We thank Matthew Sitkowski and Daniel Stern for helpful discussions that benefitted this work. We gratefully acknowledge Chun-Chieh Wu and two anonymous reviewers for outstanding critical reviews of this manuscript that led to significant improvements. C. Rozoff was supported by ONR Grant N00014-07-1-0163 and NOAA Grants NA06NES4400002 and NA10NES4400013. D. Nolan was supported in part by NSF Grant ATM-0756308. F. Zhang was supported by ONR Grant N000140910526, NOAA HFIP, and NSF Grant 0840651. J. Fang was supported by the Nature Science Foundation of China Grants 40921160382 and 40830958, and State Key Basic Program of China 2009CB421502. The WRF simulation was carried out at the Texas Advanced Computing Center.
Abarca, S. F., , and K. L. Corbosiero, 2011: Secondary eyewall formation in WRF simulations of hurricanes Rita and Katrina (2005). Geophys. Res. Lett., 38, L07802, doi:10.1029/2011GL047015.
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, 1715–1731.
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, 885–901.
Didlake, A. C., , and R. A. Houze, 2011: Kinematics of the secondary eyewall observed in Hurricane Rita (2005). J. Atmos. Sci., 68, 1620–1636.
Fudeyasu, H., , and Y. Wang, 2011: Balanced contribution to the intensification of a tropical cyclone simulated in TCM4: Outer-core spinup process. J. Atmos. Sci., 68, 430–449.
Hack, J. J., , and W. H. Schubert, 1986: Nonlinear response of atmospheric vortices to heating by organized cumulus convection. J. Atmos. Sci., 43, 1559–1573.
Hogsett, W., , and D.-L. Zhang, 2009: Numerical simulation of Hurricane Bonnie (1998). Part III: Energetics. J. Atmos. Sci., 66, 2678–2696.
Hong, S.-Y., , J. Dudhia, , and S.-H. Chen, 2004: A revised approach to ice microphysical processes for the parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103–120.
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. Soc., 69, 662–674.
Judt, F., , and S. S. Chen, 2010: Convectively generated potential vorticity in rainbands and formation of the secondary eyewall in Hurricane Rita of 2005. J. Atmos. Sci., 67, 3581–3599.
Kossin, J. P., , and M. Sitkowski, 2009: An objective model for identifying secondary eyewall formation in hurricanes. Mon. Wea. Rev., 137, 876–892.
Kuo, H.-C., , L.-Y. Lin, , C.-P. Chang, , and R. T. Williams, 2004: The formation of concentric vorticity structures in typhoons. J. Atmos. Sci., 61, 2722–2734.
Kuo, H.-C., , W. H. Schubert, , C.-L. Tsai, , and Y.-F. Kuo, 2008: Vortex interactions and barotropic aspects of concentric eyewall formation. Mon. Wea. Rev., 136, 5183–5198.
Maclay, K. S., , M. DeMaria, , and T. H. Vonder Haar, 2008: Tropical cyclone inner-core kinetic energy evolution. Mon. Wea. Rev., 136, 4882–4898.
Mallen, K. J., , M. T. Montgomery, , and B. Wang, 2005: Reexamining the near-core radial structure of the tropical cyclone primary circulation: Implications for vortex resiliency. J. Atmos. Sci., 62, 408–425.
Martinez, Y., , G. Brunet, , and M. K. Yau, 2010: On the dynamics of two-dimensional hurricane-like concentric rings vortex formation. J. Atmos. Sci., 67, 3253–3268.
Martinez, Y., , G. Brunet, , M. K. Yau, , and X. Wang, 2011: On the dynamics of concentric eyewall genesis: Space–time empirical normal modes diagnosis. J. Atmos. Sci., 68, 457–476.
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, 435–465.
Moon, Y., , and D. S. Nolan, 2010: The dynamic response of the hurricane wind field to spiral rainband heating. J. Atmos. Sci., 67, 1779–1805.
Moon, Y., , D. S. Nolan, , and M. Iskandarani, 2010: On the use of two-dimensional incompressible flow to study secondary eyewall formation in tropical cyclones. J. Atmos. Sci., 67, 3765–3773.
Noh, Y., , W.-G. Cheon, , S.-Y. Hong, , and S. Raasch, 2003: Improvement of the K-profile model for the planetary boundary layer based on large eddy simulation data. Bound.-Layer Meteor., 107, 401–427.
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, 2989–3020.
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, 2717–2745.
Nolan, D. S., , Y. Moon, , and D. P. Stern, 2007: Tropical cyclone intensification from asymmetric convection: Energetics and efficiency. J. Atmos. Sci., 64, 3377–3405.
Nong, S., , and K. Emanuel, 2003: A numerical study of the genesis of concentric eyewalls in hurricanes. Quart. J. Roy. Meteor. Soc., 129, 3323–3338.
Qiu, X., , Z.-M. Tan, , and Q. Xiao, 2010: The roles of vortex Rossby waves in hurricane secondary eyewall formation. Mon. Wea. Rev., 138, 2092–2109.
Ritchie, E. A., , and W. M. Frank, 2007: Interactions between simulated tropical cyclones and an environment with a variable Coriolis parameter. Mon. Wea. Rev., 135, 1889–1905.
Rotunno, R., , and K. A. Emanuel, 1987: An air–sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axisymmetric numerical model. J. Atmos. Sci., 44, 542–561.
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, 583–593.
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, 595–605.
Shapiro, L. J., , and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci., 39, 378–394.
Sitkowski, M., , J. P. Kossin, , and C. M. Rozoff, 2011: Intensity and structure changes during hurricane eyewall replacement cycles. Mon. Wea. Rev., 139, 3829–3847.
Sitkowski, M., , J. P. Kossin, , C. M. Rozoff, , and J. Knaff, 2012: Hurricane eyewall replacement cycle thermodynamics and the relict inner eyewall circulation. Mon. Wea. Rev., in press.
Skamarock, W. C., , J. B. Klemp, , J. Dudhia, , D. O. Gill, , D. M. Barker, , W. Wang, , and J. G. Powers, 2005: A description of the Advanced Research WRF Version 2. NCAR Tech. Note NCAR/TN-468+ST, 88 pp.
Smith, R. K., , M. T. Montgomery, , and S. Vogl, 2008: A critique of Emanuel’s hurricane model and potential intensity theory. Quart. J. Roy. Meteor. Soc., 134, 551–561.
Terwey, W. D., , and M. T. Montgomery, 2008: Secondary eyewall formation in two idealized, full-physics modeled hurricanes. J. Geophys. Res., 113, D12112, doi:10.1029/2007JD008897.
Wang, Y., 2008b: Structure and formation of an annular hurricane simulated in a fully compressible, nonhydrostatic model—TCM4. J. Atmos. Sci., 65, 1505–1527.
Willoughby, H. E., , J. A. Clos, , and M. G. Shoreibah, 1982: Concentric eyewalls, secondary wind maxima, and the evolution of the hurricane vortex. J. Atmos. Sci., 39, 395–411.
Wu, C.-C., , H.-J. Cheng, , Y. Wang, , and K.-H. Chou, 2009: A numerical investigation of the eyewall evolution of a landfalling typhoon. Mon. Wea. Rev., 137, 21–40.
Wu, C.-C., , Y.-H. Huang, , and G.-Y. Lien, 2012: Concentric eyewall formation in Typhoon Sinlaku (2008). Part I: Assimilation of T-PARC data based on the ensemble Kalman filter (EnKF). Mon. Wea. Rev., 140, 506–527.
Xu, J., , and Y. Wang, 2010a: Sensitivity of tropical cyclone inner core size and intensity to the radial distribution of surface entropy flux. J. Atmos. Sci., 67, 1831–1852.
Xu, J., , and Y. Wang, 2010b: Sensitivity of the simulated tropical cyclone inner-core size to the initial vortex size. Mon. Wea. Rev., 138, 4135–4157.
Zhang, Q.-H., , Y.-H. Kuo, , and S.-J. Chen, 2005: Interaction between concentric eye-walls in super typhoon Winnie (1997). Quart. J. Roy. Meteor. Soc., 131, 3183–3204.
Zhou, X., , and B. Wang, 2011: Mechanism of concentric eyewall replacement cycles and associated intensity changes. J. Atmos. Sci., 68, 972–988.
It should be noted that (1) and (2) use ground-relative wind speeds. The storm, on average, moves toward the northwest at 1.8 m s−1 due to the β effect, but a budget for storm-relative winds produces virtually identical results and is therefore not included.
Experimentation of time intervals between 1 and 6 h for the time integration of q and for ΔKE and time lags of 1–6 h between Q and ΔKE yielded similar results.