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000800060 019__ $$a1004673038$$a1004942935
000800060 020__ $$a9783319654126$$q(electronic book)
000800060 020__ $$a3319654128$$q(electronic book)
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000800060 08204 $$a620.1/0640151$$223
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000800060 1001_ $$aSkiba, Yuri N.$$q(Yuri Nickolavich)
000800060 24510 $$aMathematical problems of the dynamics of incompressible fluid on a rotating sphere /$$cYuri N. Skiba.
000800060 260__ $$aCham :$$bSpringer,$$c2017.
000800060 300__ $$a1 online resource.
000800060 336__ $$atext$$btxt$$2rdacontent
000800060 337__ $$acomputer$$bc$$2rdamedia
000800060 338__ $$aonline resource$$bcr$$2rdacarrier
000800060 504__ $$aIncludes bibliographical references and index.
000800060 5050_ $$aPreface; Contents; 1 Introduction; 2 Spaces of Functions on a Sphere; 2.1 Spherical Harmonics; 2.2 Geographical Coordinates Maps; 2.3 Orthogonal Projections on Hn and Fractional Derivatives; 2.4 Hilbert Spaces Hs on a Sphere; 2.5 Space C(S) of Continuous Functions on a Sphere; 2.6 Some Estimates in the Norms of Lp(S) and Lp(0,T; X); 3 Solvability of Vorticity Equation on a Sphere; 3.1 Vortex Dynamics of Viscous Incompressible Fluid; 3.2 Properties of Jacobian Determinant; 3.3 Unique Solvability of a Non-Stationary Problem; 3.4 Solvability of a Stationary Vorticity Equation
000800060 5058_ $$a4.7 Distance Between Solutions4.8 Euler Angles; 5 Stability of Rossby-Haurwitz (RH) Waves; 5.1 Conservation Laws for Arbitrary Perturbations to RH Wave; 5.2 Invariant Sets, Quotient Space and Norm of Perturbations; 5.3 A Hyperbolic Law for Perturbations from M-n and M+n; 5.4 Geometric Interpretation of Variations in the Perturbation Energy; 5.5 Liapunov Instability of Non-Zonal RH Wave; 5.6 Exponential Instability of RH Wave; 5.7 Normal Mode Instability of Zonal RH Waves and LP Flows; 6 Stability of Modons and Wu-Verkley Waves; 6.1 Steady Wu-Verkley Waves and Modons
000800060 5058_ $$a6.2 Conservation Law for Disturbances of WV Wave and Modon6.3 Conditions for Exponential Instability of WV Waves and Modons; 6.4 Bounds of Growth Rate and Orthogonality of Unstable Modes; 6.5 Dipole Modons Moving Along the Same Latitudinal Circle; 6.6 Liapunov Instability of Dipole Modons; 7 Linear and Nonlinear Stability of Flows; 7.1 Shear Flow Stability; 7.2 Linear Stability of Zonal Flows; 7.3 Nonlinear Stability; 7.4 Instantaneous Evolution of Kinetic Energy of Perturbations; 7.5 The First Mechanism of Generation of the Energy of Perturbation Near a Zonal Jet
000800060 5058_ $$a7.6 Generalized Eliassen-Palm Flux and the Eigenvalue Problem Method7.7 Numerical Example: Analysis of Climatic January Circulation; 8 Numerical Study of Linear Stability; 8.1 Method of Normal Modes; 8.2 Spectrum of Linearized Operator for Viscous Fluid; 8.3 One Estimate in Terms of the Graph Norm of Operator; 8.4 Spectral Approximation; 8.5 Rate of Convergence Estimates; 8.6 Spectrum of Linearized Operator for Ideal Fluid; 8.7 Stability Matrix in the Basis of Spherical Harmonics; 8.8 Stationary States Having Block Diagonal Structure of Stability Matrix
000800060 506__ $$aAccess limited to authorized users.
000800060 520__ $$aThis 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.
000800060 588__ $$aDescription based on print version record.
000800060 650_0 $$aFluid dynamics$$xMathematics.
000800060 77608 $$iPrint version:$$z9783319654119$$z331965411X$$w(OCoLC)994639481
000800060 852__ $$bebk
000800060 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-65412-6$$zOnline Access$$91397441.1
000800060 909CO $$ooai:library.usi.edu:800060$$pGLOBAL_SET
000800060 980__ $$aEBOOK
000800060 980__ $$aBIB
000800060 982__ $$aEbook
000800060 983__ $$aOnline
000800060 994__ $$a92$$bISE