Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere

Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere
Author: Yuri N. Skiba
Publisher: Springer
Total Pages: 246
Release: 2017-09-21
Genre: Mathematics
ISBN: 3319654128

This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.

Incompressible Flow

Incompressible Flow
Author: Ronald L. Panton
Publisher: John Wiley & Sons
Total Pages: 912
Release: 2013-08-05
Genre: Science
ISBN: 1118013433

The most teachable book on incompressible flow— now fully revised, updated, and expanded Incompressible Flow, Fourth Edition is the updated and revised edition of Ronald Panton's classic text. It continues a respected tradition of providing the most comprehensive coverage of the subject in an exceptionally clear, unified, and carefully paced introduction to advanced concepts in fluid mechanics. Beginning with basic principles, this Fourth Edition patiently develops the math and physics leading to major theories. Throughout, the book provides a unified presentation of physics, mathematics, and engineering applications, liberally supplemented with helpful exercises and example problems. Revised to reflect students' ready access to mathematical computer programs that have advanced features and are easy to use, Incompressible Flow, Fourth Edition includes: Several more exact solutions of the Navier-Stokes equations Classic-style Fortran programs for the Hiemenz flow, the Psi-Omega method for entrance flow, and the laminar boundary layer program, all revised into MATLAB A new discussion of the global vorticity boundary restriction A revised vorticity dynamics chapter with new examples, including the ring line vortex and the Fraenkel-Norbury vortex solutions A discussion of the different behaviors that occur in subsonic and supersonic steady flows Additional emphasis on composite asymptotic expansions Incompressible Flow, Fourth Edition is the ideal coursebook for classes in fluid dynamics offered in mechanical, aerospace, and chemical engineering programs.

Collected Papers in Honor of Yoshihiro Shibata

Collected Papers in Honor of Yoshihiro Shibata
Author: Tohru Ozawa
Publisher: Springer Nature
Total Pages: 396
Release: 2023-01-01
Genre: Mathematics
ISBN: 3031192524

Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here — on the occasion of his 70th birthday — are written by world-renowned researchers and celebrate his decades of outstanding achievements.

Treatise on Geophysics, Volume 8

Treatise on Geophysics, Volume 8
Author: Peter L. Olson
Publisher: Elsevier
Total Pages: 373
Release: 2010-05-18
Genre: Science
ISBN: 0444535772

Treaties on Geophysics: Core Dynamics, Volume 8, provides a comprehensive review of the current state of understanding of core dynamics. The book begins by analyzing a subject of long-standing and on-going controversy: the gross energetics of the core. It then explains the important elements of dynamo theory; actual fluid motions in the core; the basic physical principles involved in thermochemical convection in the core and the basic equations governing the convection; and turbulence and the small-scale dynamics of the core. This is followed by discussions of the state of knowledge on rotation-induced core flows; the use of first-principles numerical models of self-sustaining fluid dynamos; and the behavior of polarity reversals in numerical dynamo models. The remaining chapters cover the various roles the inner core plays in core dynamics and the geodynamo; experiments that have shaped knowledge about the flows in the core that produce the geodynamo and govern its evolution; and ways the mantle can affect core dynamics, and corresponding ways the core can affect the mantle. - Self-contained volume starts with an overview of the subject then explores each topic with in depth detail - Extensive reference lists and cross references with other volumes to facilitate further research - Full-color figures and tables support the text and aid in understanding - Content suited for both the expert and non-expert

Stability of Fluid Motions I

Stability of Fluid Motions I
Author: D. D. Joseph
Publisher: Springer Science & Business Media
Total Pages: 295
Release: 2013-03-07
Genre: Science
ISBN: 364280991X

The study of stability aims at understanding the abrupt changes which are observed in fluid motions as the external parameters are varied. It is a demanding study, far from full grown"whose most interesting conclusions are recent. I have written a detailed account of those parts of the recent theory which I regard as established. Acknowledgements I started writing this book in 1967 at the invitation of Clifford Truesdell. It was to be a short work on the energy theory of stability and if I had stuck to that I would have finished the writing many years ago. The theory of stability has developed so rapidly since 1967 that the book I might then have written would now have a much too limited scope. I am grateful to Truesdell, not so much for the invitation to spend endless hours of writing and erasing, but for the generous way he has supported my efforts and encouraged me to higher standards of good work. I have tried to follow Truesdell's advice to write this work in a clear and uncomplicated style. This is not easy advice for a former sociologist to follow; if I have failed it is not due to a lack of urging by him or trying by me. My research during the years 1969-1970 was supported in part by a grant from the Guggenheim foundation to study in London.

Numerical Analysis of Spectral Methods

Numerical Analysis of Spectral Methods
Author: David Gottlieb
Publisher: SIAM
Total Pages: 175
Release: 1977-01-01
Genre: Technology & Engineering
ISBN: 9781611970425

A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.

Treatise on Geophysics

Treatise on Geophysics
Author:
Publisher: Elsevier
Total Pages: 5604
Release: 2015-04-17
Genre: Science
ISBN: 0444538038

Treatise on Geophysics, Second Edition, is a comprehensive and in-depth study of the physics of the Earth beyond what any geophysics text has provided previously. Thoroughly revised and updated, it provides fundamental and state-of-the-art discussion of all aspects of geophysics. A highlight of the second edition is a new volume on Near Surface Geophysics that discusses the role of geophysics in the exploitation and conservation of natural resources and the assessment of degradation of natural systems by pollution. Additional features include new material in the Planets and Moon, Mantle Dynamics, Core Dynamics, Crustal and Lithosphere Dynamics, Evolution of the Earth, and Geodesy volumes. New material is also presented on the uses of Earth gravity measurements. This title is essential for professionals, researchers, professors, and advanced undergraduate and graduate students in the fields of Geophysics and Earth system science. Comprehensive and detailed coverage of all aspects of geophysics Fundamental and state-of-the-art discussions of all research topics Integration of topics into a coherent whole