THE MEAN DENSITY OF THE EARTH
CONTENTS THE EQUATIONS OF HYDRODYNAMICS GENERAL CONSERVATION LAW IN A CONTINUOUS MEDIUM THE CONTINUITY EQUATION - MASS CONSERVATION LAW THE NAVIER-STOKES EQUATION - MOMENTUM BALANCE THE ANGULAR MOMENTUM BALANCE THE ENERGY EQUATION PRODUCTION OF THE TOTAL ENTROPY FUNDAMENTAL IDEAS IN THEORETICAL DESCRIPTION OF THE PHENOMENON OF CONVECTION ADIABATIC GRADIENT FILTERING SOUND WAVES REVIEW EXERCISES REFERENCES THE OBERBECK-BOUSSINESQ CONVECTION DERIVATION OF THE OBERBECK-BOUSSINESQ EQUATIONS MOMENTUM BALANCE ENERGY BALANCE ENERGETIC PROPERTIES OF BOUSSINESQ SYSTEMS CONSERVATION OF MASS AND VALUES OF THE MEAN PRESSURE AT BOUNDARIES BOUSSINESQ UP-DOWN SYMMETRIES LINEAR STABILITY ANALYSIS AT CONVECTION THRESHOLD - COMPENDIUM OF RESULTS FOR DIFFERENT PHYSICAL CONDITIONS TWO ISOTHERMAL, STRESS-FREE BOUNDARIES, Q ¼ 0 TWO ISOTHERMAL RIGID BOUNDARIES, Q ¼ 0 ONE RIGID AND ONE STRESS-FREE BOUNDARY, BOTH ISOTHERMAL, Q ¼ 0 TWO STRESS-FREE, FIXED-THERMAL-FLUX BOUNDARIES, Q ¼ 0 TWO RIGID, FIXED-THERMAL-FLUX BOUNDARIES, Q ¼ 0 THE EFFECT OF RADIATIVE HEATING, Q 6¼ 0, AT TWO STRESS-FREE, ISOTHERMAL BOUNDARIES CONSTRAINTS FROM RAPID ROTATION AT TWO STRESS-FREE, ISOTHERMAL BOUNDARIES, Q ¼ 0 SUMMARY A WORD ON WEAKLY NONLINEAR ESTIMATES SHORT INTRODUCTION INTO THE PATTERN SELECTION PROBLEM NEAR THRESHOLD FULLY DEVELOPED CONVECTION VALIDITY OF THE APPROXIMATION AND SUMMARY ANELASTIC CONVECTION DERIVATION OF THE ANELASTIC EQUATIONS PRODUCTION OF THE TOTAL ENTROPY WITHIN THE ANELASTIC APPROXIMATION BOUSSINESQ LIMIT THE REFERENCE STATE SIMPLI?CATIONS THROUGH ENTROPY FORMULATIONS BOUNDARY CONDITIONS FOR THE ENTROPY CONSTANT THERMAL DIFFUSIVITY FORMULATION FOR AN IDEAL GAS WITH NON-VANISHING HEAT SINK BRAGINSKY AND ROBERTS’ FORMULATION FOR TURBULENT CONVECTION ENERGETIC PROPERTIES OF ANELASTIC SYSTEMS ISOTHERMAL BOUNDARIES, PERFECT GAS, UNIFORM FLUID PROPERTIES, G ¼ CONST BOUNDARIES HELD AT CONSTANT HEAT FLUX, PERFECT GAS, UNIFORM FLUID PROPERTIES, G ¼ CONST LINEAR STABILITY ANALYSIS (IDEAL GAS, Q ¼ 0, ISOTHERMAL, STRESS-FREE AND IMPERMEABLE BOUNDARIES, CONSTANT ”, K, G AND CP) THE GROWTH RATE OF THE CONVECTIVE INSTABILITY IN THE LIMIT H 1 FULLY DEVELOPED, STRATI?ED CONVECTION THE HYDROSTATIC CONDUCTION REFERENCE STATE AND THE HYDROSTATIC ADIABATIC STATE RELATION BETWEEN ENTROPY AND TEMPERATURE JUMPS ACROSS THE BOUNDARY LAYERS “SUBADIABATIC” TEMPERATURE GRADIENT IN THE BULK VERTICAL PRO?LES OF MEAN TEMPERATURE AND ENTROPY THE NUSSELT, RAYLEIGH AND REYNOLDS NUMBERS ESTIMATES OF THE MEAN SUPERADIABATIC HEAT FLUX IN A FULLY DEVELOPED STATE ESTIMATES OF THE RATIOS RS, RD, RT AND RU SCALING LAWS FOR FULLY DEVELOPED STRATI?ED CONVECTION WITH ISENTROPIC BOUNDARIES DISCUSSION COMPARISON OF ANELASTIC SYSTEMS AND RELATION TO THE ADIABATIC REFERENCE STATE FORMULATION ANELASTIC VERSUS BOUSSINESQ APPROXIMATIONS INCLUSION OF COMPOSITIONAL EFFECTS COMPOSITIONAL AND HEAT FLUXES BOUNDARY CONDITIONS ON THE MASS FRACTION PRODUCTION OF THE TOTAL ENTROPY AND THE SECOND LAW OF THERMODYNAMICS HYDROSTATIC REFERENCE STATE MIXTURE OF IDEAL GASES BUOYANCY FORCE FINAL SET OF EQUATIONS GLOBAL BALANCE DE?NITIONS OF THE RAYLEIGH AND NUSSELT NUMBERS BOUSSINESQ EQUATIONS WEAK SOLUTION LIMIT, N 1 MIXTURE OF IDEAL GASES IN THE WEAK SOLUTION LIMIT