Advanced Atmospheric Dynamics

Preface Chapter 1 Atmospheric Motion Equations and Their Conservation Properties 1.1 Full derivative and local derivative 1.2 Vector form of the motion equations in the rotating reference system 1.3 Continuity equation 1.4 State equation 1.5 Thermodynamic energy equation 1.6 Water vapor equation 1.7 Fundamental equations in the spherical coordinate system 1.8 Fundamental equations in the local rectangular coordinate system 1.9 General vertical coordinates and their equations in the hydrostatic case 1.10 Fundamental conservation properties of atmospheric motion 1.11 Scale analysis method 1.12 Scale analysis of the atmospheric basic motion equations 1.13 Simplification of the atmospheric basic motion equations 1.14 Dimensionless equation 1.15 Basic equations in the p coordinate system 1.16 Equations in a generalized vertical coordinate system 1.17 σ coordinate system 1.18 θ coordinate system 1.19 Equilibrium flow field in the natural coordinate system 1.20 The basic type and nature of the equilibrium flow field 1.21 Thermal wind 1.22 Geostrophic deviation 1.23 Calculation of vertical velocity 1.24 Deep atmospheric motion equations in the non-hydrostatic case Exercises References Chapter 2 Vortex Motion of the Atmosphere 2.1 Absolute circulation theorem 2.2 Relative circulation theorem 2.3 Vorticity 2.4 Taylor-Proudman theorem 2.5 Vertical vorticity equation 2.6 Vorticity equation in the p coordinate system 2.7 Conservation law of the potential vorticity 2.8 The PV theory Exercises References Chapter 3 Waves in the Rotational Stratified Atmosphere 3.1 Basic concepts of waves 3.2 Micro-perturbation method 3.3 Acoustic wave 3.4 Lamb wave 3.5 External gravitational wave 3.6 External inertial gravitational waves 3.7 Internal gravitational wave 3.8 Rossby wave 3.9 Filtering 3.10 Mixed wave solutions in the atmosphere 3.11 Various wave characteristics 3.12 Wave characteristics in the barotropic model 3.13 Variational principle of atmospheric waves 3.14 Nonlinear waves Exercises References Chapter 4 Non-uniform Rossby Wave 4.1 Slow-varying wave train 4.2 Energy and energy flux of Rossby wave 4.3 Dispersion of Rossby wave in the 3 plane 4.4 Multi-scale method for waves 4.5 Rossby wave characteristic equation 4.6 Dispersion of Rossby wave on the sphere 4.7 Meridional propagation of Rossby wave 4.8 Vertical propagation of Rossby wave 4.9 Evolution of Rossby wave, interaction between the wave and the basic flow 4.10 Rossby wave resonance, wave-wave interaction 4.11 Momentum and heat transport by Rossby wave 4.12 EP flux Exercises References Chapter 5 Atmospheric Adjustment Theory 5.1 Physical background of quasi-geostrophic motion generation 5.2 Stages of large-scale motion processes 5.3 Geostrophic adjustment process in a barotropic atmosphere 5.4 Geostrophic adjustment process in a baroclinic atmosphere 5.5 Hydrostatic adjustment process 5.6 Semi-geostrophic adjustment process of the tropical atmosphere Exercises References Chapter 6 Quasi-geostrophic Theory of the Mid-latitude Large-scale Motion 6.1 The quasi-geostrophic motion 6.2 Quasi-geostrophic equations 6.3 Quasi-geostrophic potential tendency equation 6.4 Quasi-geostrophic o equation 6.5 An ideal model for the developing baroclinic disturbance 6.6 vector 6.7 Semingeostrophic motion and geostrophic momentum approximation Exercises References Chapter 7 Atmospheric Energetics 7.1 Basic forms of energy in the atmosphere 7.2 Atmospheric energy balance equation 7.3 Energy conversion in a hydrostatic equilibrium atmosphere 7.4 Available potential energy 7.5 Some conservation properties of the global atmosphere 7.6 Constraint of a hydrostatic equilibrium on energy relations 7.7 Energy equation for the p coordinate system 7.8 Energy equations in the o coordinate system 7.9 Lorenz energy integral constraint Exercises References Chapter 8 Stability Theory of the Atmospheric Motion 8.1 Dynamical stability concept 8.2 Inertial instability 8.3 Barotropic instability 8.4 Baroclinic instability 8.5 Mesoscale symmetric instability 8.6 Finite amplitude (weakly nonlinear) baroclinic instability 8.7 High truncation approximation method 8.8 Multi-equilibrium states in the atmosphere and their stability 8.9 Lorenz system Exercises References Chapter 9 Planetary Boundary Layer 9.1 Turbulent mean momentum equation 9.2 Eddy flux 9.3 Mixing length theory 9.4 Variation of wind with height 9.5 Ekman pumping and spin down 9.6 Turbulent diffusion equation 9.7 Turbulent transport of heat and water vapor 9.8 Effect of buoyancy on sensible turbulent transport 9.9 Criterion of the turbulence development 9.10 Ekman wind profile under the semi-geostrophic approximation 9.11 Ekman pumping under the semi-geostrophic approximation Exercises References Chapter 10 Troplenl Atmospherle Dynamicn 10.1 Senling anolysin of the tropcal wather-nralle notion 10.2 Tropieal fluetuntion 10.3 Condition instability and cumulus ceation 10.4 Physical mechanisms about the development of tropical disturbance 10.5 CISK theory of typhoon development Exercises References Chapter 11 Frontal Dynamies 11.1 General characteristics of the frontal structure 11.2 Frontogenesis and the frontogenesis function 11.3 Evolution of the non-equilibrium state and adjustment to the frontogenesisprocess 11.4 Semi-geostrophic frontogenesis theory 11.5 Primitive equation frontogenesis theory Exercises References Chapter 12 Vortex Rossby Wave Evolution Theory 12.1 Shallow water equation and mean vortex 12.2 Balanced model 12.3 Nondimensionalization and dimensionless parameters 12.4 Slow-varying linear wave dynamics 12.5 Vortex evolution of wave flux 12.6 A few special cases 12.7 Analytical discussion of the solution 12.8 Summary Exercises References