The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part II: Nonlinear Enhancement

Jeff Kepert Bureau of Meteorology Research Centre, Melbourne, Victoria, Australia

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Yuqing Wang School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii

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Abstract

Observations of wind profiles within the tropical cyclone boundary layer until recently have been quite rare. However, the recent spate of observations from the GPS dropsonde have confirmed that a low-level wind speed maximum is a common feature of the tropical cyclone boundary layer. In Part I, a mechanism for producing such a maximum was proposed, whereby strong inward advection of angular momentum generates the supergradient flow. The processes that maintain the necessary inflow against the outward acceleration due to gradient wind imbalance were identified as being (i) vertical diffusion, (ii) vertical advection, and (iii) horizontal advection, and a linear analytical model of the boundary layer flow in a translating tropical cyclone was presented and used to diagnose the properties of the jet and the near-surface flow. A significant shortcoming was that the jet was too weak, which was argued to be due to the neglect of vertical advection. Here, a high-resolution, dry, hydrostatic, numerical model using the full primitive equations and driven by an imposed pressure gradient representative of a tropical cyclone is presented. It relaxes the constraint of linearity from Part I, includes the full advection terms, and produces a markedly stronger jet, more consistent with the observations. It is shown that the vertical advection of inflow is of major importance in jet dynamics, and that its neglect was the main reason that the linear model produced too weak a jet.

It is shown that the jet in a stationary storm is between 10% and 25% supergradient, depending on the particular characteristics of the storm. The height scale (2K/I)1/2, where K is the turbulent diffusivity and I the inertial stability, obtained in Part I, is shown to fit the numerical model results well. This is typically several hundreds of meters in the cyclone core, and increases with radius. In the case of a moving Northern Hemisphere storm, it is found that the jet is most supergradient—several times stronger than in a stationary storm—at the eyewall to the left and front of the storm, as well as extending into a significant area around to the left of the storm. It is, however, much less marked to the right, where the strongest winds are found. This asymmetry is in good agreement with that found in Part I, and is dominated by the wavenumber 1 response forced by the asymmetric friction.

The factor for reducing upper winds to a near-surface equivalent, which is frequently used in operational work, is shown to have a substantial spatial variability. Larger values are found near the eye, due to the symmetric component of the solution. There is also an overall increase from right to left of the storm in the Northern Hemisphere, again consistent with the results in Part I.

Corresponding author address: Dr. Jeff D. Kepert, Bureau of Meteorology Research Centre, GPO Box 1289K, Melbourne, Vic 3001, Australia. Email: j.kepert@bom.gov.au

Abstract

Observations of wind profiles within the tropical cyclone boundary layer until recently have been quite rare. However, the recent spate of observations from the GPS dropsonde have confirmed that a low-level wind speed maximum is a common feature of the tropical cyclone boundary layer. In Part I, a mechanism for producing such a maximum was proposed, whereby strong inward advection of angular momentum generates the supergradient flow. The processes that maintain the necessary inflow against the outward acceleration due to gradient wind imbalance were identified as being (i) vertical diffusion, (ii) vertical advection, and (iii) horizontal advection, and a linear analytical model of the boundary layer flow in a translating tropical cyclone was presented and used to diagnose the properties of the jet and the near-surface flow. A significant shortcoming was that the jet was too weak, which was argued to be due to the neglect of vertical advection. Here, a high-resolution, dry, hydrostatic, numerical model using the full primitive equations and driven by an imposed pressure gradient representative of a tropical cyclone is presented. It relaxes the constraint of linearity from Part I, includes the full advection terms, and produces a markedly stronger jet, more consistent with the observations. It is shown that the vertical advection of inflow is of major importance in jet dynamics, and that its neglect was the main reason that the linear model produced too weak a jet.

It is shown that the jet in a stationary storm is between 10% and 25% supergradient, depending on the particular characteristics of the storm. The height scale (2K/I)1/2, where K is the turbulent diffusivity and I the inertial stability, obtained in Part I, is shown to fit the numerical model results well. This is typically several hundreds of meters in the cyclone core, and increases with radius. In the case of a moving Northern Hemisphere storm, it is found that the jet is most supergradient—several times stronger than in a stationary storm—at the eyewall to the left and front of the storm, as well as extending into a significant area around to the left of the storm. It is, however, much less marked to the right, where the strongest winds are found. This asymmetry is in good agreement with that found in Part I, and is dominated by the wavenumber 1 response forced by the asymmetric friction.

The factor for reducing upper winds to a near-surface equivalent, which is frequently used in operational work, is shown to have a substantial spatial variability. Larger values are found near the eye, due to the symmetric component of the solution. There is also an overall increase from right to left of the storm in the Northern Hemisphere, again consistent with the results in Part I.

Corresponding author address: Dr. Jeff D. Kepert, Bureau of Meteorology Research Centre, GPO Box 1289K, Melbourne, Vic 3001, Australia. Email: j.kepert@bom.gov.au

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  • Barnes, G. M., and M. D. Powell, 1995: Evolution of the inflow boundary layer of Hurricane Gilbert (1988). Mon. Wea. Rev, 123 , 23482368.

    • Search Google Scholar
    • Export Citation
  • Black, P. G., and G. J. Holland, 1995: The boundary layer of tropical cyclone Kerry (1979). Mon. Wea. Rev, 123 , 20072028.

  • Black, P. G., G. J. Holland, and V. Pudov, 1993: Observations of air–sea temperature difference in tropical cyclones as a function of wind speed. Extended Abstracts, Fifth BMRC Modelling Workshop: Parameterisation of Physical Processes, Melbourne, Australia, Bureau of Meteorology Research Centre, 87–88. [Available as Res. Rep. 46 from Bureau of Meteorology Research Centre, GPO Box 1289K, Melbourne, Victoria 3001, Australia.].

    • Search Google Scholar
    • Export Citation
  • Charnock, H., 1955: Wind stress on a water surface. Quart. J. Roy. Meteor. Soc, 81 , 443447.

  • Cione, J. J., P. J. Black, and S. H. Huston, 2000: Surface observations in the hurricane environment. Mon. Wea. Rev, 128 , 15501561.

  • Clarke, R. H., A. J. Dyer, R. R. Brook, D. G. Reid, and A. J. Troup, 1971: The Wangara experiment: Boundary layer data. Tech. Paper 19, CSIRO Atmospheric Research, Aspendale, Australia. 362 pp.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, 1996: Bulk parameterisation of air–sea fluxes for Tropical Ocean–Global Atmosphere Coupled Ocean Atmosphere Response Experiment. J. Geophys. Res, 101 , (C),. 37473764.

    • Search Google Scholar
    • Export Citation
  • Galperin, B., L. H. Kantha, S. Hassid, and A. Rosati, 1988: A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci, 45 , 5562.

    • Search Google Scholar
    • Export Citation
  • Gerrity, J. P., T. L. Black, and R. E. Treadon, 1994: The numerical solution of the Mellor–Yamada level 2.5 turbulent kinetic energy equation in the Eta model. Mon. Wea. Rev, 122 , 16401646.

    • Search Google Scholar
    • Export Citation
  • Grell, G. A., J. Dudhia, and D. R. Stauffer, 1994: A description of the Fifth-Generation Penn State/NCAR Mesoscale Model (MM5). NCAR/TN-398+STR, National Center for Atmospheric Research, Boulder, CO, 107 pp.

    • Search Google Scholar
    • Export Citation
  • Helfand, H. M., and J. C. LaBraga, 1988: Design of a nonsingular level 2.5 second order closure model for the prediction of atmospheric turbulence. J. Atmos. Sci, 45 , 113132.

    • Search Google Scholar
    • Export Citation
  • Hock, T. F., and J. L. Franklin, 1999: The NCAR GPS dropwindsonde. Bull. Amer. Meteor. Soc, 80 , 407420.

  • Holland, G. J., 1980: An analytic model of the wind and pressure profiles in hurricanes. Mon. Wea. Rev, 108 , 12121218.

  • Holland, G. J., T. McGeer, and H. Youngren, 1992: Autonomous aerosondes for economical atmospheric soundings anywhere on the globe. Bull. Amer. Meteor. Soc, 73 , 19871998.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and M. Kanamitsu, 1988: Time schemes for strongly nonlinear damping equations. Mon. Wea. Rev, 116 , 19451958.

  • Kepert, J. D., 2001: The dynamics of boundary layer jets within the tropical cyclone core. Part I: Linear theory. J. Atmos. Sci, 58 , 24692484.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., and G. J. Holland, 1997: The North West Cape tropical cyclone boundary layer monitoring station. Preprints, 22d Conf. on Hurricanes and Tropical Meteorology, Fort Collins, CO, Amer. Meteor. Soc., 82–83.

    • Search Google Scholar
    • Export Citation
  • Korolev, V. S., S. A. Petrichenko, and V. D. Pudov, 1990: Heat and moisture exchange between the ocean and atmosphere in tropical storms Tess and Skip. Meteor. Gidrol, 2 , 108111. (English translation in Sov. Meteor. Hydrol., 2, 92–94).

    • Search Google Scholar
    • Export Citation
  • Liu, W. T., K. B. Katsaros, and J. A. Businger, 1979: Bulk parameterization of the air–sea exchanges of heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci, 36 , 17221735.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and T. Yamada, 1974: A heirarchy of turbulent closure models for planetary boundary layers. J. Atmos. Sci, 31 , 17911806.

    • Search Google Scholar
    • Export Citation
  • Moss, M. S., and F. J. Merceret, 1976: A note on several low-level features of Hurricane Eloise (1975). Mon. Wea. Rev, 104 , 967971.

  • Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys, 21 , 251269.

  • Powell, M. D., 1990a: Boundary layer structure and dynamics in outer hurricane rainbands. Part I: Mesoscale rainfall and kinematic structure. Mon. Wea. Rev, 118 , 891917.

    • Search Google Scholar
    • Export Citation
  • Powell, M. D., 1990b: Boundary layer structure and dynamics in outer hurricane rainbands. Part I: Downdraft modification and mixed layer recovery. Mon. Wea. Rev, 118 , 918938.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., M. T. Montgomery, R. K. Taft, T. A. Guinn, S. R. Fulton, P. Kossin, and J. P. Edwards, 1999: Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes. J. Atmos. Sci, 56 , 11971223.

    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., 1983: The asymmetric boundary layer under a translating hurricane. J. Atmos. Sci, 40 , 19841998.

  • Smagorinsky, J., S. Manabe, and J. L. Holloway Jr., . 1965: Numerical results from a nine-level general circulation model of the atmosphere. Mon. Wea. Rev, 93 , 727768.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., 1968: The surface boundary layer of a hurricane. Tellus, 20 , 473483.

  • Smith, S. D., 1988: Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. J. Geophys. Res, 93 , 1546715472.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., 1996: On the forward-in-time upstream advection scheme for non-uniform and time-dependent flow. Meteor. Atmos. Phys, 61 , 2738.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., 1998: On the bogussing of tropical cyclones in numerical models: The influence of vertical structure. Meteor. Atmos. Phys, 65 , 153170.

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

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