Dynamic Meteorology

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.