Asymptotic Modeling of Atmospheric Flows

Equations.- 8.2 Some Considerations concerning the Singular Nature of the Boussinesq Approximation.- 8.3 Three New Forms of the Boussinesq Equations.- 8.3.1 Taking into Account the Shearing of a Basic Wind; the So-called Long Equation.- 8.3.2 Generalized Boussinesq-Type Equations.- 8.3.3 Quasi-static Boussinesq Equations; the Problem of Meso-scale Circulations.- 8.4 Concerning a Linear Theory of the Boussinesq Waves $$left( {{rm{Ro}}not equiv infty } right)$$.- 8.5 The Problem of Adjustment to the Boussinesq State.- 8.6 Complementary Remarks.- 9. The Isochoric Approximation.- 9.1 The Isochoric Equations.- 9.2 Some Considerations concerning the Singular Nature of the Isochoric Approximation.- 9.3 The Relation Between the Isochoric and Boussinesq Approximations.- 9.4 Wave Phenomena in the Isochoric Flows.- 9.4.1 The Long Wave Theory.- 9.4.2 The Short Wave Theory.- 9.4.3 Solitary Internal Waves.- 9.5 Complementary Remarks.- 10. The Deep Convection Approximation.- 10.1 The "Anelastic" Equations of Ogura and Phillips.- 10.2 The Deep Convection Equations According to Zeytounian.- 10.2.1 The Quasi-static Deep Convection Equations.- 10.2.2 A New Approach for the Derivation of the Deep Convection Equations (Case of the Adiabatic Atmosphere).- 10.3 The Relation Between the Boussinesq and the Deep Convection Approximations.- 10.4 Complementary Remarks.- 11. The Quasi-geostrophic and Ageostrophic Models.- 11.1 The Classical Quasi-geostrophic Model.- 11.2 The Adjustment to Geostrophy.- 11.3 The Ekman Steady Boundary Layer and the Ackerblom Problem.- 11.4 The So-called "Ageostrophic" Model.- 11.4.1 The Equation for the Ageostrophic Model.- 11.4.2 The Problem of the Unsteady Ekman Boundary Layer. Adjustment to the Ackerblom Model.- 11.4.3 The Problem of Adjustment to Ageostrophy.- 11.4.4 The Second Approximation Steady Ekman Problem.- 11.5 Complementary Remarks.- 12. Models Derived from the Theory of Low Mach Number Flows.- 12.1 The So-called Classical "Quasi-nondivergent" Model and Its Limitations.- 12.1.1 Analysis of Singularities Related to the Monin-Charney Limiting Process.- 12.2 The Generalized Quasi-nondivergent Model and Its Limitations.- 12.3 Analysis of Guiraud and Zeytounian's Recent Results.- 12.4 The Problem of Adjustment to the Quasi-nondivergent Flow.- 12.5 Complementary Remarks.- 13. The Models for the Local and Regional Scale Atmospheric Flows.- 13.1 The Free Circulation Models.- 13.1.1 Inner Degeneracies.- 13.1.2 Outer Degeneracies.- 13.1.3 Matching. Formulation of the Free Circulation Problem.- 13.2 The Models for the Asymptotic Analysis of Lee Waves.- 13.2.1 Emergence of the Vertical Structure. Condition for z ? +?.- 13.2.2 The General Requirement for Trapped Lee Waves.- 13.2.3 Non-linear Models for Two-Dimensional Steady Lee Waves.- 13.2.4 Asymptotic Interpretation of the Long Model in the Troposphere.- 13.2.5 Asymptotic Representation of Three-Dimensional Linearized Lee Waves in the Lower Atmosphere.- 13.3 Modeling of the Interaction Phenomenon Between Free and Forced Circulations.- 13.3.1 Formulation of the Regional Boundary Layer Problem.- 13.3.2 The Interaction Model.- 13.4 Complementary Remarks.- 13.4.1 A Model for the Local Winds of Slopes and Valleys.- 13.4.2 Double Layer Periodic Slope (or Valley) Winds.- 13.4.3 Low Mach Number Flow over a Relief.- 13.4.4 Asymptotic Formulation of the Rayleigh-Bénard Problem via the Boussinesq Approximation for Expansible Liquids.- Appendix. The Hydrostatic Forecasting Equations for Large-Synoptic-Scale Atmospheric Processes.- A.1 The Governing Equations.- A.2 The Hydrostatic Model Equations.- A.3 The Large-Scale, Synoptic, Boundary Layer Equations.- References.