Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Equilibrium thermodynamics of sea water
- 3 Balance equations
- 4 Molecular flux laws
- 5 The gravitational potential
- 6 The basic equations
- 7 Dynamic impact of the equation of state
- 8 Free wave solutions on a sphere
- 9 Asymptotic expansions
- 10 Reynolds decomposition
- 11 Boussinesq approximation
- 12 Large-scale motions
- 13 Primitive equations
- 14 Representation of vertical structure
- 15 Ekman layers
- 16 Planetary geostrophic flows
- 17 Tidal equations
- 18 Medium-scale motions
- 19 Quasi-geostrophic flows
- 20 Motions on the f-plane
- 21 Small-scale motions
- 22 Sound waves
- Appendix A Equilibrium thermodynamics
- Appendix B Vector and tensor analysis
- Appendix C Orthogonal curvilinear coordinate systems
- Appendix D Kinematics of fluid motion
- Appendix E Kinematics of waves
- Appendix F Conventions and notation
- References
- Index
2 - Equilibrium thermodynamics of sea water
Published online by Cambridge University Press: 03 February 2010
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Equilibrium thermodynamics of sea water
- 3 Balance equations
- 4 Molecular flux laws
- 5 The gravitational potential
- 6 The basic equations
- 7 Dynamic impact of the equation of state
- 8 Free wave solutions on a sphere
- 9 Asymptotic expansions
- 10 Reynolds decomposition
- 11 Boussinesq approximation
- 12 Large-scale motions
- 13 Primitive equations
- 14 Representation of vertical structure
- 15 Ekman layers
- 16 Planetary geostrophic flows
- 17 Tidal equations
- 18 Medium-scale motions
- 19 Quasi-geostrophic flows
- 20 Motions on the f-plane
- 21 Small-scale motions
- 22 Sound waves
- Appendix A Equilibrium thermodynamics
- Appendix B Vector and tensor analysis
- Appendix C Orthogonal curvilinear coordinate systems
- Appendix D Kinematics of fluid motion
- Appendix E Kinematics of waves
- Appendix F Conventions and notation
- References
- Index
Summary
The basic equations of oceanic motion assume local thermodynamic equilibrium. The ocean is viewed as consisting of many fluid parcels. Each of these fluid parcels is assumed to be in thermodynamic equilibrium though the ocean as a whole is far from thermodynamic equilibrium. Later we make the continuum hypothesis and assume that these parcels are sufficiently small from a macroscopic point of view to be treated as points but sufficiently large from a microscopic point of view to contain enough molecules for equilibrium thermodynamics to apply. This chapter considers the equilibrium thermodynamics that holds for each of these fluid parcels or points. The thermodynamic state is described by thermodynamic variables. Most of this chapter defines these thermodynamic variables and the relations that hold among them. An important point is that sea water is a two-component system, consisting of water and sea salt. Gibbs' phase rule then implies that the thermodynamic state of sea water is completely determined by the specification of three independent thermodynamic variables. Different choices can be made for these independent variables. Pressure, temperature, and salinity are one common choice. All other variables are functions of these independent variables. In principle, these functions can be derived from the microscopic properties of sea water, by means of statistical mechanics. This has not been accomplished yet. Rather, these functions must be determined empirically from measurements and are documented in figures, tables, and numerical formulae.We do not present these figures, tables, and formulae in any detail.
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- Chapter
- Information
- The Equations of Oceanic Motions , pp. 10 - 31Publisher: Cambridge University PressPrint publication year: 2006