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  • 1
    Monograph available for loan
    Monograph available for loan
    Lectures on geophysical fluid dynamics (1998)
    New York [u.a.] : Oxford Univ. Press
    Details Availability
    Call number: AWI A15-05-0034 ; PIK N 450-99-0434
    Description / Table of Contents: Contents: 1 Fundamentals. - 1. Eulerian and Lagrangian Descriptions. - 2. Mass Conservation. - 3. Functionals and Variational Principles. - 4. Hamilton's Principle for Point Masses. - 5.Hamilton's Principle for a Barotropic Fluid. - 6. Nonhomentropic Flow. - 7. Variable Composition. - 8. Equations of Motion for an Ideal Fluid. - 9. The Method of Averaging. - 10. Momentum Equation by the Method of Averaging. - 11. An Example of Kinetic Theory. - 12. Thermodynamic Constraints on Molecular Diffusion. - 13. Macroscopic Averages of the Equations of Motion. - 14. Stirring and Mixing. - 15. Static Stability. - 16. Potential Density and Potential Temperature. - 17. The Equation of State for Seawater. - 18. Statistical Mechanics: The Idea lGas. - 2 Introduction to Geophysical Fluid Dynamics. - 1. Equations Of Motion in Rotating Coordinates. - 2. Geostrophic, Hydrostatic Flow. - 3. The Shallow-water Equations. - 4. Potential Vorticity. - 5. The Quasigeostrophic Equation. - 6. A Second Look at the Quasigeostrophic Equation. - 7. Plane-wave Solutions of the Linear Equations. - 8. A Practical Benefit Of Filtering Out Inertia-gravity Waves. - 9. Geostrophic Adjustment. - 10. A Third Look at the Quasigeostrophic Equation. - 11. Rigid-lid Approximation. - 12. Two-layer Equations. - 13. Two-layer Rossby Waves. - 14. Available Potential Energy. - 15. Baroclinic Instability. - 16. Primitive Equations for the Ocean. - 17. Primitive Equations for the Atmosphere. - 18. Primitive Equations in Isentropic Coordinates. - 19. Quasigeostrophic Equations for Continuously Stratified Flow. - 20. Two-level Quasigeostrophic Equations. - 21. Quasigeostrophic Flow over Topography. - 3 Noninertial Theory of Ocean Circulation. - 1. Overview. - 2. Rotating Sector Models. - 3. Boundary-layer Methods. - 4. Theory of the Depth-averaged Circulation. - 5. Ekman Layers. - 6. A Second Look at Ekman Layers. - 7. Spin-up in the Laboratory. - 8. Simplified Inertia-less Equations. - 9. Linear Solutions of the Simplified Equations. - 10. The Case of Homogeneous Fluid. - 11. The Case of Stratified Fluid. - 12. Spin-up in the Ocean. - 13. The Effect Of Bottom Topography. - 14. Stratified Flow over Bottom Topography. - 15. A Nonlinear Model. - 16. The Thermocline. - 4 Vorticity and Turbulence. - 1. The Vorticity Equation. - 2. Ertel's Theorem. - 3. A Deeper Look at Potential Vorticity. - 4. Alternative Statements of the Vorticity Law. - 5. Turbulence. - 6. Kolmogorov's Theory. - 7. Intermittency and the Beta-model. - 8. Two-dimensional Turbulence. - 9. More Two-dimensional Turbulence. - 10. Energy Transfer in Two and Three Dimensions. - 5 Statistical Fluid Dynamics. - 1. The Closure Problem of Turbulence. - 2. The Eddy-damped Markovian Model. - 3. Stochastic Model Representation. - 4. Entropy. - 5. The Entropy Principle. - 6. Equilibrium Statistical Mechanics. - 7. The Meaning of Absolute Equilibrium. - 6 Geostrophic Turbulence. - 1. Quasigeostrophic Flow over Topography. - 2. The Statistical Mechanics of Flow over Topography. - 3. Flow on the Beta-plane. - 4. Stratified Quasigeostrophic Flow. - 5. Two-layer Turbulence. - 7 Hamiltonian Fluid Dynamics. - 1. Symmetry and Conservation Laws. - 2. The Particle-relabeling Symmetry Property. - 3. Sound Waves in One Dimension: The Conservation of Wave Action. - 4. Sound Waves in One Dimension: The Equations for the Mean Flow. - 5. Sound Waves in Three Dimensions: Particle-relabeling and Nonacceleration. - 6. Approximations and Constraints. - 7. The Canonical Equations. - 8. Eulerian Forms of Hamilton's Principle. - 9. The Geometrical View of Dynamics. - 10. Noncanonical Hamiltonian Dynamics. - 11. Poisson Brackets for Fluids. - 12. Pseudoenergy, Stability, and Available Energy. - 13. Dynamical Approximations: The Semigeostrophic Equations. - References. - Index.
    Type of Medium: Monograph available for loan
    Pages: XIII, 378 S. , graph. Darst.
    ISBN: 0195108086
    Location: A 18 - must be ordered
    Branch Library: AWI Library
    Branch Library: PIK Library
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  • 2
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    Shallow water equations with a complete Coriolis force and topography (2005)
    American Institute of Physics
    Details
    Publication Date: 2005-01-01
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
    Published by American Institute of Physics
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  • 3
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    On the vorticity of long gravity waves in water of variable depth (1997)
    Elsevier
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    Publication Date: 1997-05-01
    Print ISSN: 0165-2125
    Electronic ISSN: 1878-433X
    Topics: Geosciences , Physics
    Published by Elsevier
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  • 4
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    A general method for conserving quantities related to potential vorticity in numerical models (2005)
    Institute of Physics
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    Publication Date: 2005-06-06
    Print ISSN: 0951-7715
    Electronic ISSN: 1361-6544
    Topics: Mathematics , Physics
    Published by Institute of Physics
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  • 5
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    Large-scale semigeostrophic equations for use in ocean circulation models (1996)
    Cambridge University Press
    Details
    Publication Date: 1996-07-01
    Description: Hamiltonian approximation methods yields approximate dynamical equations that apply to nearly geostrophic flow at scales larger than the internal Rossby deformation radius. These equations incorporate fluid inertia with the same order of accuracy as the semi-geostrophic equations, but are nearly as simple (in appropriate coordinates) as the equations obtained by completely omitting the inertia.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 6
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    Practical use of Hamilton's principle (1983)
    Cambridge University Press
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    Publication Date: 1983-07-01
    Description: Hamilton's principle of mechanics has special advantages as the beginning point for approximations. First, it is extremely succinct. Secondly, it easily accommodates moving disconnecting fluid boundaries. Thirdly, approximations-however strong-that maintain the symmetries of the Hamiltonian will automatically preserve the corresponding conservation laws. For example, Hamilton’s principle allows useful analytical and numerical approximations to the equations governing the motion of a homogeneous rotating fluid with free boundaries. © 1983, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Analogous formulation of electrodynamics and two-dimensional fluid dynamics (2014)
    Cambridge University Press
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    Publication Date: 2014-11-18
    Description: A single, simply stated approximation transforms the equations for a two-dimensional perfect fluid into a form that is closely analogous to Maxwell's equations in classical electrodynamics. All the fluid conservation laws are retained in some form. Waves in the fluid interact only with vorticity and not with themselves. The vorticity is analogous to electric charge density, and point vortices are the analogues of point charges. The dynamics is equivalent to an action principle in which a set of fields and the locations of the point vortices are varied independently. We recover classical, incompressible, point vortex dynamics as a limiting case. Our full formulation represents the generalization of point vortex dynamics to the case of compressible flow. © 2014 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    An alternative view of generalized Lagrangian mean theory (2013)
    Cambridge University Press
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    Publication Date: 2013-02-19
    Description: If the variables describing wave-mean flow interactions are chosen to include a set of fluid-particle labels corresponding to the mean flow, then the generalized Lagrangian mean (GLM) theory takes the form of an ordinary classical field theory. Its only truly distinctive features then arise from the distinctive feature of fluid dynamics as a field theory, namely, the particle-relabelling symmetry property, which corresponds by Noether's theorem to the many vorticity conservation laws of fluid mechanics. The key feature of the formulation is that all the dependent variables depend on a common set of space-time coordinates. This feature permits an easy and transparent derivation of the GLM equations by use of the energy-momentum tensor formalism. The particle-relabelling symmetry property leads to the GLM potential vorticity law in which pseudo-momentum is the only wave activity term present. Thus the particle-relabelling symmetry explains the prominent importance of pseudo-momentum in GLM theory. © Cambridge University Press 2013.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    Entropy budget and coherent structures associated with a spectral closure model of turbulence (2018)
    Cambridge University Press
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    Publication Date: 2018-10-29
    Description: We 'derive' the eddy-damped quasi-normal Markovian model (EDQNM) by a method that replaces the exact equation for the Fourier phases with a solvable stochastic model, and we analyse the entropy budget of the EDQNM. We show that a quantity that appears in the probability distribution of the phases may be interpreted as the rate at which entropy is transferred from the Fourier phases to the Fourier amplitudes. In this interpretation, the decrease in phase entropy is associated with the formation of structures in the flow, and the increase of amplitude entropy is associated with the spreading of the energy spectrum in wavenumber space. We use Monte Carlo methods to sample the probability distribution of the phases predicted by our theory. This distribution contains a single adjustable parameter that corresponds to the triad correlation time in the EDQNM. Flow structures form as the triad correlation time becomes very large, but the structures take the form of vorticity quadrupoles that do not resemble the monopoles and dipoles that are actually observed. © 2018 Cambridge University Press.
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    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    Variational treatment of inertia–gravity waves interacting with a quasi-geostrophic mean flow (2016)
    Cambridge University Press
    Details
    Publication Date: 2016-11-14
    Description: The equations for three-dimensional hydrostatic Boussinesq dynamics are equivalent to a variational principle that is closely analogous to the variational principle for classical electrodynamics. Inertia-gravity waves are analogous to electromagnetic waves, and available potential vorticity (i.e. the amount by which the potential vorticity exceeds the potential vorticity of the rest state) is analogous to electric charge. The Lagrangian can be expressed as the sum of three parts. The first part corresponds to quasi-geostrophic dynamics in the absence of inertia-gravity waves. The second part corresponds to inertia-gravity waves in the absence of quasi-geostrophic flow. The third part represents a coupling between the inertia-gravity waves and quasi-geostrophic motion. This formulation provides the basis for a general theory of inertia-gravity waves interacting with a quasi-geostrophic mean flow. © 2016 Cambridge University.
    Print ISSN: 0022-1120
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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