ATMOSPHERIC DIFFUSION

By A. NASAL

THE BASIC EQUATIONS OF ATMOSPHERIC MOTION TIME DERIVATIVES IN FLUIDS THE FLUID DESCRIPTION ACCORDING TO EULER AND LAGRANGE THE MATERIAL DERIVATIVE OF A FLUID ELEMENT THE MATERIAL DERIVATIVE OF VOLUME INTEGRALS SUMMARY THE EQUATION OF CONTINUITY A EULERIAN DERIVATION A LAGRANGIAN DERIVATION USING THE MATERIAL DERIVATIVE THE MOMENTUM EQUATION THE VOLUME FORCES SURFACE FORCES (1): THE PRESSURE GRADIENT FORCE SURFACE FORCES (2): FRICTION THE TOTAL MOMENTUM EQUATION THE EQUATIONS OF MOTION IN A ROTATING FRAME OF REFERENCE THE TIME DERIVATIVE IN A ROTATING FRAME OF REFERENCE THE MOMENTUM EQUATION IN THE ROTATING FRAME OF REFERENCE THE EQUATION OF CONTINUITY IN THE ROTATING FRAME OF REFERENCE THE EQUATIONS OF MOTION ON THE SPHERE VELOCITY AND MATERIAL DERIVATIVE IN SPHERICAL COORDINATES THE TRANSFORMED EQUATIONS OF MOTION SYNOPTIC SCALE ANALYSIS THE GEOSTROPHIC EQUILIBRIUM THE HYDROSTATIC EQUILIBRIUM RECOMMENDATIONS FOR FURTHER READING ELEMENTARY THERMODYNAMICS AND ENERGETICS OF DRY AIR FUNDAMENTALS THERMODYNAMIC SYSTEMS THERMODYNAMIC STATE AND THERMODYNAMIC EQUILIBRIUM TEMPERATURE EQUATIONS OF STATE ENERGY CHANGE OF A THERMODYNAMIC SYSTEM THE FUNDAMENTAL LAWS OF THERMODYNAMICS THE FIRST LAW OF THERMODYNAMICS AND INTERNAL ENERGY THE HEAT CAPACITIES OF AN IDEAL GAS ADIABATIC AND ISOTHERMAL CHANGES OF STATE OF AN IDEAL GAS THE SECOND LAW OF THERMODYNAMICS THE CARNOT PROCESS ENTROPY AS STATE VARIABLE ENTROPY AND POTENTIAL TEMPERATURE OF DRY AIR THE PROGNOSTIC EQUATIONS FOR TEMPERATURE AND ENTROPY IN DRY AIR PREDICTION OF TEMPERATURE THE PREDICTION OF ENTROPY AND POTENTIAL TEMPERATURE THE EQUATIONS IN A ROTATING FRAME OF REFERENCE SPHERICAL COORDINATES POTENTIAL TEMPERATURE AND STATIC STABILITY STABLE AND UNSTABLE STRATI?CATION BUOYANCY OSCILLATIONS ELEMENTARY PROPERTIES AND APPLICATIONS OF THE BASIC EQUATIONS SUMMARY OF THE BASIC EQUATIONS THE IMPORTANCE OF THE BASIC EQUATIONS FOR WEATHER PREDICTION CONSERVATION LAWS CONSERVATION OF ENERGY CONSERVATION OF ANGULAR MOMENTUM THE PRIMITIVE EQUATIONS THE PRIMITIVE EQUATIONS IN PRESSURE COORDINATES ARBITRARY VERTICAL COORDINATES PRESSURE COORDINATES BALANCED FLOWS THE NATURAL COORDINATES GEOSTROPHIC FLOW INERTIAL FLOW CYCLOSTROPHIC FLOW THE GRADIENT WIND THERMAL WIND VORTEX DYNAMICS VORTICITY RELATIVE, ABSOLUTE, AND PLANETARY VORTICITY VORTEX LINES, VORTEX TUBES, AND VORTEX FLUX CIRCULATION RELATIVE AND ABSOLUTE CIRCULATION THE GENERAL CIRCULATION THEOREM THE KELVIN THEOREM THE VORTICITY EQUATION THE DERIVATION VORTEX-TUBE STRETCHING AND VORTEX TILTING SUMMARY OF THE IMPACTS ON RELATIVE VORTICITY THE FROZEN-IN PROPERTY OF ABSOLUTE VORTICITY POTENTIAL VORTICITY AN ALGEBRAIC DERIVATION OF THE PROGNOSTIC EQUATION FOR POTENTIAL VORTICITY A DERIVATION OF POTENTIAL-VORTICITY CONSERVATION FROM THE GENERAL CIRCULATION THEOREM VORTEX DYNAMICS AND THE PRIMITIVE EQUATIONS THE PRIMITIVE EQUATIONS IN ISENTROPIC COORDINATES THE PRIMITIVE VORTICITY EQUATION IN ISENTROPIC COORDINATES THE POTENTIAL VORTICITY OF THE PRIMITIVE EQUATIONS FLOW OVER A MOUNTAIN RIDGE THE DYNAMICS OF THE SHALLOW-WATER EQUATIONS DERIVATION OF THE EQUATIONS THE CONTINUITY EQUATION CONSERVATION PROPERTIES ENERGY CONSERVATION QUASIGEOSTROPHIC DYNAMICS THE TANGENTIAL ?-PLANE SCALING THE SHALLOW-WATER EQUATIONS ON THE ?-PLANE THE QUASIGEOSTROPHIC APPROXIMATION: DERIVATION BY SCALE ASYMPTOTICS THE QUASIGEOSTROPHIC APPROXIMATION: DERIVATION FROM THE CONSERVATION OF SHALLOW-WATER POTENTIAL VORTICITY WAVE SOLUTIONS OF THE SHALLOW-WATER EQUATIONS PERTURBATION APPROACH WAVES ON THE F-PLANE WAVES ON THE ? PLANE: QUASIGEOSTROPHIC ROSSBY WAVES GEOSTROPHIC ADJUSTMENT THE GENERAL SOLUTION OF THE LINEAR SHALLOW-WATER EQUATIONS ON AN F PLANE THE ADJUSTMENT PROCESS QUASIGEOSTROPHIC DYNAMICS OF THE STRATI?ED ATMOSPHERE QUASIGEOSTROPHIC THEORY AND ITS POTENTIAL VORTICITY ANALYSIS OF MOMENTUM AND CONTINUITY EQUATION ANALYSIS OF THE ENTROPY EQUATION QUASIGEOSTROPHIC POTENTIAL VORTICITY IN THE STRATI?ED ATMOSPHERE THE RELATIONSHIP WITH GENERAL POTENTIAL VORTICITY QUASIGEOSTROPHIC THEORY IN PRESSURE COORDINATES A QUASIGEOSTROPHIC TWO-LAYER MODEL QUASIGEOSTROPHIC ENERGETICS OF THE STRATI?ED ATMOSPHERE THE CONTINUOUSLY STRATI?ED ATMOSPHERE THE TWO-LAYER MODEL ROSSBY WAVES IN THE STRATI?ED ATMOSPHERE ROSSBY WAVES IN THE TWO-LAYER MODEL ROSSBY WAVES IN AN ISOTHERMAL CONTINUOUSLY STRATI?ED ATMOSPHERE BAROCLINIC INSTABILITY BAROCLINIC INSTABILITY IN THE TWO-LAYER MODEL BAROCLINIC INSTABILITY IN A CONTINUOUSLY STRATI?ED ATMOSPHERE THE PLANETARY BOUNDARY LAYER ANELASTICS AND THE BOUSSINESQ THEORY THE ANELASTIC EQUATIONS THE BOUSSINESQ EQUATIONS INSTABILITIES IN THE BOUNDARY LAYER THE TAYLOR–GOLDSTEIN EQUATION NEUTRAL STRATI?CATION (N2 = 0) NO SHEAR (DU/DZ = 0) AND CONSTANT STRATI?CATION N2 THE GENERAL CASE: THE RICHARDSON CRITERION OF HOWARD AND MILES THE AVERAGED EQUATIONS OF MOTION TURBULENCE AND MEAN FLOW THE REYNOLDS EQUATIONS GRADIENT ANSATZ AND MIXING LENGTH THE TURBULENT KINETIC ENERGY THE PROGNOSTIC EQUATION SOURCES AND SINKS THE PRANDTL LAYER THE MOMENTUM FLUX THE WIND PRO?LE THE IN?UENCE OF STRATI?CATION THE EKMAN LAYER THE EKMAN-SPIRAL EKMAN PUMPING THE INTERACTION BETWEEN ROSSBY WAVES AND THE MEAN FLOW BASICS OF QUASIGEOSTROPHIC THEORY THE GOVERNING EQUATIONS THE QUASIGEOSTROPHIC ENSTROPHY EQUATION WITHIN LINEAR DYNAMICS ROSSBY-WAVE PROPAGATION WAVE PROPAGATION WITHIN WKB THEORY ROSSBY-WAVE PROPAGATION INTO THE STRATOSPHERE THE ELIASSEN–PALM FLUX DE?NITION THE ELIASSEN–PALM RELATIONSHIP WAVE ACTION AND ELIASSEN–PALM FLUX WITHIN WKB THEORY THE TRANSFORMED EULERIAN MEAN (TEM) THE TEM IN THE CONTEXT OF QUASIGEOSTROPHY THE MASS-WEIGHTED CIRCULATION IN ISENTROPIC COORDINATES THE RELATION BETWEEN THE RESIDUAL CIRCULATION AND THE MASS-WEIGHTED CIRCULATION THE NON-ACCELERATION THEOREM THE MERIDIONAL CIRCULATION SOME ESSENTIALS OF THE EMPIRICAL BASIS THE HADLEY CIRCULATION THE BASIC EQUATIONS OF A MODEL WITHOUT WAVE DRIVING A SOLUTION WITHOUT MERIDIONAL CIRCULATION HIDE’S THEOREM A SIMPLI?ED DESCRIPTION OF THE HADLEY CELL THE SUMMER–WINTER ASYMMETRY THE WAVE-DRIVEN HADLEY CIRCULATION THE CIRCULATION IN THE MIDLATITUDES THE PHENOMENOLOGY OF THE FERREL CELL EDDY FLUXES AND BAROTROPIC JET STREAM A TWO-LAYER MODEL 10 GRAVITY WAVES AND THEIR IMPACT ON THE ATMOSPHERIC FLOW 10 1 SOME EMPIRICAL FACTS 10 2 THE FUNDAMENTAL WAVE MODES OF AN ATMOSPHERE AT REST EQUATIONS OF MOTION AND ENERGETICS FREE WAVES ON THE F-PLANE IN AN ISOTHERMAL ATMOSPHERE 10 3 THE INTERACTION BETWEEN MESOSCALE GRAVITY WAVES AND A SYNOPTIC-SCALE FLOW A REFORMULATION OF THE DYNAMICAL EQUATIONS SCALING FOR SYNOPTIC-SCALE FLOW AND FOR INERTIA-GRAVITY WAVES NON-DIMENSIONAL EQUATIONS AND WKB ANSATZ LEADING-ORDER RESULTS: EQUILIBRIA, DISPERSION AND POLARIZATION RELATIONS, EIKONAL EQUATIONS THE NEXT ORDER OF THE EQUATIONS WAVE ACTION WAVE IMPACT ON THE SYNOPTIC-SCALE FLOW GENERALIZATION TO GRAVITY-WAVE SPECTRA: PHASE-SPACE WAVE-ACTION DENSITY 10 3 10 SUMMARY 10 4 CRITICAL LEVELS AND RE?ECTING LEVELS CRITICAL LEVELS RE?ECTING LEVELS 10 5 THE MIDDLE-ATMOSPHERE GRAVITY-WAVE IMPACT EXTENSION OF THE TEM BY GRAVITY-WAVE EFFECTS THE GRAVITY-WAVE EFFECT ON THE RESIDUAL CIRCULATION AND ON THE ZONAL-MEAN FLOW 10 6 REFERENCES AND RECOMMENDATIONS FOR FURTHER READING