Dynamic Meteorology

1. ABOUT THE DISCIPLINE 'DYNAMIC METEOROLOGY' The name 'dynamic meteorology' is traditional for designating a university course as well as the scientific branch of meteorology as a whole. While there is no need to abandon this name, it needs contemporary treatment and specifications in its definition. A synonym for it could be 'dynamics (more precisely, hydrodynamics or fluid dynamics) of the atmosphere'. It suggests the relationship of this discipline to general hydrodynamics and applied mathematics and its pronounced theoretical nature. Besides the atmosphere, however, our planet has another (liquid) envelope - the hydrosphere (world's ocean), which also concerns ocean dynamics and, therefore, it is necessary to define, from a unified standpoint, the subject and aims of the disciplines dealing with the dynamics of the processes which take place in both fluid spheres. Such a unified standpoint offers the so-called geophysical fluid dynamics. During the past few years this description is encountered quite often in scientific literature concerning the Earth as a planet. Obviously, a scientific branch or a science is created whose subject is our planet and the investigation methods are borrowed from classical fluid dynamics and applied mathematics, including the most recent numerical methods. As can be seen from its very suitable name, it is the dynamics of quite definite geophysical fluids (atmosphere, ocean and even the liquid inside of the Earth) and not of some abstract (often perfect) flUids, as in classical hydrodynamics.

1. Introduction to Dynamic Meteorology (Kinematics of the Atmospheric Motions).- 1. Methods for the Description of Continuous Media.- a. Lagrange’s Method.- b. Euler’s Method.- c. Types of Derivatives.- 2. Kinematic Characteristics of the Pressure Field.- a. Pressure Systems.- b. Pressure-Features Movement.- c. Evolution of Pressure Systems.- 3. Geometrical Characteristics of the Wind Field.- a. Streamlines.- b. Trajectory.- 4. Differential and Integral Characteristics of the Wind Field.- a. Divergence.- b. Vorticity.- c. Vortex Lines and Tubes.- d. Deformation.- 5. A Linear Wind Field Around an Arbitrary Point.- a. Decomposition of the Velocity.- b. Analysis of the Results.- 6. The Continuity Equation.- a. Derivation of the Equation.- b. Analysis and Particular Cases.- 7. Barotropy and Baroclinicity of the Atmosphere.- a. Barotropy.- b. Baroclinicity.- 8. On the Use of Scalar, Vector, and Tensor Notations.- Problems.- I: The Dynamics of An Ideal (Without Friction) Atmosphere.- 2. Equations of Thermo-Hydrodynamics of the Atmosphere (Weather Equations).- 1. The Thermodynamic Energy Equation.- a. General Form.- b. Alternative Forms and Particular Cases.- c. Heat Sources.- 2. The Equations of Motion.- a. General Form.- b. Application to the Atmosphere.- c. Boussinesq Approximation.- 3. Weather Equations in Spherical Coordinates.- a. Preliminary Preparation.- b. Introduction of Spherical Coordinates.- 4. Weather Equations in Local (Standard) Coordinates: Boundary Conditions.- a. Introduction of Local Coordinates.- b. The Boussinesq Approximation.- c. Boundary Conditions.- 5. Equations of Motion in Cylindrical and Natural Coordinates: The Shallow-Water Approximation.- a. Introduction of Cylindrical Coordinates.- b. The Natural (s, n) Coordinates.- c. The ‘Shallow-Water’ Approximation.- 6. Weather Equations in Generalized Vertical Coordinates.- a. Preliminary Formulae.- b. Transformation of Equations.- c. Boundary Conditions.- Problems.- 3. Simplification of Weather Equations.- 1. Methods for Simplification of Weather Equations.- a. General Characteristics.- b. Scale Analysis and Similarity.- 2. Scale Analysis of Weather Equations.- a. Choice of Scales.- b. Simplification of the Equations.- c. Some Remarks.- 3. Weather Equations in p, ?, ? and Other Vertical Coordinates.- a. Isobaric p System.- b. Isobaric ? System.- c. Isentropic ? System.- d. Other Vertical Coordinates.- 4. Ageostrophic and Thermal Winds.- a. Ageostrophic Wind.- b. Thermal Wind.- 5. Vorticity, Divergence and Balance Equations.- a. The Vorticity Equation.- b. Vorticity Conservation Laws.- c. Simplification of the Vorticity Equation.- d. Divergence and Balance Equations.- 6. Gradient Wind at Curvilinear Isobars.- a. Natural Coordinates.- b. Cartesian Coordinates.- 7. Pressure-Velocity Relationships in the Low-Latitudes Atmosphere.- a. Linear Approach.- b. Two-Dimensional Nonlinear Approach.- c. Three-Dimensional Nonlinear Approach.- 8. Lagrangian Approach to the Problem of Simplification.- a. Middle Latitudes.- b. Low Latitudes.- c. Global-Scale Oscillations.- 9. Spectral Approach to the Problem of Simplification.- a. General Discussion.- b. Examples of Low-Order Systems.- Problems.- 4. Energetics of the Atmosphere.- 1. Types of Energy and Energy Conversions.- a. Definitions.- b. Energy Conversions.- 2. The Energy Balance Equation Per Unit Air Mass.- a. The Energy Balance Equation in z Coordinates.- b. The Energy Balance Equation in p Coordinates.- 3. Integral Forms of the Energy Balance Equations.- a. Subsidiary Formulae.- b. Closed Air Mass.- c. Vertical Air Column.- Problems.- 5. Waves and Instabilities in the Atmosphere.- 1. General Information on Wave Motions: The Perturbation Method.- a. Mathematical Description.- b. The Perturbation Method.- c. Types of Waves in the Atmosphere.- 2. Sound Waves in the Atmosphere.- a. Constant Basic State.- b. Variable Basic State.- 3. Surface (External) Gravity Waves.- a. Long Waves.- b. Short Waves.- c. Equatorial Atmosphere.- 4. Internal Gravity Waves.- a. Waves on Internal Boundary Surfaces.- b. Waves in a Continuously Stratified Atmosphere.- 5. The Rossby Waves.- a. Two-Dimensional Pure Waves.- b. Two-Dimensional Mixed Waves.- c. Three-Dimensional Rossby Waves.- 6. Orographic Waves.- a. Topographic Rossby Waves.- b. Mountain Waves.- c. Taylor’s Column.- 7. Empirical Evidence for the Existence of Wave Motions in the Atmosphere.- a. Gravity Waves.- b. Inertial Waves.- 8. Dynamic Instability of Atmospheric Motions.- a. General Considerations.- b. Inertial Instability.- c. Barotropic Instability.- d. Baroclinic Instability.- e. Convective Instability.- 9. A Concept of Nonlinear Waves in the Atmosphere.- a. Solitary Waves (Solitons).- b. Atmospheric Solitons.- Problems.- 6. The Mutual Adjustment of Meteorological Elements.- 1. Geostrophic Adjustment: One-Dimensional Model.- a. Significance of the Problem.- b. One-Dimensional Model.- 2. Geostrophic Adjustment: Two-Dimensional Model.- a. Starting Equations.- b. Character of the Adjustment Process.- c. Adjustment Activity of the Fields.- 3. Three-Dimensional Adjustment Models.- a. Geostrophic Adjustment.- b. Geostrophic-Hydrostatic Adjustment.- 4. Waves and Adjustment on a Sphere.- a. Beta Approximation.- b. Spherical Earth.- c. One-Dimensional Spectral Model.- Problems.- 7. The Theoretical Basis of Meteorological Forecasts.- 1. Synoptic Variations of Meteorological Elements — Early Theories.- a. Classification of the Causes.- b. Kibel’s Theory.- 2. Barotropic Prognostic Models.- a. Quasi-Geostrophic Approximation.- b. Quasi-Solenoidal Approximation.- c. Energetics of the Model.- d. Nonlinear Interactions.- 3. Baroclinic Prognostic Models.- a. Quasi-Geostrophic Approximation.- b. Quasi-Solenoidal Approximation.- c. The Two-Layer Baroclinic Model.- 4. Prognostic Models with Primitive Equations.- a. General Characteristics.- b. Initialization.- 5. Methods for Cloudiness and Precipitation Forecasting.- a. Basic Equations.- b. Semiempirical Method.- c. Method of Invariants.- 6. Predictability of the Meteorological Elements.- a. The Nature of the Problem.- b. Range of Predictability.- c. Numerical Experiments of Predictability.- Problems.- II: The Dynamics of A Real (With Friction) Atmosphere.- 8. The General Theory of Atmospheric Turbulence.- 1. Turbulent Motions: General Information.- a. Definition for Turbulence.- b. Methods for Description.- c. On the Averaging Procedure.- 2. The Reynolds Equations.- a. Derivation of the Equations.- b. Analysis and Interpretation of the Results.- 3. Fundamentals of the Semiempirical Theory of Turbulence.- a. Equations for the Reynolds Stresses.- b. Energy Balance Equation.- c. Coefficients of Turbulence.- 4. Fundamentals of the Statistical Theory of Turbulence.- a. Homogeneous and Isotropic Turbulence.- b. Locally Homogeneous and Isotropic Turbulence.- c. Microstructure of Scalar Fields.- Problems.- 9. The Dynamics of the Atmospheric Surface Layer.- 1. Turbulent Surface Layer: General Properties.- a. Definition of Surface Layer (SL).- b. Energetics of the SL.- c. Semiempirical Equations.- 2. Vertical Profiles of the Wind and Other Meteorological Elements in the Surface Layer.- a. Neutral Stratification: Logarithmic Law.- b. Arbitrary Stratification: Power Model.- 3. The Similarity Theory for the Structure of the Surface Layer.- a. Fundamental Suppositions and Formulae.- b. Asymptotic Cases.- c. Universal Functions.- 4. Microstructure of Atmospheric Turbulence in the Surface Layer.- a. Spatial Microstructure.- b. Time Microstructure.- c. Practical Applications.- 5. Turbulent Diffusion of Admixtures in the Surface Layer.- a. Semiempirical Equation of Diffusion.- b. Particular Solutions and Analysis.- 6. Horizontally Nonhomogeneous Surface Layer.- a. Adjustment of Scalar Characteristics.- b. Adjustment of the Wind.- Problems.- 10. The Dynamics of the Atmospheric Planetary Boundary Layer.- 1. Turbulent Planetary Boundary Layer (PBL): General Properties.- a. Definition for PBL: Equations.- b. Ekman Model.- 2. K Models of the PBL.- a. Barotropic PBL.- b. Baroclinic PBL.- 3. Nonlinear l-Models of the PBL.- a. Explicit Expressions for l(z).- b. Implicit Expressions for l(z).- 4. Similarity Theory for the PBL.- a. Parametrization of the PBL.- b. Universal Dependences.- c. Experimental Data and Significance of the Problem.- 5. Vertical Motions in the PBL.- a. General Information and Formulae.- b. Ekman PBL.- c. Vorticity Generation in the PBL.- 6. Some Special Questions of PBL Theory.- a. The PBL Above Mountains.- b. Local Circulations in the PBL.- c. Nonstationary PBL.- Problems.- 11. The General Circulation of the Atmosphere.- 1. Characteristic Peculiarities and Structure of General Atmospheric Circulation (GAC).- a. Factors Determining GAC.- b. Structural Elements of GAC.- c. Theoretical Description of GAC.- 2. Analytical and Numerical Models of GAC.- a. Blinova’s Model.- b. Monin’s Model.- c. Numerical Models and Experiments.- 3. GAC as Quasi-Two-Dimensional Turbulence.- a. Empirical Data.- b. Theory of Atmospheric Macroturbulence.- 4. Lagrangian Description of the Atmospheric Macroturbulence and Diffusion.- a. Theoretical Results.- b. Empirical Data.- Problems.- References.- Appendix: Retrospective View of Dynamic Meteorology: Perspectives.- Biographical Data.