurricanes. Mon. Wea. Rev. 108, 1212–1218. doi:10.1175/1520-0493(1980)108<1212:AAMOTW>2.0.CO;2.
   Web of Science ®Google Scholar
• Holton, J. A. 2004. An Introduction to Dynamic Meteorology Vol. 88, 4th ed. Academic Press, New York, p. 535.
   Google Scholar
• Joseph, D. D. 1965. On the stability of Boussinesq equations. Arch. Rational Mech. Anal. 20, 59–71. doi:10.1007/BF00250190.
   Google Scholar
• Kelvin, L. 1880. Vibrations of a columnar vortexn. Phil. Mag. 10, 155–168.
   Google Scholar
• Kieu, C. 2015. Hurricane maximum potential intensity equilibrium. Quart. J. Roy. Meteorol Soc. 141, 2471–2480. doi:10.1002/qj.2556.
   Web of Science ®Google Scholar
• Kieu, C., and Wang, Q. 2017a. On the scale dynamics of the tropical cyclone intensity. Dcds-B. 22, 44–54. doi:10.3934/dcdsb.2017196.
   Google Scholar
• Kieu, C., and Wang, Q. 2017b. Stability of the tropical cyclone intensity equilibrium. J. Atmos. Sci. 74, 3591–3608. doi:10.1175/JAS-D-17-0028.1.
   Web of Science ®Google Scholar
• Kieu, C., and Zhang, D.-L. 2009. An analytical model for the rapid intensification of tropical cyclones. Quart. J. Roy. Meteorol Soc. 135, 1336–1349. doi:10.1002/qj.433.
   Web of Science ®Google Scholar
• Kieu, C., and Zhang, D.-L. 2010. On the consistency between dynamical and thermodynamic equations with prescribed vertical motion in an analytical tropical cyclone model. Quart. J. Roy. Meteorol Soc. 136, 1927–1930. doi:10.1002/qj.671.
   Web of Science ®Google Scholar
• Liu, Y., Zhang, D.-L., and Yau, M. K. 1997. A multiscale numerical study of Hurricane Andrew (1992). Part I: explicit simulation and verification. Mon. Wea. Rev. 125, 3073–3093. doi:10.1175/1520-0493(1997)125<3073:AMNSOH>2.0.CO;2.
   Web of Science ®Google Scholar
• Malkus, J. S., and Riehl, H. 1960. On the dynamics and energy transformation in steady-state hurricanes. Tellus 12, 1–20.
   Google Scholar
• Marks, F. D., Black, P. G., Montgomery, M. T., and Burpee, R. W. 2008. Structure of the eye and eyewall of hurricane Hugo (1989). Mon. Wea. Rev. 136, 1237–1259. doi:10.1175/2007MWR2073.1.
   Web of Science ®Google Scholar
• McNoldy, B. D. 2004. Triple eyewall in hurricane Juliette. Bull. Amer. Meteor. Soc. 85, 1663–1666. doi:10.1175/BAMS-85-11-1663.
   Web of Science ®Google Scholar
• Miller, M. J. 1974. On the use of pressure as vertical co-ordinate in modelling convection. Quart. J. Roy. Meteorol Soc. 100, 155–162. doi:10.1002/qj.49710042403.
   Web of Science ®Google Scholar
• Miller, M. J., and White, A. A. 1984. On the use of pressure as vertical co-ordinate in modelling convection. Quart. J. Roy. Meteorol Soc. 110, 515–533. doi:10.1002/qj.49711046413.
   Web of Science ®Google Scholar
• Ogura, Y., and Phillips, N. A. 1962. Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci. 19, 173–179. doi:10.1175/1520-0469(1962)019<0173:SAODAS>2.0.CO;2.
   Web of Science ®Google Scholar
• Riehl, H. 1963. Same relationship between wind and thermal structure of steady-state hurricanes. J. Atmos. Sci. 20, 276–287. doi:10.1175/1520-0469(1963)020<0276:SRBWAT>2.0.CO;2.
   Web of Science ®Google Scholar
• Rozoff, C. M., Schubert, W. H., and Kossin, J. P. 2008. Some dynamical aspects of tropical cyclone concentric eyewalls. Quart. J. Roy. Meteorol Soc. 134, 583–593. doi:10.1002/qj.237.
   Web of Science ®Google Scholar
• Schonemann, D., and Frisius, T. 2012. Dynamical system analysis of a low-order tropical cyclone model. Tellus A 64, 15817. doi:10.3402/tellusa.v64i0.15817.
   Google Scholar
• Schubert, W. H., and Hack, J. J. 1982. Inertial stability and tropical cyclone development. J. Atmos. Sci. 39, 1687–1697. doi:10.1175/1520-0469(1982)039<1687:ISATCD>2.0.CO;2.
   Web of Science ®Google Scholar
• Schubert, W. H., Rozoff, C. M., Vigh, J. L., McNoldy, B. D., and Kossin, J. P. 2007. On the distribution of subsidence in the hurricane eye. Quart. J. Roy. Meteorol Soc. 133, 595–605. doi:10.1002/qj.49.
   Web of Science ®Google Scholar
• Serrin, J. 1959. On the stability of viscous fluid motions. Arch. Rational Mech. Anal. 3, 1–13. doi:10.1007/BF00284160.
   Web of Science ®Google Scholar
• Sitkowski, M., Kossin, J. P., and Rozoff, C. M. 2011. Intensity and structure changes during hurricane eyewall replacement cycles. Mon. Wea. Rev. 139, 3829–3847. doi:10.1175/MWR-D-11-00034.1.
   Web of Science ®Google Scholar
• Straughan, B. 2004. The Energy Method, Stability, and Nonlinear Convection. Applied Mathematical Sciences, vol. 91. 2nd ed. Springer-Verlag, New York.
   Google Scholar
• Sun, L. 2011. A typhoon-like vortex solution of incompressible 3D inviscid flow. Theor. Appl. Mech. Lett. 1, 042003. doi:10.1063/2.1104203.
   Google Scholar
• Wang, C. Y. 1991. Exact solutions of the steady-state Navier–Stokes equations. Annu. Rev. Fluid Mech. 23, 159–177. doi:10.1146/annurev.fl.23.010191.001111.
   Web of Science ®Google Scholar
• Wilhelmson, R., and Ogura, Y. 1972. The pressure perturbation and the numerical modeling of a cloud. J. Atmos. Sci. 29, 1295–1307. doi:10.1175/1520-0469(1972)029<1295:TPPATN>2.0.CO;2.
   Web of Science ®Google Scholar
• Willoughby, H. E. 1979. Forced secondary circulations in hurricanes. J. Geophys. Res. 84, 3173–3183.
   Web of Science ®Google Scholar
• Wirth, V., and Dunkerton, T. J. 2006. A unified perspective on the dynamics of axisymmetric hurricanes and monsoons. J. Atmos. Sci. 63, 2529–2547. doi:10.1175/JAS3763.1.
   Web of Science ®Google Scholar
• Wu, J. Z., Ma, H. Y., and Zhou, M. D. 2006. Vorticity and Vortex Dynamics. 1st ed. Springer-Verlag, Berlin Heidelberg, pp. 776.
   Google Scholar
• Zhang, D.-L., and Kieu, C. Q. 2006. Potential vorticity diagnosis of a simulated hurricane. Part II: quasi-balanced contributions to forced secondary circulations. J. Atmos. Sci. 63, 2898–2914. doi:10.1175/JAS3790.1.
   Web of Science ®Google Scholar
• Zhou, X., Wang, B., Ge, X., and Li, T. 2011. Impact of secondary eyewall heating on tropical cyclone intensity change. J. Atmos. Sci. 68, 450–456. doi:10.1175/2010JAS3624.1.
   Web of Science ®Google Scholar