Longitudinal instabilities and secondary flows in the planetary boundary layer: A review

Within the past decade, satellite pictures have shown persistent cloud patterns which indicate that the flow in the atmospheric planetary boundary layer is often organized into helical secondary circulations aligned parallel to the mean flow. Theory and observation agree that both convection in the presence of shear and the dynamic inflection point instabilities of the Ekman layer lead to these flow patterns. The observations and theory are reviewed with emphasis on the dynamics-dominated flow.

[1]  L. Howard,et al.  Stability of stratified shear flows , 1973 .

[2]  M. Boussinesq Essai sur la théorie des eaux courantes , 1873 .

[3]  N. Phillips,et al.  Scale Analysis of Deep and Shallow Convection in the Atmosphere , 1962 .

[4]  S. Fritz,et al.  CLOUD STREETS OVER THE CARIBBEAN SEA1 , 1961 .

[5]  M. Lemone,et al.  The Relationship of Trade Wind Cumulus Distribution to Subcloud Layer Fluxes and Structure , 1976 .

[6]  A. Faller,et al.  The angle of windrows in the ocean , 1964 .

[7]  A. H. Woodcock Soaring over the Open Sea , 1942 .

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

[9]  E. Caponi,et al.  Laboratory studies of wind-driven Langmuir circulations , 1978 .

[10]  Harold Jeffreys,et al.  Some Cases of Instability in Fluid Motion , 1928 .

[11]  R. Lindzen,et al.  Stability of a Helmholtz Velocity Profile in a Continuously Stratified, Infinite Boussinesq Fluid—Applications to Clear Air Turbulence , 1974 .

[12]  P. Drazin The stability of a shear layer in an unbounded heterogeneous inviscid fluid , 1958, Journal of Fluid Mechanics.

[13]  P. Welander,et al.  On the generation of wind streaks on the sea surface by action of surface film , 1963 .

[14]  T. Asai Three-Dimensional Features of Thermal Convection in a Plane Couette Flow (輻射ガス力学の運動方程式の研究会報告集) , 1970 .

[15]  Resonant Parallel Shear Instability in the Stably Stratified Planetary Boundary Layer , 1976 .

[16]  G. Veronis,et al.  Finite amplitude cellular convection , 1958, Journal of Fluid Mechanics.

[17]  K. S. Gage,et al.  The stability of thermally stratified plane Poiseuille flow , 1968, Journal of Fluid Mechanics.

[18]  H. Jeffreys LXXVI.The stability of a layer of fluid heated below , 1926 .

[19]  John W. Miles,et al.  On the stability of heterogeneous shear flows , 1961, Journal of Fluid Mechanics.

[20]  P. Tatro Experiments on Ekman layer instability , 1967, Journal of Fluid Mechanics.

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

[22]  J. Deardorff Numerical Investigation of Neutral and Unstable Planetary Boundary Layers , 1972 .

[23]  Louis N. Howard,et al.  Hydrodynamic Stability of Parallel Flow of Inviscid Fluid , 1966 .

[24]  William R. Moninger,et al.  The Influence of a Capping Inversion on the Dynamic and. Convective Instability of a Boundary Layer Model with Shear , 1975 .

[25]  J. Angell,et al.  A Lagrangian Study of Helical Circulations in the Planetary Boundary Layer , 1968 .

[26]  Ruby Krishnamurti,et al.  On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow , 1970, Journal of Fluid Mechanics.

[27]  R. Stewart,et al.  ON THE MECHANISM OF LANGMUIR CIRCULATIONS AND THEIR ROLE IN EPILIMNION MIXING1 , 1969 .

[28]  D. Koppel On the Stability of Flow of a Thermally Stratified Fluid under the Action of Gravity , 1964 .

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

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

[31]  R. Kropfli,et al.  Persistent Horizontal Rolls in the Urban Mixed Layer as Revealed by Dual-Doppler Radar , 1978 .

[32]  Robert A. Brown Similarity parameters from first-order closure and data , 1978 .

[33]  V. Barcilon Stability of a non‐divergent Ekman layer , 1965 .

[34]  Margaret A. LeMone,et al.  The Structure and Dynamics of Horizontal Roll Vortices in the Planetary Boundary Layer , 1973 .

[35]  S. Leibovich,et al.  A rational model for Langmuir circulations , 1976, Journal of Fluid Mechanics.

[36]  Lord Rayleigh,et al.  LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side , 1916 .

[37]  A. Faller,et al.  Instability of the Stratified Ekman Boundary Layer and the Generation of Internal Waves. , 1972 .

[38]  H. Squire On the Stability for Three-Dimensional Disturbances of Viscous Fluid Flow between Parallel Walls , 1933 .

[39]  Margaret A. LeMone,et al.  Modulation of Turbulence Energy by Longitudinal Rolls in an Unstable Planetary Boundary Layer , 1976 .

[40]  R. Krishnamurti On the transition to turbulent convection. Part 2. The transition to time-dependent flow , 1970, Journal of Fluid Mechanics.

[41]  H. Kuo Perturbations of Plane Couette Flow in Stratified Fluid and Origin of Cloud Streets , 1963 .

[42]  D. Etling,et al.  On the instability of a planetary boundary layer with Rossby number similarity , 1975 .

[43]  Francis P. Bretherton,et al.  The critical layer for internal gravity waves in a shear flow , 1967, Journal of Fluid Mechanics.

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

[45]  R. G. Fleagle,et al.  BOMEX: An Appraisal of Results. , 1972, Science.

[46]  J. Kuettner Cloud bands in the earth's atmosphere. Observations and theory , 1971 .

[47]  A. Mercer,et al.  On the behaviour of small disturbances in plane Couette flow , 1962, Journal of Fluid Mechanics.

[48]  J. Thompson,et al.  Stability of a Stratified Free Shear Layer , 1971 .

[49]  R. Strauch,et al.  Secondary flow fields in the planetary boundary layer estimated from dual‐Doppler radar measurements during snow conditions , 1975 .

[50]  S. Hanna The Formation of Longitudinal Sand Dunes by Large Helical Eddies in the Atmosphere , 1969 .

[51]  K. Hardy,et al.  Radar investigations of convective patterns in the clear atmosphere. , 1969 .

[52]  A. Mercer,et al.  On the behaviour of small disturbances in plane Couette flow with a temperature gradient , 1965, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[53]  R. Krishnamurti On Cellular Cloud Patterns. Part 3: Applicability of the Mathematical and Laboratory Models , 1975 .

[54]  H. Görtler Instabilität laminarer Grenzschichten an konkaven Wänden gegenüber gewissen dreidimensionalen Störungen , 1941 .

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

[56]  I. Langmuir SURFACE MOTION OF WATER INDUCED BY WIND. , 1938, Science.

[57]  R. Strauch,et al.  Three‐dimensional air motion measured in snow , 1974 .

[58]  E. Gossard Dynamic Stability of an Isentropic Shear Layer in a Statically Stable Medium , 1974 .

[59]  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.

[60]  W. L. Jones Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study , 1968, Journal of Fluid Mechanics.

[61]  A. R. Low On the Criterion for Stability of a Layer of Viscous Fluid Heated from below , 1929 .

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

[63]  S. Chandrasekhar,et al.  The instability of a layer of fluid heated below and subject to Coriolis forces. II , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[64]  J. Angell A Comparison of Circulations in Transverse and Longitudinal Planes in an Unstable Planetary Boundary Layer , 1972 .

[65]  Richard Vynne Southwell,et al.  On maintained convective motion in a fluid heated from below , 1940, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[66]  D. Christopherson NOTE ON THE VIBRATION OF MEMBRANES , 1940 .

[67]  Ralph Markson,et al.  Atmospheric Electrical Detection of Organized Convection , 1975, Science.

[68]  T. Asai Thermal Instability of a Shear Flow Turning the Direction with Height , 1972 .

[69]  D. J. Benney A non-linear theory for oscillations in a parallel flow , 1961, Journal of Fluid Mechanics.

[70]  J. Kuettner The Band Structure of the Atmosphere , 1959 .

[71]  D. A. Haugen,et al.  An experimental study of Reynolds stress and heat flux in the atmospheric surface layer , 1971 .

[72]  Friedrich H. Busse,et al.  Instabilities of longitudinal convection rolls in couette flow , 1977 .

[73]  J. T. Stuart Nonlinear Stability Theory , 1971, Handbook of Marine Craft Hydrodynamics and Motion Control.

[74]  J. Miles On the stability of heterogeneous shear flows. Part 2 , 1963, Journal of Fluid Mechanics.

[75]  C. Vest,et al.  The effect of shear and stratification on the stability of a rotating fluid layer , 1973, Journal of Fluid Mechanics.

[76]  J. Kaimal,et al.  Turbulence Structure in the Convective Boundary Layer , 1976 .

[77]  I. Tani Production of longitudinal vortices in the boundary layer along a concave wall , 1962 .

[78]  G. Taylor Experiments with Rotating Fluids , 1921 .