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Geophysical waves and flows. Theory and applications in the atmosphere, hydrosphere and geosphere. (English) Zbl 1387.86002

Cambridge: Cambridge University Press (ISBN 978-1-107-18619-4/hbk; 978-1-316-88885-8/ebook). xiii, 505 p. (2017).
This is a very useful and handy book on theory, mathematical derivations and applications of waves and flows in fluids in numerous geophysical configurations encountered in environments of the earth’s atmosphere, oceans and mantle. It can serve both as a good textbook for graduate students and a reference book for professional researchers in particular fields of geophysics.
The text in 13+505 pages is organized in 35 Chapters grouped into 8 Parts followed by References and Index. Part I containing the first two Chapters is introductory with basic definitions and explanations regarding the subject of the book. Six Chapters 3–8 of Part II deal with theoretical and mathematical essentials of fluid kinematics, dynamics and rheology. This includes geophysical flows with deformation, strain and stress tensors, related thermodynamics, statics and dynamics of perturbations, boundary layers and introduction to effects in rotating fluids. Part III with Chapters 9–14 is devoted to a variety of waves in non-rotating fluids such as elastic waves, deep water waves, linear and non-linear, dispersive and non-dispersive shallow water waves, capillary waves, interfacial, and internal gravity waves. Part IV with Chapters 15–18 deals with waves in rotating fluids such as geostrophic, inertial and Rossby waves, rotationally modified Poincaré, interfacial and internal gravity waves, and equatorial, costal and topographic waves. Part V treats flows of non-rotating geophysical fluids. Its Chapters 19–24 describe theory of steady and unsteady channel flows including formation of hydraulic shock wave discontinuities, flash floods, and gravitationally forced flows. Problems of rotating geophysical flows are dealt with in Chapters 25–28 in Part VI. Here one finds details on Ekman layers and atmospheric flows such as general circulation, thermal winds, jet streams, and vortex formation including hurricanes and tornados. One chapter is devoted to effects of atmospheric motions in formation and transports of ocean currents and thermohaline circulation. Various types of silicate flows in the Earth’s molten interior are treated in Part VII where Chapters 29–35 cover the basic theory of the flow dynamics with equations for given thermodynamic conditions. This includes modelling the heat balance and transport, plate tectonics, essentials of volcanism, and lava flows. The final Part VIII comprises 7 Appendices each offering basic introductory essentials on fluid dynamics starting from necessary mathematical elements, dimensions and units, through kinematics, dynamics and thermodynamics to waves and fluid flows.

MSC:

86-02 Research exposition (monographs, survey articles) pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
86A99 Geophysics
76A10 Viscoelastic fluids
76U05 General theory of rotating fluids
76B60 Atmospheric waves (MSC2010)
76B65 Rossby waves (MSC2010)
76D17 Viscous vortex flows
76D33 Waves for incompressible viscous fluids
76B70 Stratification effects in inviscid fluids
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