ALBERT

Note: Contents: Series foreword. - Preface. - Select bibliography. - The authors. - 1 Observed flow in the Earth's midlalitudes. - 1.1 Vertical structure. - 1.2 Horizontal structure. - 1.3 Transient activity. - 1.4 Scales of motion. - 1.5 The Norwegian frontal model of cyclones. - Theme 1 Fluid dynamics of the midlatitude atmosphere. - 2 Fluid dynamics in an inertial frame of reference. - 2.1 Definition of fluid. - 2.2 Flow variables and the continuum hypothesis. - 2.3 Kinematics: characterizing fluid flow. - 2.4 Governing physical principles. - 2.5 Lagrangian and Eulerian perspectives. - 2.6 Mass conservation equation. - 2.7 First Law of Thermodynamics. - 2.8 Newton's Second Law of Motion. - 2.9 Bernoulli's Theorem. - 2.10 Heating and water vapour. - 3 Rotating frames of reference. - 3.1 Vectors in a rotating frame of reference. - 3.2 Velocity and Acceleration. - 3.3 The momentum equation in a rotating frame. - 3.4 The centrifugal pseudo-force. - 3.5 The Coriolis pseudo-force. - 3.6 The Taylor-Proudman theorem. - 4 The spherical Earth. - 4.1 Spherical polar coordinates. - 4.2 Scalar equations. - 4.3 The momentum equations. - 4.4 Energy and angular momentum.- 4.5 The shallow atmosphere approximation. - 4.6 The beta effect and the spherical Earth. - 5 Scale analysis and its applications. - 5.1 Principles of scaling methods. - 5.2 The use of a reference atmosphere. - 5.3 The horizontal momentum equations. - 5.4 Natural coordinates, geostrophic and gradient wind balance. - 5.5 Vertical motion. - 5.6 The vertical momentum equation. - 5.7 The mass continuity equation. - 5.8 The thermodynamic energy equation. - 5.9 Scalings for Rossby numbers that are not small. - 6 Alternative vertical coordinates. - 6.1 A general vertical coordinate. - 6.2 Isobaric coordinates. - 6.3 Other pressure-based vertical coordinates. - 6.4 Isentropic coordinates. - 7 Variations of density and the basic equations. - 7.1 Boussinesq approximation. - 7.2 Anelastic approximation. - 7.3 Stratification and gravity waves. - 7.4 Balance, gravity waves and Richardson number. - 7.5 Summary of the basic equation sets. - 7.6 The energy of atmospheric motions. - Theme 2 Rotation in the atmosphere. - 8 Rotation in the atmosphere. - 8.1 The concept of vorticity. - 8.2 The vorticity equation. - 8.3 The vorticity equation for approximate sets of equations. - 8.4 The solenoidal term. - 8.5 The expansion/contraction term. - 8.6 The stretching and tilting terms. - 8.7 Friction and vorticity. - 8.8 The vorticity equation in alternative vertical coordinates. - 8.9 Circulation. - 9 Vorticity and the barotropic vorticity equation. - 9.1 The barotropic vorticity equation. - 9.2 Poisson's equation and vortex interactions. - 9.3 Flow over a shallow hill. - 9.4 Ekman pumping. - 9.5 Rossby waves and the beta plane. - 9.6 Rossby group velocity. - 9.7 Rossby ray tracing. - 9.8 Inflexion point instability. - 10 Potential vorticity. - 10.1 Potential vorticity. - 10.2 Alternative derivations of Ertel's theorem. - 10.3 The principle of invertibility. - 10.4 Shallow water equation potential vorticity. - 11 Turbulence and atmospheric flow. - 11.1 The Reynolds number . - 11.2 Three-dimensional flow at large Reynolds number. - 11.3 Two-dimensional flow at large Reynolds number. - 11.4 Vertical mixing in a stratified fluid. - 11.5 Reynolds stresses. - Theme 3 Balance in atmospheric flow. - 12 Quasi-geostrophic flows. - 12.1 Wind and temperature in balanced flows. - 12.2 The quasi-geostrophic approximation. - 12.3 Quasi-geostrophic potential vorticity. - 12.4 Ertel and quasi-geostrophic potential vorticities. - 13 The omega equation. - 13.1 Vorticity and thermal advection form. - 13.2 Sutcliffe Form. - 13.3 Q-vector form. - 13.4 Ageostrophic flow and the maintenance of balance. - 13.5 Balance and initialization. - 14 Linear theories of baroclinic instability. - 14.1 Qualitative discussion. - 14.2 Stability analysis of a zonal flow. - 14.3 Rossby wave interpretation of the stability conditions. - 14.4 The Eady model. - 14.5 The Charney and other quasi-geostrophic models. - 14.6 More realistic basic states. - 14.7 Initial value problem. - 15 Frontogenesis. - 15.1 Frontal scales. - 15.2 Ageostrophic circulation. - 15.3 Description of frontal collapse. - 15.4 The semi-geostrophic Eady model. - 15.5 The confluence model. - 15.6 Upper-level frontogenesis. - 16 The nonlinear development of baroclinic waves. - 16.1 The nonlinear domain. - 16.2 Semi-geostrophic baroclinic waves. - 16.3 Nonlinear baroclinic waves on realistic jetson the sphere. - 16.4 Eddy transports and zonal mean flow changes. - 16.5 Energetics of baroclinic waves. - 17 The potential vorticity perspective. - 17.1 Setting the scene. - 17.2 Potential vorticity and vertical velocity. - 17.3 Life cycles of some baroclinic waves. - 17.4 Alternative perspectives. - 17.5 Midlatitude blocking. - 17.6 Frictional and heating effects. - 18 Rossby wave propagation and potential vorticity mixing. - 18.1 Rossby wave propagation. - 18.2 Propagation of Rossby waves into the stratosphere. - 18.3 Propagation through a slowly varying medium. - 18.4 The Eliassen-Palm flux and group velocity. - 18.5 Baroclinic life cycles and Rossby waves. - 18.6 Variations of amplitude. - 18.7 Rossby waves and potential vorticity steps. - 18.8 Potential vorticity steps and the Rhines scale. - Appendices. - Appendix A: Notation. - Appendix B: Revision of vectors and vector calculus. - B.1 Vectors and their algebra. - B.2 Products of vectors. - B.3 Scalar fields and the grad operator. - B.4 The divergence and curl operators. - B.5 Gauss' and Stokes' theorems. - B.6 Some useful vector identities. - Index.