Why Rolls are Prevalent in the Hurricane Boundary Layer

Recent remote sensing observations show that the hurricane boundary layer flow, although energetic, is not a region of homogeneous turbulence. In fact, the observations convincingly demonstrate that a large fraction of the turbulent flow in the regions away from the deep convective rainbands is highly organized into intense horizontal roll vortices that are approximately aligned with the mean wind and span the depth of the boundary layer. These observations show that rolls strongly increase the flux of momentum between the underlying surface and the main body of the storm compared to an equivalent hurricane boundary layer flow without rolls. The linear and nonlinear dynamics of hurricane boundary layer roll formation are outlined and it is shown why rolls are, in fact, the expected basic hurricane boundary layer state. The model presented here explains the hurricane roll features currently documented in field programs and makes predictions that can be tested in future experiments. The primary effects of rolls on the boundary layer fluxes are inherently nonlocal and nongradient and hence cannot be captured by standard downgradient turbulence parameterizations used in hurricane simulations. However, the nonlinear theory is the proper starting point for developing boundary layer parameterizations that include roll modification of the turbulent fluxes.

[1]  A. Faller Instability and transition of disturbed flow over a rotating disk , 1991, Journal of Fluid Mechanics.

[2]  P. K. Sen,et al.  On the stability of plane Poiseuille flow to finite-amplitude disturbances, considering the higher-order Landau coefficients , 1983, Journal of Fluid Mechanics.

[3]  E. F. Bradley,et al.  Flux-Profile Relationships in the Atmospheric Surface Layer , 1971 .

[4]  D. Etling,et al.  Roll vortices in the planetary boundary layer: A review , 1993 .

[5]  R. Moser,et al.  Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions , 1991 .

[6]  Yuqing Wang,et al.  Vortex Rossby Waves in a Numerically Simulated Tropical Cyclone. Part II: The Role in Tropical Cyclone Structure and Intensity Changes* , 2002 .

[7]  Jeffrey D. Kepert,et al.  The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part II: Nonlinear Enhancement , 2001 .

[8]  Jeffrey D. Kepert,et al.  The dynamics of boundary layer jets within the tropical cyclone core. Part I: Linear theory , 2001 .

[9]  Robert A. Brown,et al.  On the Inflection Point Instability of a Stratified Ekman Boundary Layer. , 1972 .

[10]  G. Young,et al.  Supplement to Rolls, Streets, Waves, and More , 2002 .

[11]  Kerry A. Emanuel,et al.  The Theory of Hurricanes , 1991 .

[12]  T. Herbert On perturbation methods in nonlinear stability theory , 1983, Journal of Fluid Mechanics.

[13]  G. Young,et al.  ROLLS, STREETS, WAVES, AND MORE: A Review of Quasi-Two-Dimensional Structures in the Atmospheric Boundary Layer , 2002 .

[14]  N. Gregory,et al.  On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk , 1955, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[15]  Gad Levy,et al.  The Contribution of Organized Roll Vortices to the Surface Wind Vector in Baroclinic Conditions , 1998 .

[16]  M. R. Malik,et al.  Instability and transition in rotating disk flow , 1981 .

[17]  Kathryn M. Butler,et al.  Three‐dimensional optimal perturbations in viscous shear flow , 1992 .

[18]  J. T. Stuart On the non-linear mechanics of hydrodynamic stability , 1958, Journal of Fluid Mechanics.

[19]  Mujeeb R. Malik,et al.  The neutral curve for stationary disturbances in rotating-disk flow , 1986, Journal of Fluid Mechanics.

[20]  K. Emanuel,et al.  Dissipative heating and hurricane intensity , 1998 .

[21]  Inez Y. Fung The organization of spiral rainbands in a hurricane. , 1977 .

[22]  W. Timothy Liu,et al.  An Operational Large-Scale Marine Planetary Boundary Layer Model , 1982 .

[23]  A. Faller Large Eddies in the Atmospheric Boundary Layer and Their Possible Role in the Formation of Cloud Rows , 1965 .

[24]  T. Asai,et al.  On the Stability of Ekman Boundary Layer Flow with Thermally Unstable Stratification , 1973 .

[25]  M. Montgomery,et al.  Axisymmetric Spindown Dynamics of Hurricane-like Vortices , 2001 .

[26]  Anne E. Trefethen,et al.  Hydrodynamic Stability Without Eigenvalues , 1993, Science.

[27]  R. Lingwood,et al.  Absolute instability of the boundary layer on a rotating disk , 1995, Journal of Fluid Mechanics.

[28]  V. Gryanik,et al.  Third-Order Transport and Nonlocal Turbulence Closures for Convective Boundary Layers* , 1999 .

[29]  M. Yau,et al.  Spiral Bands in a Simulated Hurricane. Part I: Vortex Rossby Wave Verification , 2001 .

[30]  S. Chandrasekhar Hydrodynamic and Hydromagnetic Stability , 1961 .

[31]  W. Liu,et al.  Bulk Parameterization of Air-Sea Exchanges of Heat and Water Vapor Including the Molecular Constraints at the Interface , 1979 .

[32]  L. Mahrt,et al.  A two-scale mixing formulation for the atmospheric boundary layer , 1995 .

[33]  J. W. Glendening Lineal eddy features under strong shear conditions , 1996 .

[34]  Robert A. Brown A Secondary Flow Model for the Planetary Boundary Layer , 1970 .

[35]  W. Timothy Liu,et al.  Microwave Remote Sensing of Tropical Cyclones from Space , 2002 .

[36]  B. W. Atkinson,et al.  Mesoscale shallow convection in the atmosphere , 1996 .

[37]  Winslow,et al.  Intense sub-kilometer-scale boundary layer rolls observed in hurricane fran , 1998, Science.

[38]  W. Large,et al.  Open Ocean Momentum Flux Measurements in Moderate to Strong Winds , 1981 .

[39]  J. Businger,et al.  Viscous Dissipation of Turbulence Kinetic Energy in Storms , 2001 .

[40]  Philip Hall,et al.  An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[41]  M. Powell,et al.  Reduced drag coefficient for high wind speeds in tropical cyclones , 2003, Nature.

[42]  Philippe Drobinski,et al.  On the Origin of Near-Surface Streaks in the Neutrally-Stratified Planetary Boundary Layer , 2003 .

[43]  P. Hildebrand,et al.  Small-Scale Spiral Bands Observed in Hurricanes Andrew, Hugo, and Erin , 1998 .

[44]  Brian F. Farrell,et al.  Optimal excitation of perturbations in viscous shear flow , 1988 .

[45]  J. H. Ferziger,et al.  A numerical study of the turbulent Ekman layer , 1990, Journal of Fluid Mechanics.

[46]  Jean-Luc Redelsperger,et al.  The structure of the near neutral atmospheric surface layer as observed during the CASES'99 experiment , 2004 .

[47]  A. Eliassen On the Ekman Layer in a circular Vortex , 1971 .

[48]  R. Foster Structure and energetics of optimal Ekman layer perturbations , 1997, Journal of Fluid Mechanics.

[49]  Dan S. Henningson,et al.  Pseudospectra of the Orr-Sommerfeld Operator , 1993, SIAM J. Appl. Math..

[50]  G. Holland An Analytic Model of the Wind and Pressure Profiles in Hurricanes , 1980 .

[51]  M. Montgomery,et al.  Hurricane Maximum Intensity: Past and Present , 2000 .

[52]  Kerry Emanuel,et al.  An Air-Sea Interaction Theory for Tropical Cyclones. Part I: Steady-State Maintenance , 1986 .

[53]  Steven Businger,et al.  An Observational Case for the Prevalence of Roll Vortices in the Hurricane Boundary Layer , 2005 .

[54]  D. Lilly On the Instability of Ekman Boundary Flow , 1966 .

[55]  Scott A. Braun,et al.  Sensitivity of High-Resolution Simulations of Hurricane Bob (1991) to Planetary Boundary Layer Parameterizations , 2000 .

[56]  K. Emanuel Sensitivity of Tropical Cyclones to Surface Exchange Coefficients and a Revised Steady-State Model incorporating Eye Dynamics , 1995 .

[57]  A. Faller,et al.  A Numerical Study of the Instability of the Laminar Ekman Boundary Layer , 1966 .