Geostrophic Wave Circulations
Yong Zhu
Contents
2 On Rossby waves
2.1 Introduction
2.2 In Cartesian coordinates
2.3 In pressure coordinates
2.4 Propagation mechanism
2.5 Effect of wind divergence
2.6 Geostrophic balance
2.7 Summaries
3 Geostrophic waves
3.1 Introduction
3.2 The primitive equations
3.3 Geostrophic perturbation equations
3.4 Small-oscillation approximation
3.5 Mean circulation equations
3.5.1 The first-order mean circulation equations
3.5.2 The second-order mean circulation equations
3.5.3 Free mean meridional circulation
3.6 Remainder equations
3.7 Geostrophic wave solutions
3.8 Wave angles
3.9 Wave structure
3.10 Summaries
4 Dynamics of geostrophic waves
4.1 Introduction
4.2 b-effect and wave propagation
4.2.1 A simple review
4.2.2 Inertial circles on f-plane
4.2.3 Inertial circles on b-plane
4.3 Propagation mechanism
4.4 Geostrophic balance
4.5 Divergence and vorticity
4.5.1 Horizontal divergence
4.5.2 Vertical relative vorticity
4.6 Kinetic energy balance
4.6.1 Horizontal kinetic energy
4.6.2 Vertical kinetic energy
4.7 Summaries
5 Momentum and heat balances
5.1 Introduction
5.2 Angular momentum flux
5.3 Zonal momentum balance
5.4 Meridional momentum balance
5.5 Heat flux
5.6 Heat balance
5.7 Directional flux
5.7.1 Calculating formula
5.7.2 Zonal mean and perturbation components
5.7.3 Path mean and deviation
5.8 Remote responses
5.8.1 In velocity field
5.8.2 In thermal field
5.9 Geopotential wave amplitude
5.10 Equilibrium waves
5.11 Summaries
6 Orographic stationary waves
6.1 Introduction
6.2 Response to orographic forcing
6.3 Asymmetric orographic forcing
6.3.1 Friction torque
6.3.2 Mountain torque
6.3.3 Secondary forcings
6.4 Orographic waves in extratropical regions
6.4.1 In the Northern Hemisphere
6.4.2 In the Southern Hemisphere
6.5 Stationary wavelength
6.6 Stationary wave baroclinity
6.7 Resonance
6.7.1 On previous studies
6.7.2 Mountain waves or lee waves
6.8 Summaries
7 Thermal stationary waves
7.1 Introduction
7.2 Linear and nonlinear responses to thermal forcing
7.3 Thermal waves at middle latitudes
7.4 Seasonal changes
7.5 Subtropical stationary waves
7.5.1 In summer
7.5.2 In winter
7.6 Thermal waves in the lower troposphere
7.7 Vertical extension of stationary waves
7.7.1 A simple review
7.7.2 Self-forcing mechanism
7.8 Summaries
8 Variabilities in the troposphere
8.1 Introduction
8.2 Phase of blocking waves
8.3 Blocking in the Northern Hemisphere
8.4 Blocking in the Southern Hemisphere
8.5 Multiple equilibrium states
8.6 Self-feedback of momentum
8.6.1 Zonal momentum feedback
8.6.2 Meridional momentum feedback
8.7 Self-feedback of heat
8.7.1 Nonlinear feedback
8.7.2 Linear feedback
8.8 Effects of external and internal forcing
8.9 Summaries
9 Zonal mean circulation field
9.1 Introduction
9.2 Mean temperature profile
9.3 Mean zonal wind profile
9.4 Effect of static stability
9.5 Mean meridional circulation
9.5.1 The basic equation
9.5.2 Relation to momentum transport
9.6 Numerical experiments
9.6.1 Mean meridional circulation
9.6.2 Circulation mechanisms
9.6.3 Mean meridional and vertical velocities
9.7 Eddy transport of momentum and heat
9.7.1 Angular momentum transport
9.7.2 Heat transport
9.8 Summaries
10 Nonlinear instability and blocking
10.1 Introduction
10.2 Breaking layers
10.3 The superposition in breaking layers
10.4 Onset of blocking
10.4.1 Thermally forced baroclinic instability
10.4.2 Blocking positions
10.5 Development of blocking
10.6 Maintenance of blocking
10.6.1 Stationary baroclinity
10.6.2 Blocking amplitude
10.6.3 Blocking baroclinity
10.7 Decay of blocking
10.8 On wave interactions
10.9 Summaries
11 Stratospheric warm pools
11.1 Introduction
11.2 Breaking layers in stratosphere
11.3 Abnormal wave group
11.4 Coherent heating
11.5 Lower frequency coherent heating
11.6 Propagation velocity
11.7 Thermal structure
11.8 Summaries
12 Stratospheric sudden warming
12.1 Introduction
12.2 Instability mechanism
12.3 Zonal mean heating
12.3.1 The early stage
12.3.2 The late stage
12.4 Reversal of zonal circulation
12.4.1 Zonal momentum balance
12.4.2 Mean zonal acceleration
12.5 Heat and momentum fluxes
12.6 Imbalance heating
12.7 Summaries
13 Stochastic instability
13.1 Introduction
13.2 Perturbation equations
13.3 Belt parameters
13.4 Vacillating waves
13.5 Wave instability
13.5.1 Critical baroclinity
13.5.2 For cyclogenesis
13.5.3 The most unstable disturbances
13.5.4 Unstable waveband
13.6 Incipient development
13.7 Further development
13.7.1 Linear adjustment
13.7.2 Meridional size
13.7.3 Zonal size
13.7.4 E-folding time
13.7.5 Cyclone distribution
13.8 Summaries
A Group velocity of anisotropic waves
A.1 Introduction
A.2 Historical review
A.3 Dependence on coordinates
A.3.1 Basic relationships
A.3.2 Without changing wave dimension
A.3.3 In change of wave dimension
A.3.4 Example of Rossby wave
A.4 General group velocity
A.4.1 Calculation formula
A.4.2 Independent of coordinates
A.5 Gaussian wave packet
A.6 Oblique group velocity
A.7 Conservation of mean energy
A.8 Wave action
A.9 Ray-tracing equations
A.10 Path-tracing equations
B List of symbols
References
Index