The Role of Turbulence in an Intense Tropical Cyclone: Momentum Diffusion, Eddy Viscosities, and Mixing Lengths

Chibueze N. Oguejiofor aUniversity of Notre Dame, South Bend, Indiana

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George H. Bryan bNSF National Center for Atmospheric Research, Boulder, Colorado

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Richard Rotunno bNSF National Center for Atmospheric Research, Boulder, Colorado

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Peter P. Sullivan bNSF National Center for Atmospheric Research, Boulder, Colorado

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David H. Richter aUniversity of Notre Dame, South Bend, Indiana

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Abstract

Improved representation of turbulent processes in numerical models of tropical cyclones (TCs) is expected to improve intensity forecasts. To this end, the authors use a large-eddy simulation (with 31-m horizontal grid spacing) of an idealized category 5 TC to understand the role of turbulent processes in the inner core of TCs and their role on the mean intensity. Azimuthally and temporally averaged budgets of the momentum fields show that TC turbulence acts to weaken the maximum tangential velocity, diminish the strength of radial inflow into the eye, and suppress the magnitude of the mean eyewall updraft. Turbulent flux divergences in both the vertical and radial directions are shown to influence the TC mean wind field, with the vertical being dominant in most of the inflowing boundary layer and the eyewall (analogous to traditional atmospheric boundary layer flows), while the radial becomes important only in the eyewall. The validity of the downgradient eddy viscosity hypothesis is largely confirmed for mean velocity fields, except in narrow regions which generally correspond to weak gradients of the mean fields, as well as a narrow region in the eye. This study also provides guidance for values of effective eddy viscosities and vertical mixing length in the most turbulent regions of intense TCs, which have rarely been measured observationally. A generalized formulation of effective eddy viscosity (including the Reynolds normal stresses) is presented.

Significance Statement

This study uses a turbulence-resolving simulation of a category 5 tropical cyclone to understand the role of turbulence in intense storms. Results show that turbulence clearly modulates storm structure and intensity. This study provides guidance for the values of turbulent quantities (which are usually parameterized in comparatively coarse operational TC forecast models) in scarcely observed regions of intense storms. Furthermore, a complete formulation of the effective eddy viscosities is proposed, incorporating contributions from typically ignored Reynolds normal stress terms.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Chibueze N. Oguejiofor, coguejio@nd.edu

Abstract

Improved representation of turbulent processes in numerical models of tropical cyclones (TCs) is expected to improve intensity forecasts. To this end, the authors use a large-eddy simulation (with 31-m horizontal grid spacing) of an idealized category 5 TC to understand the role of turbulent processes in the inner core of TCs and their role on the mean intensity. Azimuthally and temporally averaged budgets of the momentum fields show that TC turbulence acts to weaken the maximum tangential velocity, diminish the strength of radial inflow into the eye, and suppress the magnitude of the mean eyewall updraft. Turbulent flux divergences in both the vertical and radial directions are shown to influence the TC mean wind field, with the vertical being dominant in most of the inflowing boundary layer and the eyewall (analogous to traditional atmospheric boundary layer flows), while the radial becomes important only in the eyewall. The validity of the downgradient eddy viscosity hypothesis is largely confirmed for mean velocity fields, except in narrow regions which generally correspond to weak gradients of the mean fields, as well as a narrow region in the eye. This study also provides guidance for values of effective eddy viscosities and vertical mixing length in the most turbulent regions of intense TCs, which have rarely been measured observationally. A generalized formulation of effective eddy viscosity (including the Reynolds normal stresses) is presented.

Significance Statement

This study uses a turbulence-resolving simulation of a category 5 tropical cyclone to understand the role of turbulence in intense storms. Results show that turbulence clearly modulates storm structure and intensity. This study provides guidance for the values of turbulent quantities (which are usually parameterized in comparatively coarse operational TC forecast models) in scarcely observed regions of intense storms. Furthermore, a complete formulation of the effective eddy viscosities is proposed, incorporating contributions from typically ignored Reynolds normal stress terms.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Chibueze N. Oguejiofor, coguejio@nd.edu

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  • Aberson, S. D., M. L. Black, R. A. Black, R. W. Burpee, J. J. Cione, C. W. Landsea, and F. D. Marks Jr., 2006a: Thirty years of tropical cyclone research with the NOAA P-3 aircraft. Bull. Amer. Meteor. Soc., 87, 10391056, https://doi.org/10.1175/BAMS-87-8-1039.

    • Search Google Scholar
    • Export Citation
  • Aberson, S. D., M. T. Montgomery, M. Bell, and M. Black, 2006b: Hurricane Isabel (2003): New insights into the physics of intense storms. Part II: Extreme localized wind. Bull. Amer. Meteor. Soc., 87, 13491354, https://doi.org/10.1175/BAMS-87-10-1349.

    • Search Google Scholar
    • Export Citation
  • Aberson, S. D., J. A. Zhang, and K. N. Ocasio, 2017: An extreme event in the eyewall of Hurricane Felix on 2 September 2007. Mon. Wea. Rev., 145, 20832092, https://doi.org/10.1175/MWR-D-16-0364.1.

    • Search Google Scholar
    • Export Citation
  • Ahern, K., M. A. Bourassa, R. E. Hart, J. A. Zhang, and R. F. Rogers, 2019: Observed kinematic and thermodynamic structure in the hurricane boundary layer during intensity change. Mon. Wea. Rev., 147, 27652785, https://doi.org/10.1175/MWR-D-18-0380.1.

    • Search Google Scholar
    • Export Citation
  • Aksoy, A., J. J. Cione, B. A. Dahl, and P. D. Reasor, 2022: Tropical cyclone data assimilation with Coyote uncrewed aircraft system observations, very frequent cycling, and a new online quality control technique. Mon. Wea. Rev., 150, 797820, https://doi.org/10.1175/MWR-D-21-0124.1.

    • Search Google Scholar
    • Export Citation
  • Alford, A. A., M. I. Biggerstaff, and G. Carrie, 2023: Using ground-based radar observations to evaluate asymmetric convection and eyewall dynamics during the landfall of Hurricane Harvey (2017). J. Atmos. Sci., 80, 18671889, https://doi.org/10.1175/JAS-D-22-0053.1.

    • Search Google Scholar
    • Export Citation
  • Anthes, R. A., 1974: The dynamics and energetics of mature tropical cyclones. Rev. Geophys., 12, 495522, https://doi.org/10.1029/RG012i003p00495.

    • Search Google Scholar
    • Export Citation
  • Biswas, G., and V. Eswaran, 2002: Turbulent Flows: Fundamentals, Experiments and Modeling. CRC Press, 456 pp.

  • Black, P. G., and Coauthors, 2007: Air–sea exchange in hurricanes: Synthesis of observations from the coupled boundary layer air–sea transfer experiment. Bull. Amer. Meteor. Soc., 88, 357374, https://doi.org/10.1175/BAMS-88-3-357.

    • Search Google Scholar
    • Export Citation
  • Blackadar, A. K., 1962: The vertical distribution of wind and turbulent exchange in a neutral atmosphere. J. Geophys. Res., 67, 30953102, https://doi.org/10.1029/JZ067i008p03095.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., 2012: Effects of surface exchange coefficients and turbulence length scales on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 140, 11251143, https://doi.org/10.1175/MWR-D-11-00231.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and J. M. Fritsch, 2002: A benchmark simulation for moist nonhydrostatic numerical models. Mon. Wea. Rev., 130, 29172928, https://doi.org/10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and R. Rotunno, 2009: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Mon. Wea. Rev., 137, 17701789, https://doi.org/10.1175/2008MWR2709.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., N. A. Dahl, D. S. Nolan, and R. Rotunno, 2017a: An eddy injection method for large-eddy simulations of tornado-like vortices. Mon. Wea. Rev., 145, 19371961, https://doi.org/10.1175/MWR-D-16-0339.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., R. P. Worsnop, J. K. Lundquist, and J. A. Zhang, 2017b: A simple method for simulating wind profiles in the boundary layer of tropical cyclones. Bound.-Layer Meteor., 162, 475502, https://doi.org/10.1007/s10546-016-0207-0.

    • Search Google Scholar
    • Export Citation
  • Byrne, D., and J. A. Zhang, 2013: Height-dependent transition from 3-D to 2-D turbulence in the hurricane boundary layer. Geophys. Res. Lett., 40, 14391442, https://doi.org/10.1002/grl.50335.

    • Search Google Scholar
    • Export Citation
  • Cangialosi, J. P., E. Blake, M. DeMaria, A. Penny, A. Latto, E. Rappaport, and V. Tallapragada, 2020: Recent progress in tropical cyclone intensity forecasting at the National Hurricane Center. Wea. Forecasting, 35, 19131922, https://doi.org/10.1175/WAF-D-20-0059.1.

    • Search Google Scholar
    • Export Citation
  • Cécé, R., and Coauthors, 2021: A 30 m scale modeling of extreme gusts during Hurricane Irma (2017) landfall on very small mountainous islands in the Lesser Antilles. Nat. Hazards Earth Syst. Sci., 21, 129145, https://doi.org/10.5194/nhess-21-129-2021.

    • Search Google Scholar
    • Export Citation
  • Chen, X., 2022: How do planetary boundary layer schemes perform in hurricane conditions: A comparison with large-eddy simulations. J. Adv. Model. Earth Syst., 14, e2022MS003088, https://doi.org/10.1029/2022MS003088.

    • Search Google Scholar
    • Export Citation
  • Chen, X., and F. D. Marks, 2024: Parameterizations of boundary layer mass fluxes in high-wind conditions for tropical cyclone simulations. J. Atmos. Sci., 81, 7791, https://doi.org/10.1175/JAS-D-23-0086.1.

    • Search Google Scholar
    • Export Citation
  • Chen, X., G. H. Bryan, J. A. Zhang, J. J. Cione, and F. D. Marks, 2021: A framework for simulating the tropical cyclone boundary layer using large-eddy simulation and its use in evaluating PBL parameterizations. J. Atmos. Sci., 78, 35593574, https://doi.org/10.1175/JAS-D-20-0227.1.

    • Search Google Scholar
    • Export Citation
  • Cione, J. J., E. Kalina, E. Uhlhorn, A. Farber, and B. Damiano, 2016: Coyote unmanned aircraft system observations in Hurricane Edouard (2014). Earth Space Sci., 3, 370380, https://doi.org/10.1002/2016EA000187.

    • Search Google Scholar
    • Export Citation
  • Cione, J. J., and Coauthors, 2020: Eye of the storm: Observing hurricanes with a small unmanned aircraft system. Bull. Amer. Meteor. Soc., 101, E186E205, https://doi.org/10.1175/BAMS-D-19-0169.1.

    • Search Google Scholar
    • Export Citation
  • Darko, J., L. Folsom, H. Park, M. Minamide, M. Ono, and H. Su, 2022: A sampling-based path planning algorithm for improving observations in tropical cyclones. Earth Space Sci., 9, e2020EA001498, https://doi.org/10.1029/2020EA001498.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18, 495527, https://doi.org/10.1007/BF00119502.

    • Search Google Scholar
    • Export Citation
  • DeMaria, M., C. R. Sampson, J. A. Knaff, and K. D. Musgrave, 2014: Is tropical cyclone intensity guidance improving? Bull. Amer. Meteor. Soc., 95, 387398, https://doi.org/10.1175/BAMS-D-12-00240.1.

    • Search Google Scholar
    • Export Citation
  • Drennan, W. M., J. A. Zhang, J. R. French, C. McCormick, and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part II: Latent heat flux. J. Atmos. Sci., 64, 11031115, https://doi.org/10.1175/JAS3889.1.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., 1959: On the formation of fronts in the atmosphere. The Atmosphere and the Sea in Motion (Rossby Memorial Volume), B. Bolin, Ed., Rockefeller Institute Press, 277–287.

  • Emanuel, K., 2017: Will global warming make hurricane forecasting more difficult? Bull. Amer. Meteor. Soc., 98, 495501, https://doi.org/10.1175/BAMS-D-16-0134.1.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585605, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1997: Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 10141026, https://doi.org/10.1175/1520-0469(1997)054<1014:SAOHIC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Foster, R., 2013: Signature of large aspect ratio roll vortices in synthetic aperture radar images of tropical cyclones. Oceanography, 26 (2), 5867, https://doi.org/10.5670/oceanog.2013.31.

    • Search Google Scholar
    • Export Citation
  • Foster, R. C., 2005: Why rolls are prevalent in the hurricane boundary layer. J. Atmos. Sci., 62, 26472661, https://doi.org/10.1175/JAS3475.1.

    • Search Google Scholar
    • Export Citation
  • French, J. R., W. M. Drennan, J. A. Zhang, and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part I: Momentum flux. J. Atmos. Sci., 64, 10891102, https://doi.org/10.1175/JAS3887.1.

    • Search Google Scholar
    • Export Citation
  • Gray, W. M., 1966: On the scales of motion and internal stress characteristics of the hurricane. J. Atmos. Sci., 23, 278288, https://doi.org/10.1175/1520-0469(1966)023<0278:OTSOMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Guimond, S. R., G. M. Heymsfield, P. D. Reasor, and A. C. Didlake Jr., 2016: The rapid intensification of Hurricane Karl (2010): New remote sensing observations of convective bursts from the Global Hawk platform. J. Atmos. Sci., 73, 36173639, https://doi.org/10.1175/JAS-D-16-0026.1.

    • Search Google Scholar
    • Export Citation
  • Guimond, S. R., J. A. Zhang, J. W. Sapp, and S. J. Frasier, 2018: Coherent turbulence in the boundary layer of Hurricane Rita (2005) during an eyewall replacement cycle. J. Atmos. Sci., 75, 30713093, https://doi.org/10.1175/JAS-D-17-0347.1.

    • Search Google Scholar
    • Export Citation
  • Han, J., and C. S. Bretherton, 2019: TKE-based moist eddy-diffusivity mass-flux (EDMF) parameterization for vertical turbulent mixing. Wea. Forecasting, 34, 869886, https://doi.org/10.1175/WAF-D-18-0146.1.

    • Search Google Scholar
    • Export Citation
  • Hinze, J. O., 1959: Turbulence. McGraw-Hill, 568 pp.

  • Hinze, J. O., 1976: Memory effects in turbulence. Z. Angew. Math. Mech., 56, T403T415, https://doi.org/10.1002/zamm.19760561007.

  • Holland, G. J., 1997: The maximum potential intensity of tropical cyclones. J. Atmos. Sci., 54, 25192541, https://doi.org/10.1175/1520-0469(1997)054<2519:TMPIOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ito, J., T. Oizumi, and H. Niino, 2017: Near-surface coherent structures explored by large eddy simulation of entire tropical cyclones. Sci. Rep., 7, 3798, https://doi.org/10.1038/s41598-017-03848-w.

    • Search Google Scholar
    • Export Citation
  • Kepert, J., and Y. Wang, 2001: The dynamics of boundary layer jets within the tropical cyclone core. Part II: Nonlinear enhancement. J. Atmos. Sci., 58, 24852501, https://doi.org/10.1175/1520-0469(2001)058<2485:TDOBLJ>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2012: Choosing a boundary layer parameterization for tropical cyclone modeling. Mon. Wea. Rev., 140, 14271445, https://doi.org/10.1175/MWR-D-11-00217.1.

    • Search Google Scholar
    • Export Citation
  • Kosiba, K. A., and J. Wurman, 2014: Finescale dual-Doppler analysis of hurricane boundary layer structures in Hurricane Frances (2004) at landfall. Mon. Wea. Rev., 142, 18741891, https://doi.org/10.1175/MWR-D-13-00178.1.

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

    • Search Google Scholar
    • Export Citation
  • Li, X., and Z. Pu, 2023: Dynamic mechanisms associated with the structure and evolution of roll vortices and coherent turbulence in the Hurricane Boundary Layer: A large eddy simulation during the landfall of hurricane Harvey. Bound.-Layer Meteor., 186, 615636, https://doi.org/10.1007/s10546-022-00775-w.

    • Search Google Scholar
    • Export Citation
  • Liu, Q., L. Wu, N. Qin, J. Song, and N. Wei, 2022: Wind gusts associated with tornado-scale vortices in the tropical cyclone boundary layer: A numerical simulation. Front. Earth Sci., 10, 945058, https://doi.org/10.3389/feart.2022.945058.

    • Search Google Scholar
    • Export Citation
  • Lorsolo, S., J. L. Schroeder, P. Dodge, and F. Marks Jr., 2008: An observational study of hurricane boundary layer small-scale coherent structures. Mon. Wea. Rev., 136, 28712893, https://doi.org/10.1175/2008MWR2273.1.

    • Search Google Scholar
    • Export Citation
  • Lorsolo, S., J. A. Zhang, F. Marks, and J. Gamache, 2010: Estimation and mapping of hurricane turbulent energy using airborne Doppler measurements. Mon. Wea. Rev., 138, 36563670, https://doi.org/10.1175/2010MWR3183.1.

    • Search Google Scholar
    • Export Citation
  • Louis, J.-F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17, 187202, https://doi.org/10.1007/BF00117978.

    • Search Google Scholar
    • Export Citation
  • Louis, J.-F., M. Tiedtke, and J.-F. Geleyn, 1982: A short history of the operational PBL parameterization at ECMWF. Workshop on Planetary Boundary Layer Parameterization, Reading, United Kingdom, ECMWF, 59–79, https://www.ecmwf.int/en/elibrary/75473-short-history-pbl-parameterization-ecmwf.

  • Malkus, J. S., and H. Riehl, 1960: On the dynamics and energy transformations in steady-state hurricanes. Tellus, 12A (1), 120, https://doi.org/10.3402/tellusa.v12i1.9351.

    • Search Google Scholar
    • Export Citation
  • Marks, F. D., Jr., and R. A. Houze, 1987: Inner core structure of Hurricane Alicia from airborne Doppler radar observations. J. Atmos. Sci., 44, 12961317, https://doi.org/10.1175/1520-0469(1987)044<1296:ICSOHA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Marks, F. D., P. G. Black, M. T. Montgomery, and R. W. Burpee, 2008: Structure of the eye and eyewall of Hurricane Hugo (1989). Mon. Wea. Rev., 136, 12371259, https://doi.org/10.1175/2007MWR2073.1.

    • Search Google Scholar
    • Export Citation
  • Mason, P. J., and R. I. Sykes, 1982: A two-dimensional numerical study of horizontal roll vortices in an inversion capped planetary boundary layer. Quart. J. Roy. Meteor. Soc., 108, 801823, https://doi.org/10.1002/qj.49710845805.

    • Search Google Scholar
    • Export Citation
  • Mason, P. J., and D. J. Thomson, 1992: Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech., 242, 5178, https://doi.org/10.1017/S0022112092002271.

    • Search Google Scholar
    • Export Citation
  • Masters, J. M., 1999: Hunting Hugo: Ten years ago, the hurricane hunters had one of their wildest rides ever. Weatherwise, 52, 2027, https://doi.org/10.1080/00431679909604327.

    • Search Google Scholar
    • Export Citation
  • Ming, J., J. A. Zhang, and R. F. Rogers, 2015: Typhoon kinematic and thermodynamic boundary layer structure from dropsonde composites. J. Geophys. Res. Atmos., 120, 31583172, https://doi.org/10.1002/2014JD022640.

    • Search Google Scholar
    • Export Citation
  • Moeng, C.-H., and P. P. Sullivan, 2014: Large-eddy simulation. Encyclopedia of Atmospheric Sciences, 2nd ed. G. North, F. Zhang and J. Pyle, Eds., Academic Press, 232–240.

  • Montgomery, M. T., and R. K. Smith, 2014: Paradigms for tropical cyclone intensification. Aust. Meteor. Oceanogr. J., 64, 3766, https://doi.org/10.22499/2.6401.005.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., and R. K. Smith, 2017: Recent developments in the fluid dynamics of tropical cyclones. Annu. Rev. Fluid Mech., 49, 541574, https://doi.org/10.1146/annurev-fluid-010816-060022.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., M. M. Bell, S. D. Aberson, and M. L. Black, 2006: Hurricane Isabel (2003): New insights into the physics of intense storms. Part I: Mean vortex structure and maximum intensity estimates. Bull. Amer. Meteor. Soc., 87, 13351348, https://doi.org/10.1175/BAMS-87-10-1335.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., G. Thompson, and V. Tatarskii, 2009: Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of one- and two-moment schemes. Mon. Wea. Rev., 137, 9911007, https://doi.org/10.1175/2008MWR2556.1.

    • Search Google Scholar
    • Export Citation
  • Morrison, I., S. Businger, F. Marks, P. Dodge, and J. A. Businger, 2005: An observational case for the prevalence of roll vortices in the hurricane boundary layer. J. Atmos. Sci., 62, 26622673, https://doi.org/10.1175/JAS3508.1.

    • Search Google Scholar
    • Export Citation
  • Muñoz-Esparza, D., B. Kosović, J. Mirocha, and J. van Beeck, 2014: Bridging the transition from mesoscale to microscale turbulence in numerical weather prediction models. Bound.-Layer Meteor., 153, 409440, https://doi.org/10.1007/s10546-014-9956-9.

    • Search Google Scholar
    • Export Citation
  • Munters, W., C. Meneveau, and J. Meyers, 2016: Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms. Bound.-Layer Meteor., 159, 305328, https://doi.org/10.1007/s10546-016-0127-z.

    • Search Google Scholar
    • Export Citation
  • Nardi, K. M., C. M. Zarzycki, V. E. Larson, and G. H. Bryan, 2022: Assessing the sensitivity of the tropical cyclone boundary layer to the parameterization of momentum flux in the community earth system model. Mon. Wea. Rev., 150, 883906, https://doi.org/10.1175/MWR-D-21-0186.1.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., N. A. Dahl, G. H. Bryan, and R. Rotunno, 2017: Tornado vortex structure, intensity, and surface wind gusts in large-eddy simulations with fully developed turbulence. J. Atmos. Sci., 74, 15731597, https://doi.org/10.1175/JAS-D-16-0258.1.

    • Search Google Scholar
    • Export Citation
  • Palmén, E. H., and C. W. Newton, 1969: Atmospheric Circulation Systems: Their Structure and Physical Interpretation. Academic Press, 603 pp.

  • Panofsky, H. A., 1953: The variation of the turbulence spectrum with height under superadiabatic conditions. Quart. J. Roy. Meteor. Soc., 79, 150153, https://doi.org/10.1002/qj.49707933913.

    • Search Google Scholar
    • Export Citation
  • Panofsky, H. A., and R. A. McCormick, 1960: The spectrum of vertical velocity near the surface. Quart. J. Roy. Meteor. Soc., 86, 495503, https://doi.org/10.1002/qj.49708637006.

    • Search Google Scholar
    • Export Citation
  • Persing, J., M. T. Montgomery, J. C. McWilliams, and R. K. Smith, 2013: Asymmetric and axisymmetric dynamics of tropical cyclones. Atmos. Chem. Phys., 13, 12 29912 341, https://doi.org/10.5194/acp-13-12299-2013.

    • Search Google Scholar
    • Export Citation
  • Prandtl, L., 1932: Zur turbulenten Strömung in Rohren und längs Platten. Ergebnisse der aerodynamischen Versuchsanstalt zu Göttingen Lfg. 4, De Gruyter, 18–29.

  • Protzko, D. E., S. R. Guimond, C. R. Jackson, J. W. Sapp, Z. Jelenak, and P. S. Chang, 2023: Documenting coherent turbulent structures in the boundary layer of intense hurricanes through Wavelet Analysis on IWRAP and SAR data. IEEE Trans. Geosci. Remote Sens., 61, 4105316, https://doi.org/10.1109/TGRS.2023.3305998.

    • Search Google Scholar
    • Export Citation
  • Richter, D. H., C. Wainwright, D. P. Stern, G. H. Bryan, and D. Chavas, 2021: Potential low bias in high-wind drag coefficient inferred from dropsonde data in hurricanes. J. Atmos. Sci., 78, 23392352, https://doi.org/10.1175/JAS-D-20-0390.1.

    • Search Google Scholar
    • Export Citation
  • Rogers, R., and Coauthors, 2006: The Intensity Forecasting Experiment: A NOAA multiyear field program for improving tropical cyclone intensity forecasts. Bull. Amer. Meteor. Soc., 87, 15231538, https://doi.org/10.1175/BAMS-87-11-1523.

    • Search Google Scholar
    • Export Citation
  • Rogers, R., S. Lorsolo, P. Reasor, J. Gamache, and F. Marks, 2012: Multiscale analysis of tropical cyclone kinematic structure from airborne Doppler radar composites. Mon. Wea. Rev., 140, 7799, https://doi.org/10.1175/MWR-D-10-05075.1.

    • Search Google Scholar
    • Export Citation
  • Rossby, C., and R. B. Montgomery, 1935: The Layer of Frictional Influence in Wind and Ocean Currents. Papers in Physical Oceanography and Meteorology. Vol. 3. Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 101 pp.

  • 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, 542561, https://doi.org/10.1175/1520-0469(1987)044<0542:AAITFT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., and G. H. Bryan, 2012: Effects of parameterized diffusion on simulated hurricanes. J. Atmos. Sci., 69, 22842299, https://doi.org/10.1175/JAS-D-11-0204.1.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., Y. Chen, W. Wang, C. Davis, J. Dudhia, and G. Holland, 2009: Large-eddy simulation of an idealized tropical cyclone. Bull. Amer. Meteor. Soc., 90, 17831788, https://doi.org/10.1175/2009BAMS2884.1.

    • Search Google Scholar
    • Export Citation
  • Rozoff, C. M., D. S. Nolan, G. H. Bryan, E. A. Hendricks, and J. Knievel, 2023: Large-eddy simulations of the tropical cyclone boundary layer at landfall in an idealized urban environment. J. Appl. Meteor. Climatol., 62, 14571478, https://doi.org/10.1175/JAMC-D-23-0024.1.

    • Search Google Scholar
    • Export Citation
  • Schlichting, H., and J. Kestin, 1961: Boundary Layer Theory. Vol. 121, Springer, 817 pp.

  • Sellwood, K. J., J. A. Sippel, and A. Aksoy, 2023: Assimilation of coyote small uncrewed aircraft system observations in Hurricane Maria (2017) using operational HWRF. Wea. Forecasting, 38, 901919, https://doi.org/10.1175/WAF-D-22-0214.1.

    • Search Google Scholar
    • Export Citation
  • Shea, D. J., and W. M. Gray, 1973: The hurricane’s inner core region. I. Symmetric and asymmetric structure. J. Atmos. Sci., 30, 15441564, https://doi.org/10.1175/1520-0469(1973)030<1544:THICRI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations: I. The basic experiment. Mon. Wea. Rev., 91, 99164, https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., and M. T. Montgomery, 2010: Hurricane boundary-layer theory. Quart. J. Roy. Meteor. Soc., 136, 16651670, https://doi.org/10.1002/qj.679.

    • Search Google Scholar
    • Export Citation
  • Smith, R. K., M. T. Montgomery, and N. Van Sang, 2009: Tropical cyclone spin-up revisited. Quart. J. Roy. Meteor. Soc., 135, 13211335, https://doi.org/10.1002/qj.428.

    • Search Google Scholar
    • Export Citation
  • Sparks, N., K. K. Hon, P. W. Chan, S. Wang, J. C. L. Chan, T. C. Lee, and R. Toumi, 2019: Aircraft observations of tropical cyclone boundary layer turbulence over the South China Sea. J. Atmos. Sci., 76, 37733783, https://doi.org/10.1175/JAS-D-19-0128.1.

    • Search Google Scholar
    • Export Citation
  • Stanisic, M. M., 2012: The Mathematical Theory of Turbulence. Springer Science and Business Media, 429 pp.

  • Stern, D. P., and G. H. Bryan, 2018: Using simulated dropsondes to understand extreme updrafts and wind speeds in tropical cyclones. Mon. Wea. Rev., 146, 39013925, https://doi.org/10.1175/MWR-D-18-0041.1.

    • Search Google Scholar
    • Export Citation
  • Stern, D. P., G. H. Bryan, and S. D. Aberson, 2016: Extreme low-level updrafts and wind speeds measured by dropsondes in tropical cyclones. Mon. Wea. Rev., 144, 21772204, https://doi.org/10.1175/MWR-D-15-0313.1.

    • Search Google Scholar
    • Export Citation
  • Stern, D. P., G. H. Bryan, C.-Y. Lee, and J. D. Doyle, 2021: Estimating the risk of extreme wind gusts in tropical cyclones using idealized large-eddy simulations and a statistical–dynamical model. Mon. Wea. Rev., 149, 41834204, https://doi.org/10.1175/MWR-D-21-0059.1.

    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Vol. 13, Springer Science and Business Media, 670 pp.

  • Sullivan, P. P., J. C. McWilliams, J. C. Weil, E. G. Patton, and H. J. S. Fernando, 2020: Marine atmospheric boundary layers above heterogeneous SST: Across-front winds. J. Atmos. Sci., 77, 42514275, https://doi.org/10.1175/JAS-D-20-0062.1.

    • Search Google Scholar
    • Export Citation
  • Tang, J., D. Byrne, J. A. Zhang, Y. Wang, X.-t. Lei, D. Wu, P.-z. Fang, and B.-k. Zhao, 2015: Horizontal transition of turbulent cascade in the near-surface layer of tropical cyclones. J. Atmos. Sci., 72, 49154925, https://doi.org/10.1175/JAS-D-14-0373.1.

    • Search Google Scholar
    • Export Citation
  • Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence. MIT Press, 320 pp.

  • Tsukada, T., and T. Horinouchi, 2020: Estimation of the tangential winds and asymmetric structures in typhoon inner core region using Himawari-8. Geophys. Res. Lett., 47, e2020GL087637, https://doi.org/10.1029/2020GL087637.

    • Search Google Scholar
    • Export Citation
  • Wajsowicz, R. C., 1993: A consistent formulation of the anisotropic stress tensor for use in models of the large-scale ocean circulation. J. Comput. Phys., 105, 333338, https://doi.org/10.1006/jcph.1993.1079.

    • Search Google Scholar
    • Export Citation
  • Wang, A., Y. Pan, G. H. Bryan, and P. M. Markowski, 2023: Modeling near-surface turbulence in large-eddy simulations of a tornado: An application of thin boundary layer equations. Mon. Wea. Rev., 151, 15871607, https://doi.org/10.1175/MWR-D-22-0060.1.

    • Search Google Scholar
    • Export Citation
  • Wang, S., and Q. Jiang, 2017: Impact of vertical wind shear on roll structure in idealized hurricane boundary layers. Atmos. Chem. Phys., 17, 35073524, https://doi.org/10.5194/acp-17-3507-2017.

    • Search Google Scholar
    • Export Citation
  • Wicker, L. J., and W. C. Skamarock, 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 20882097, https://doi.org/10.1175/1520-0493(2002)130<2088:TSMFEM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Worsnop, R. P., G. H. Bryan, J. K. Lundquist, and J. A. Zhang, 2017: Using large-eddy simulations to define spectral and coherence characteristics of the hurricane boundary layer for wind-energy applications. Bound.-Layer Meteor., 165, 5586, https://doi.org/10.1007/s10546-017-0266-x.

    • Search Google Scholar
    • Export Citation
  • Wu, L., Q. Liu, and Y. Li, 2018: Prevalence of tornado-scale vortices in the tropical cyclone eyewall. Proc. Natl. Acad. Sci. USA, 115, 83078310, https://doi.org/10.1073/pnas.1807217115.

    • Search Google Scholar
    • Export Citation
  • Wu, L., Q. Liu, and Y. Li, 2019: Tornado-scale vortices in the tropical cyclone boundary layer: Numerical simulation with the WRF–LES framework. Atmos. Chem. Phys., 19, 24772487, https://doi.org/10.5194/acp-19-2477-2019.

    • Search Google Scholar
    • Export Citation
  • Wurman, J., and J. Winslow, 1998: Intense sub-kilometer-scale boundary layer rolls observed in Hurricane Fran. Science, 280, 555557, https://doi.org/10.1126/science.280.5363.555.

    • Search Google Scholar
    • Export Citation
  • Wurman, J., and K. Kosiba, 2018: The role of small-scale vortices in enhancing surface winds and damage in Hurricane Harvey (2017). Mon. Wea. Rev., 146, 713722, https://doi.org/10.1175/MWR-D-17-0327.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., and W. M. Drennan, 2012: An observational study of vertical eddy diffusivity in the hurricane boundary layer. J. Atmos. Sci., 69, 32233236, https://doi.org/10.1175/JAS-D-11-0348.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., and M. T. Montgomery, 2012: Observational estimates of the horizontal eddy diffusivity and mixing length in the low-level region of intense hurricanes. J. Atmos. Sci., 69, 13061316, https://doi.org/10.1175/JAS-D-11-0180.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., and F. D. Marks, 2015: Effects of horizontal diffusion on tropical cyclone intensity change and structure in idealized three-dimensional numerical simulations. Mon. Wea. Rev., 143, 39813995, https://doi.org/10.1175/MWR-D-14-00341.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., W. M. Drennan, P. G. Black, and J. R. French, 2009: Turbulence structure of the hurricane boundary layer between the outer rainbands. J. Atmos. Sci., 66, 24552467, https://doi.org/10.1175/2009JAS2954.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., F. D. Marks, M. T. Montgomery, and S. Lorsolo, 2010: An estimation of turbulent characteristics in the low-level region of intense Hurricanes Allen (1980) and Hugo (1989). Mon. Wea. Rev., 139, 14471462, https://doi.org/10.1175/2010MWR3435.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., R. F. Rogers, D. S. Nolan, and F. D. Marks Jr., 2011: On the characteristic height scales of the hurricane boundary layer. Mon. Wea. Rev., 139, 25232535, https://doi.org/10.1175/MWR-D-10-05017.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, J. A., R. F. Rogers, P. D. Reasor, and J. Gamache, 2023: The mean kinematic structure of the tropical cyclone boundary layer and its relationship to intensity change. Mon. Wea. Rev., 151, 6384, https://doi.org/10.1175/MWR-D-21-0335.1.