• Adams, J., 1993: MUDPACK-2: Multigrid software for approximating elliptic partial differential equations on uniform grids with any resolution. Appl. Math. Comput., 53 , 235249.

    • Search Google Scholar
    • Export Citation
  • Arnason, G., 1958: A convergent method for solving the balance equation. J. Meteor., 15 , 220225.

  • Bishop, C. H., and A. J. Thorpe, 1994: Potential vorticity and the electrostatic analogy: Quasi-geostrophic theory. Quart. J. Roy. Meteor. Soc., 120 , 713731.

    • Search Google Scholar
    • Export Citation
  • Challa, M., and R. L. Pfeffer, 1980: Effects of eddy fluxes of angular momentum on the model hurricane development. J. Atmos. Sci., 37 , 16031618.

    • Search Google Scholar
    • Export Citation
  • Davis, C. A., 1992: Piecewise potential vorticity inversion. J. Atmos. Sci., 49 , 13971411.

  • Davis, C. A., and K. A. Emanuel, 1991: Potential vorticity diagnostics of cyclogenesis. Mon. Wea. Rev., 119 , 19291953.

  • Davis, C. A., and M. L. Weisman, 1994: Balanced dynamics of mesoscale vortices produced in simulated convective systems. J. Atmos. Sci., 51 , 20052030.

    • Search Google Scholar
    • Export Citation
  • Davis, C. A., E. D. Grell, and M. A. Shapiro, 1996: The balanced dynamical nature of a rapidly intensifying oceanic cyclone. Mon. Wea. Rev., 124 , 326.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., 1952: Slow thermally or frictionally controlled meridional circulation in a circular vortex. Astrophys. Norv., 5 , 1960.

    • Search Google Scholar
    • Export Citation
  • Franklin, J. L., S. J. Lord, S. E. Feuer, and F. D. Marks, 1993: The kinematic structure of Hurricane Gloria (1985) determined from nested analyses of dropwindsonde and Doppler radar data. Mon. Wea. Rev., 121 , 24332451.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., and F. P. Bretherton, 1972: Atmospheric frontogenesis models: Mathematical formulation and solution. J. Atmos. Sci., 29 , 1137.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111 , 877946.

    • Search Google Scholar
    • Export Citation
  • Huo, Z-H., D-L. Zhang, and J. R. Gyakum, 1999a: The interaction of potential vorticity anomalies in extratropical cyclogenesis. Part I: Static piecewise inversion. Mon. Wea. Rev., 127 , 25462561.

    • Search Google Scholar
    • Export Citation
  • Huo, Z-H., D-L. Zhang, and J. R. Gyakum, 1999b: The interaction of potential vorticity anomalies in extratropical cyclogenesis. Part II: Sensitivity to initial perturbations. Mon. Wea. Rev., 127 , 25632575.

    • Search Google Scholar
    • Export Citation
  • Krishnamurti, T. N., 1968: A diagnostic balance model for studies of weather systems of low and high latitudes, Rossby number less than 1. Mon. Wea. Rev., 96 , 197207.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., D-L. Zhang, and M. K. Yau, 1997: A multiscale numerical study of Hurricane Andrew (1992). Part I: Explicit simulation and verification. Mon. Wea. Rev., 125 , 30733093.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., D-L. Zhang, and M. K. Yau, 1999: A multiscale numerical study of Hurricane Andrew (1992). Part II: Kinematics and inner-core structures. Mon. Wea. Rev., 127 , 25972616.

    • Search Google Scholar
    • Export Citation
  • Marks, F. D., R. A. Houze, and J. F. Gamache, 1992: Dual-aircraft investigation of the inner core of Hurricane Norbert. Part I: Kinematic structure. J. Atmos. Sci., 49 , 919942.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 1985: A uniformly valid model spanning the regimes of geostrophic and isotropic, stratified turbulence: Balanced turbulence. J. Atmos. Sci., 42 , 17731774.

    • Search Google Scholar
    • Export Citation
  • Molinari, J., S. Skubis, D. Vollaro, F. Alsheimer, and H. E. Willoughby, 1998: Potential vorticity analysis of tropical cyclone intensification. J. Atmos. Sci., 55 , 26322644.

    • Search Google Scholar
    • Export Citation
  • Möller, J. D., and S. C. Jones, 1998: Potential vorticity inversion for tropical cyclones using the asymmetric balance theory. J. Atmos. Sci., 55 , 259282.

    • Search Google Scholar
    • Export Citation
  • Möller, J. D., and M. T. Montgomery, 1999: Vortex Rossby waves and hurricane intensification in a barotropic model. J. Atmos. Sci., 56 , 16741687.

    • Search Google Scholar
    • Export Citation
  • Möller, J. D., and L. J. Shapiro, 2002: Balanced contributions to the intensification of Hurricane Opal as diagnosed from a GFDL model forecast. Mon. Wea. Rev., 130 , 18661881.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and J. L. Franklin, 1998: An assessment of the balance approximation in hurricanes. J. Atmos. Sci., 55 , 21932200.

  • Olsson, P. Q., and W. R. Cotton, 1997: Balanced and unbalanced circulations in a primitive equation simulation of a midlatitude MCC. Part II: Analysis of balance. J. Atmos. Sci., 54 , 479497.

    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., 1992: Nonlinear balance and potential-vorticity thinking at large Rossby number. Quart. J. Roy. Meteor. Soc., 118 , 9871015.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Reed, R. J., M. T. Stoelinga, and Y-H. Kuo, 1992: A model-aided study of the origin and evolution of the anomalously high potential vorticity in the inner region of a rapidly deepening marine cyclone. Mon. Wea. Rev., 120 , 893913.

    • Search Google Scholar
    • Export Citation
  • Sasaki, Y. K., and J. A. McGinley, 1981: Application of the inequality constraint in adjustment of superadiabatic layers. Mon. Wea. Rev., 109 , 194196.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and B. T. Alworth, 1987: Evolution of potential vorticity in tropical cyclones. Quart. J. Roy. Meteor. Soc., 113 , 147162.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., S. A. Hausman, M. Garcia, K. V. Ooyama, and H-C. Kuo, 2001: Potential vorticity in a moist atmosphere. J. Atmos. Sci., 58 , 31483157.

    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., 1996: The motion of Hurricane Gloria: A potential vorticity diagnosis. Mon. Wea. Rev., 124 , 24972508.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., and M. T. Montgomery, 1993: A three-dimensional balance theory for rapidly rotating vortices. J. Atmos. Sci., 50 , 33223335.

    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., and J. L. Franklin, 1995: Potential vorticity in Hurricane Gloria. Mon. Wea. Rev., 123 , 14651475.

  • Shapiro, L. J., and J. L. Franklin, 1999: Potential vorticity asymmetries and tropical cyclone motion. Mon. Wea. Rev., 127 , 124131.

  • Sundqvist, H., 1970: Numerical simulation of the development of tropical cyclones with a ten-level model. Tellus, 22 , 359390.

  • Thorpe, A. J., and C. H. Bishop, 1995: Potential vorticity and the electrostatic analogy: Ertel–Rossby formulation. Quart. J. Roy. Meteor. Soc., 121 , 14771495.

    • Search Google Scholar
    • Export Citation
  • Trier, S. B., and C. A. Davis, 2002: Influence of balanced motions on heavy precipitation within a long-lived convectively generated vortex. Mon. Wea. Rev., 130 , 877899.

    • Search Google Scholar
    • Export Citation
  • Willoughby, H. E., 1979: Forced secondary circulations in hurricanes. J. Geophys. Res., 84 , 31733183.

  • Willoughby, H. E., 1990: Gradient balance in tropical cyclones. J. Atmos. Sci., 47 , 265274.

  • Wu, C-C., and K. A. Emanuel, 1995a: Potential vorticity diagnostics of hurricane movement. Part I: A case study of Hurricane Bob (1991). Mon. Wea. Rev., 123 , 6992.

    • Search Google Scholar
    • Export Citation
  • Wu, C-C., and K. A. Emanuel, 1995b: Potential vorticity diagnostics of hurricane movement. Part II: Tropical storm Ana (1991) and Hurricane Andrew (1992). Mon. Wea. Rev., 123 , 93109.

    • Search Google Scholar
    • Export Citation
  • Zhang, D-L., Y. Liu, and M. K. Yau, 2000: A multiscale numerical study of Hurricane Andrew (1992). Part III: Dynamically induced vertical motion. Mon. Wea. Rev., 128 , 37723788.

    • Search Google Scholar
    • Export Citation
  • Zhang, D-L., Y. Liu, and M. K. Yau, 2001: A multiscale numerical study of Hurricane Andrew (1992). Part IV: Unbalanced flows. Mon. Wea. Rev., 129 , 92107.

    • Search Google Scholar
    • Export Citation
  • Zhang, D-L., Y. Liu, and M. K. Yau, 2002: A multiscale numerical study of Hurricane Andrew (1992). Part V: Inner-core thermodynamics. Mon. Wea. Rev., 130 , 27452763.

    • Search Google Scholar
    • Export Citation
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Potential Vorticity Diagnosis of a Simulated Hurricane. Part I: Formulation and Quasi-Balanced Flow

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  • 1 Department of Meteorology, University of Maryland at College Park, College Park, Maryl
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Abstract

Because of the lack of three-dimensional (3D) high-resolution data and the existence of highly nonelliptic flows, few studies have been conducted to investigate the inner-core quasi-balanced characteristics of hurricanes. In this study, a potential vorticity (PV) inversion system is developed, which includes the nonconservative processes of friction, diabatic heating, and water loading. It requires hurricane flows to be statically and inertially stable but allows for the presence of small negative PV. To facilitate the PV inversion with the nonlinear balance (NLB) equation, hurricane flows are decomposed into an axisymmetric, gradient-balanced reference state and asymmetric perturbations. Meanwhile, the nonellipticity of the NLB equation is circumvented by multiplying a small parameter ε and combining it with the PV equation, which effectively reduces the influence of anticyclonic vorticity. A quasi-balanced ω equation in pseudoheight coordinates is derived, which includes the effects of friction and diabatic heating as well as differential vorticity advection and the Laplacians of thermal advection by both nondivergent and divergent winds.

This quasi-balanced PV–ω inversion system is tested with an explicit simulation of Hurricane Andrew (1992) with the finest grid size of 6 km. It is shown that (a) the PV–ω inversion system could recover almost all typical features in a hurricane, and (b) a sizeable portion of the 3D hurricane flows are quasi-balanced, such as the intense rotational winds, organized eyewall updrafts and subsidence in the eye, cyclonic inflow in the boundary layer, and upper-level anticyclonic outflow. It is found, however, that the boundary layer cyclonic inflow and upper-level anticyclonic outflow also contain significant unbalanced components. In particular, a low-level outflow jet near the top of the boundary layer is found to be highly unbalanced (and supergradient). These findings are supported by both locally calculated momentum budgets and globally inverted winds. The results indicate that this PV inversion system could be utilized as a tool to separate the unbalanced from quasi-balanced flows for studies of balanced dynamics and propagating inertial gravity waves in hurricane vortices.

Corresponding author address: Dr. Da-Lin Zhang, Department of Meteorology, University of Maryland, College Park, MD 20742. Email: dalin@atmos.umd.edu

Abstract

Because of the lack of three-dimensional (3D) high-resolution data and the existence of highly nonelliptic flows, few studies have been conducted to investigate the inner-core quasi-balanced characteristics of hurricanes. In this study, a potential vorticity (PV) inversion system is developed, which includes the nonconservative processes of friction, diabatic heating, and water loading. It requires hurricane flows to be statically and inertially stable but allows for the presence of small negative PV. To facilitate the PV inversion with the nonlinear balance (NLB) equation, hurricane flows are decomposed into an axisymmetric, gradient-balanced reference state and asymmetric perturbations. Meanwhile, the nonellipticity of the NLB equation is circumvented by multiplying a small parameter ε and combining it with the PV equation, which effectively reduces the influence of anticyclonic vorticity. A quasi-balanced ω equation in pseudoheight coordinates is derived, which includes the effects of friction and diabatic heating as well as differential vorticity advection and the Laplacians of thermal advection by both nondivergent and divergent winds.

This quasi-balanced PV–ω inversion system is tested with an explicit simulation of Hurricane Andrew (1992) with the finest grid size of 6 km. It is shown that (a) the PV–ω inversion system could recover almost all typical features in a hurricane, and (b) a sizeable portion of the 3D hurricane flows are quasi-balanced, such as the intense rotational winds, organized eyewall updrafts and subsidence in the eye, cyclonic inflow in the boundary layer, and upper-level anticyclonic outflow. It is found, however, that the boundary layer cyclonic inflow and upper-level anticyclonic outflow also contain significant unbalanced components. In particular, a low-level outflow jet near the top of the boundary layer is found to be highly unbalanced (and supergradient). These findings are supported by both locally calculated momentum budgets and globally inverted winds. The results indicate that this PV inversion system could be utilized as a tool to separate the unbalanced from quasi-balanced flows for studies of balanced dynamics and propagating inertial gravity waves in hurricane vortices.

Corresponding author address: Dr. Da-Lin Zhang, Department of Meteorology, University of Maryland, College Park, MD 20742. Email: dalin@atmos.umd.edu

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