Description / Table of Contents:
This book gives a coherent development of the current understanding of the fluid dynamics of the middle latitude atmosphere. lt is primarily aimed at post-graduate and advanced undergraduate level students and does not assume any previous knowledge of fluid mechanics, meteorology or atmospheric science. The book will be an invaluable resource for any quantitative atmospheric scientist who wishes to increase their understanding of the subject. The importance of the rotation of the Earth and the stable stratification of its atmosphere, with their implications for the balance of larger-scale flows, is highlighted throughout. Clearly structured throughout, the first of three themes deals with the development of the basic equations for an atmosphere on a rotating, spherical planet and discusses scale analyses of these equations. The second theme explores the importance of rotation and introduces vorticity and potential vorticity, as well as turbulence. In the third theme, the concepts developed in the first two themes are used to give an understanding of balanced motion in real atmospheric phenomena. lt starts with quasi-geostrophic theory and moves on to linear and nonlinear theories for mid-latitude weather systems and their fronts. The potential vorticity perspective on weather systems is highlighted with a discussion of the Rossby wave propagation and potential vorticity mixing covered in the final chapter.
Type of Medium:
Monograph available for loan
XVIII, 408 Seiten
Advancing weather and climate science
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.
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