| Description |
1 online resource |
| Series |
Cambridge monographs on mechanics |
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Cambridge monographs on mechanics.
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| Contents |
12.7 A Byproduct: The Viscous Decay Factor -- 13 Fluid Motion in Longitudinally Librating Spheres -- 13.1 Formulation -- 13.2 Asymptotic Solutions -- 13.2.1 Why Resonance Cannot Occur -- 13.2.2 Asymptotic Analysis -- 13.2.3 Three Fundamental Modes Excited -- 13.3 Linear Numerical Solution -- 13.4 Nonlinear Direct Numerical Simulation -- 14 Fluid Motion in Precessing Oblate Spheroids -- 14.1 Formulation -- 14.2 Inviscid Solution -- 14.3 Exact Nonlinear Solution -- 14.4 Viscous Solution -- 14.5 Properties of Nonlinear Precessing Flow -- 14.6 A Byproduct: The Viscous Decay Factor -- 15 Fluid Motion in Latitudinally Librating Spheroids -- 15.1 Formulation -- 15.2 Analytical Solution: Non-resonant Librating Flow -- 15.3 Analytical Solution: Resonant Librating Flow -- 15.4 Nonlinear Direct Numerical Simulation -- 15.5 Comparison: Analytical vs. Numerical -- Part 4 Convection in Uniformly Rotating Systems -- 16 Introduction -- 16.1 Rotating Convection vs. Precession/Libration -- 16.2 Key Parameters for Rotating Convection -- 16.3 Rotational Constraint on Convection -- 16.4 Types of Rotating Convection -- 16.4.1 Viscous Convection Mode -- 16.4.2 Inertial Convection Mode -- 16.4.3 Transitional Convection Mode -- 16.5 Convection in Various Rotating Geometries -- 16.5.1 Rotating Annular Channels -- 16.5.2 Rotating Circular Cylinders -- 16.5.3 Rotating Spheres or Spherical Shells -- 17 Convection in Rotating Narrow-gap Annuli -- 17.1 Formulation -- 17.2 A Finite-difference Method for Nonlinear Convection -- 17.3 Stationary Viscous Convection -- 17.3.1 Governing Equations -- 17.3.2 Asymptotic Solution for Î#x93;(Ta)1/6 1/6 = O(1) -- 17.3.4 Numerical Solution Using a Galerkin-tau Method -- 17.3.5 Comparison: Analytical vs. Numerical -- 17.3.6 Nonlinear Properties of Stationary Convection |
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17.4 Oscillatory Viscous Convection -- 17.4.1 Governing Equations -- 17.4.2 Symmetry between Two Different Oscillatory Solutions -- 17.4.3 Asymptotic Solutions Satisfying the Boundary Condition -- 17.4.4 Comparison: Analytical vs. Numerical -- 17.4.5 Comparison with an Unbounded Rotating Layer -- 17.4.6 Nonlinear Properties with Î#x93; = O(Ta-1/6) -- 17.4.7 Nonlinear Properties with Î#x93; >> O(Ta-1/6) -- 17.5 Viscous Convection with Curvature Effects -- 17.5.1 Onset of Viscous Convection -- 17.5.2 Nonlinear Properties of Viscous Convection -- 17.6 Inertial Convection: Non-axisymmetric Solutions -- 17.6.1 Asymptotic Expansion -- 17.6.2 Non-dissipative Thermal Inertial Wave -- 17.6.3 Asymptotic Solution with Stress-free Condition -- 17.6.4 Asymptotic Solution with No-slip Condition -- 17.6.5 Numerical Solution Using a Galerkin Spectral Method -- 17.6.6 Comparison: Analytical vs. Numerical -- 17.6.7 Nonlinear Properties of Inertial Convection -- 17.7 Inertial Convection: Axisymmetric Torsional Oscillation -- 18 Convection in Rotating Cylinders -- 18.1 Formulation -- 18.2 Convection with Stress-free Condition -- 18.2.1 Asymptotic Solution for Inertial Convection -- 18.2.2 Asymptotic Solution for Viscous Convection -- 18.2.3 Numerical Solution Using a Chebyshev-tau Method -- 18.2.4 Comparison: Analytical vs. Numerical -- 18.3 Convection with No-slip Condition -- 18.3.1 Asymptotic Solution for Inertial Convection -- 18.3.2 Asymptotic Solution for Viscous Convection -- 18.3.3 Numerical Solution Using a Galerkin-type Method -- 18.3.4 Comparison: Analytical vs. Numerical -- 18.3.5 Effect of Thermal Boundary Condition -- 18.3.6 Axisymmetric Inertial Convection -- 18.4 Transition to Weakly Turbulent Convection -- 18.4.1 A Finite Element Method for Nonlinear Convection -- 18.4.2 Inertial Convection: From Single Inertial Mode to Weak Turbulence |
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18.4.3 Viscous Convection: From Sidewall-localized Mode to Weak Turbulence -- 19 Convection in Rotating Spheres or Spherical Shells -- 19.1 Formulation -- 19.2 Numerical Solution using Toroidal/Poloidal Decomposition -- 19.2.1 Governing Equations under Toroidal/Poloidal Decomposition -- 19.2.2 Numerical Analysis for Stress-free or No-slip Condition -- 19.2.3 Several Numerical Solutions for 0 < Ek << 1 -- 19.2.4 Nonlinear Effects: Differential Rotation -- 19.3 Local Asymptotic Solution: A Small-gap Annular Model -- 19.3.1 The Local and Quasi-geostrophic Approximation -- 19.3.2 Asymptotic Relation for 0 < Ek << 1 -- 19.3.3 Comparison: Asymptotic vs. Numerical -- 19.4 Global Asymptotic Solution with Stress-free Condition -- 19.4.1 Hypotheses for Asymptotic Analysis -- 19.4.2 Asymptotic Analysis for Inertial Convection -- 19.4.3 Several Analytical Solutions for Inertial Convection -- 19.4.4 Differential Rotation Cannot be Sustained by Inertial Convection -- 19.4.5 Asymptotic Analysis for Viscous Convection -- 19.4.6 Typical Asymptotic Solutions for Viscous Convection -- 19.4.7 Nonlinear Effects: Differential Rotation in Viscous Convection -- 19.5 Global Asymptotic Solution with No-slip Condition -- 19.5.1 Hypotheses for Asymptotic Analysis -- 19.5.2 Asymptotic Analysis for Inertial Convection -- 19.5.3 Several Analytical Solutions for Inertial Convection -- 19.5.4 Asymptotic Analysis for Viscous Convection -- 19.5.5 Several Asymptotic Solutions for Viscous Convection -- 19.5.6 Nonlinear Effects: Differential Rotation in Viscous Convection -- 19.6 Transition to Weakly Turbulent Convection -- 19.6.1 A Finite-Element Method for Rotating Spheres -- 19.6.2 Transition to Weak Turbulence in Rotating Spheres -- 19.6.3 A Finite Difference Method for Rotating Spherical Shells -- 19.6.4 Multiple Stable Nonlinear Equilibria in Slowly Rotating Thin Spherical Shells |
| Summary |
A systematic account of the theory and modelling of rotating fluids that highlights the remarkable advances in the area and brings researchers and postgraduate students in atmospheres, oceanography, geophysics, astrophysics and engineering to the frontiers of research. Sufficient mathematical and numerical detail is provided in a variety of geometries such that the analysis and results can be readily reproduced, and many numerical tables are included to enable readers to compare or benchmark their own calculations. Traditionally, there are two disjointed topics in rotating fluids: convective fluid motion driven by buoyancy, discussed by Chandrasekhar (1961), and inertial waves and precession-driven flow, described by Greenspan (1968). Now, for the first time in book form, a unified theory is presented for three topics - thermal convection, inertial waves and precession-driven flow - to demonstrate that these seemingly complicated, and previously disconnected, problems become mathematically simple in the framework of an asymptotic approach that incorporates the essential characteristics of rotating fluids |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Rotating masses of fluid.
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Fluid mechanics.
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Fluid dynamics.
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Hydrodynamics
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TECHNOLOGY & ENGINEERING -- Hydraulics.
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Dinámica de fluidos
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Fluid dynamics
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Fluid mechanics
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Rotating masses of fluid
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| Form |
Electronic book
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| Author |
Liao, Xinhao.
|
| ISBN |
9781139024853 |
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113902485X |
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9781108296472 |
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1108296475 |
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