Sloping convection in a rotating fluid

Abstract Laboratory experiments on thermal convection in a fluid which rotates about a vertical axis and is subject to a horizontal temperature gradient show that when the rotation rate Ω exceeds a certain critical value ΩR (which depends on the acceleration of gravity, the shape and dimensions of the apparatus, the physical properties of the fluid and the distribution and intensity of the applied differential heating) Coriolis forces inhibit overturning motion in meridian planes and promote a completely different type of flow which has been termed ‘sloping convection’ or ‘baroclinic waves’. The motion is then non-axisymmetric and largely confined to meandering ‘jet streams’, with trajectories of individual fluid elements inclined at only very small (though essentially non-zero) angles to the horizontal. The kinetic energy of the waves derives from the interaction of slight vertical motions with the potential energy field maintained by differential heating, and it is dissipated by friction arising largely...

[1]  Norman A. Phillips,et al.  A SIMPLE THREE-DIMENSIONAL MODEL FOR THE STUDY OF LARGE-SCALE EXTRATROPICAL FLOW PATTERNS , 1951 .

[2]  Gareth P. Williams Thermal Convection in a Rotating Fluid Annulus. Part I. The Basic Axisymmetric Flow , 1967 .

[3]  C. Hunter The axisymmetric flow in a rotating annulus due to a horizontally applied temperature gradient , 1967, Journal of Fluid Mechanics.

[4]  Katsuyuki V. Ooyama,et al.  On the Stability of the Baroclinic Circular Vortex: a Sufficient Criterion for Instability. , 1966 .

[5]  A. W. Nielsen A study of the baroclinic instability problem and the lower boundary condition , 1971 .

[6]  P. Rhines Edge‐, bottom‐, and Rossby waves in a rotating stratified fluid , 1970 .

[7]  R. Pfeffer,et al.  Characteristics of Amplitude Vacillation in a Rotating, Differentially Heated Fluid Determined by a Multi-Probe Technique. , 1969 .

[8]  D. Dietrich A numerical study of rotating annulus flows using a modified Galerkin method , 1973 .

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

[10]  A. Simmons Planetary‐scale disturbances in the polar winter stratosphere , 1974 .

[11]  J. Pedlosky The Stability of Currents in the Atmosphere and the Ocean: Part I , 1964 .

[12]  R. Hide,et al.  Baroclinic waves in a rotating fluid subject to internal heating , 1970, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[13]  E. Spiegel Convection in Stars II. Special Effects , 1972 .

[14]  Meteorological challenges : a history , 1972 .

[15]  A. Melling,et al.  Laser anemometry: a report on EUROMECH 36 , 1972, Journal of Fluid Mechanics.

[16]  E. Eliasen,et al.  A study of the fluctuations of the atmospheric planetary flow patterns represented by spherical harmonics , 1965 .

[17]  Thomas F. Malone,et al.  Compendium of meteorology , 1951 .

[18]  I. Orlanski Instability of Frontal Waves. , 1968 .

[19]  R. Hide,et al.  Thermal Convection in a Rotating Annulus of Liquid: Effect of Viscosity on the Transition Between Axisymmetric and Non-Axisymmetric Flow Regimes , 1965 .

[20]  A. Wiin-Nielsen,et al.  On baroclinic instability of ultra-long waves' , 1971 .

[21]  P. Mason,et al.  An investigation of the structure of baroclinic waves using three-level streak photography , 1972 .

[22]  A. E. Gill,et al.  Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies , 1974 .

[23]  D. Baker,et al.  Density Gradients in a Rotating Stratified Fluid: Experimental Evidence for a New Instability , 1971, Science.

[24]  M. McIntyre A Separable Nongeostrophic Baroclinic Stability Problem , 1965 .

[25]  H. Lejenäs Energetics of a developing wave in the westerlies , 1973 .

[26]  F. Busse,et al.  Convection induced by centrifugal buoyancy , 1974, Journal of Fluid Mechanics.

[27]  E.R.G. Eckertf,et al.  Natural convection in an air layer enclosed between two vertical plates with different temperatures , 1961 .

[28]  R. Pfeffer,et al.  Synoptic Features and Energetics of Wave-Amplitude Vacillation in a Rotating, Differentially-Heated Fluid , 1974 .

[29]  J. W. Elder,et al.  Laminar free convection in a vertical slot , 1965, Journal of Fluid Mechanics.

[30]  Brian J. Hoskins,et al.  Stability of the Rossby-Haurwitz wave , 1973 .

[31]  E. Schulman The baroclinic instability of a mid-ocean circulation , 1967 .

[32]  V. Barcilon Role of the Ekman Layers in the Stability of the Symmetric Regime Obtained in a Rotating Annulus , 1964 .

[33]  A. Robinson,et al.  The Baroclinic Instability of the Open Ocean , 1974 .

[34]  T. V. Davies The forced flow of a rotating viscous liquid which is heated from below , 1953, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[35]  E. T. Eady,et al.  Long Waves and Cyclone Waves , 1949 .

[36]  R. Pfeffer,et al.  TWO KINDS OF VACILLATION IN ROTATING LABORATORY EXPERIMENTS , 1967 .

[37]  G. Platzman The Rossby wave , 1968 .

[38]  A. Monin,et al.  Weather forecasting as a problem in physics , 1972 .

[39]  B. Hunt Zonally symmetric global general circulation models with and without the hydrologic cycle , 1973 .

[40]  L. Prandtl,et al.  Essentials of fluid dynamics , 1952 .

[41]  W. W. Fowlis,et al.  Techniques and Apparatus for the Fast and Accurate Measurement of Fluid Temperature and Flow Speed Fields , 1970 .

[42]  P. Drazin Non‐linear baroclinic instability of a continuous zonal flow , 1970 .

[43]  A. Robinson The symmetric state of a rotating fluid differentially heated in the horizonal , 1959, Journal of Fluid Mechanics.

[44]  D. Fultz Experimental Analogies to Atmospheric Motions , 1951 .

[45]  J. Turner,et al.  Buoyancy Effects in Fluids , 1973 .

[46]  J. Charney,et al.  On the Stability of Internal Baroclinic Jets in a Rotating Atmosphere. , 1962 .

[47]  I. Hirota On the Dynamics of Long and Ultra-Long Waves in a Baroclinic Zonal Current , 1968 .

[48]  J. A. Brown,et al.  A Numerical Investigation of Hydrodynamic Instability and Energy Conversions in the Quasi-Geostrophic Atmosphere: Part I , 1969 .

[49]  J. S. A. Green,et al.  A problem in baroclinic stability , 1960 .

[50]  P. Gierasch,et al.  Mars - The effects of topography on baroclinic instability. , 1972 .

[51]  G. Walin Contained non-homogeneous flow under gravity or how to stratify a fluid in the laboratory , 1971, Journal of Fluid Mechanics.

[52]  N. Phillips,et al.  Some laboratory experiments on Rossby waves in a rotating annulus , 1967 .

[53]  J. Hart A laboratory study of baroclinic instability , 1972 .

[54]  P. J. Mason,et al.  Thermal Convection in a Large Rotating Fluid Annulus: Some Effects of Varying the Aspect Ratio. , 1973 .

[55]  E. Eliasen On the Interactions between the Long Baroclinic Waves and the Mean Zonal Flow , 1961 .

[56]  Three‐dimensional non‐geostrophic disturbances in a baroclinic zonal flow , 1970 .

[57]  H. Riehl,et al.  Jet stream and long waves in a steady rotating‐dishpan experiment: Structure of the circulation , 1957 .

[58]  Harvey P. Greenspan,et al.  The Theory of Rotating Fluids. By H. P. GREENSPAN. Cambridge University Press, 1968. 327 pp. £5.50. , 1972, Journal of Fluid Mechanics.

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

[60]  J. Miles Baroclinic instability of the zonal wind , 1964 .

[61]  George Veronis,et al.  On the Boussinesq Approximation for a Compressible Fluid. , 1960 .

[62]  Chung-Muh Tang The stability of continuous baroclinic models with planetary vorticity gradient , 1971 .

[63]  J. Dutton,et al.  The Theory of Available Potential Energy and a Variational Approach to Atmospheric Energetics , 1967 .

[64]  T. J. Simons The Nonlinear Dynamics of Cyclone Waves , 2007 .

[65]  C. Leovy Mars: theoretical aspects of meteorology. , 1969, Applied optics.

[66]  S. Epstein On the general analytic solution in the baroclinic instability problem , 1970 .

[67]  M. Cox,et al.  Baroclinic Instability in Ocean Currents , 1973 .

[68]  Y. Mintz,et al.  Numerical Simulation of the Atmospheric Circulation and Climate of Mars , 1969 .

[69]  H. C. Longuet-Higgins Planetary waves on a rotating sphere , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[70]  Frank Kreith,et al.  Convection Heat Transfer in Rotating Systems , 1969 .

[71]  A. Newell The Post Bifurcation Stage of Baroclinic Instability , 1972 .

[72]  Phillip Smith,et al.  The dissipation of kinetic energy in large‐scale atmospheric circulations , 1974 .

[73]  J. G. Charney,et al.  THE DYNAMICS OF LONG WAVES IN A BAROCLINIC WESTERLY CURRENT , 1947 .

[74]  E. O. Holipainen On the Effect of Friction in Baroclinic Waves , 1961 .

[75]  R. Pfeffer,et al.  Wave Dispersion in a Rotating, Differentially Heated Cylindrical Annulus Of Fluid. , 1968 .

[76]  R. Sutcliffe The quasi‐geostrophic advective wave in a baroclinic zonal current , 1951 .

[77]  H. Kuo THREE-DIMENSIONAL DISTURBANCES IN A BAROCLINIC ZONAL CURRENT , 1952 .

[78]  T. D. Lee,et al.  Difference between Turbulence in a Two‐Dimensional Fluid and in a Three‐Dimensional Fluid , 1951 .

[79]  N. Vinnichenko,et al.  The kinetic energy spectrum in the free atmosphere—1 second to 5 years , 1970 .

[80]  Francis P. Bretherton,et al.  Atmospheric Frontogenesis Models: Mathematical Formulation and Solution , 1972 .

[81]  A. D. Young,et al.  An Introduction to Fluid Mechanics , 1968 .

[82]  Peter H. Stone,et al.  On Non-Geostrophic Baroclinic Stability , 1966 .

[83]  A. Faller A DEMONSTRATION OF FRONTS AND FRONTAL WAVES IN ATMOSPHERIC MODELS , 1956 .

[84]  J. A. Kaiser,et al.  Rotating deep annulus convection , 1969 .

[85]  W. Blumen On the Stability of Quasi-Geostrophic Flow , 1968 .

[86]  F. Berson Summary of a Theoretical Investigation into the Factors Controlling the Instability of Long Waves in Zonal Currents , 1949 .

[87]  A. Burger ON THE NON-EXISTENCE OF CRITICAL WAVELENGTHS IN A CONTINUOUS BAROCLINIC STABILITY PROBLEM , 1962 .

[88]  J. Holton An introduction to dynamic meteorology , 2004 .

[89]  A. Nyberg An Aerological Study of Large-Scale Atmospheric Disturbances , 1949 .

[90]  F. Bretherton Critical layer instability in baroclinic flows , 1966 .

[91]  E. J. O'Neil The Stability of Flows in a Differentially Heated Rotating Fluid System with Rigid Bottom and Free Top , 1969 .

[92]  M. Yanai,et al.  Axially Symmetric Meridional Motions in the Baroclinic Circular Vortex: a Numerical Experiment , 1969 .

[93]  A. Loesch Resonant Interactions Between Unstable and Neutral Baroclinic Waves: Part II. , 1974 .

[94]  R. V. Garcia,et al.  A contribution to the baroclinic instability problem , 1970 .

[95]  T. Tokioka A Stability Study of Axisymmetric Flows in a Rotating Annulus , 1970 .

[96]  F. Ward The General Circulation of the Solar Atmosphere and the Maintenance of the Equatorial Acceleration. , 1965 .