Dynamical Oceanography. Part I: Fundamental Principles

Robert O. Reid

 
• Contents
• Kinematics of Fluids
  • Scalars, vectors and tensors
  • Vector and indicial notation
    • Gradient of a scalar field
    • Divergence of a vector field
    • Curl of a vector field
  • The Lagrangian and Eulerian descriptions of motion
    • Methods of representation of a vector field
  • Acceleration: Lagrangian description
    • Acceleration: Eulerian description
  • The basic kinematic modes of a fluid
  • Vorticity
    • Circulation
    • Stokes' theorem
    • Vorticity in polar coordinates
    • Computation of vorticity and circulation
  • Deformation
    • Divergence
    • Deformation in two dimensions
  • Kinematic classification of fluid motion
  • Streamfunction for two-dimensional flow
  • Velocity potential
  • Laplacian flow
    • Conformal mapping
  • Kinematic boundary condition
  • Application of the boundary condition for Laplacian flow adjacent to a solid cylinder
  • Kelvin's theorem of minimum kinetic energy
  • Addition of velocity potentials
• Geostatics and Dynamics: The Earth as a Reference System
  • Absolute gravitational force
  • Gravity
  • Gravity anomalies
  • Tidal forces
    • Equilibrium of the earth-moon system
    • Tidal forces associated with the moon
    • Tidal forces associated with the sun
    • The equlibrium surface or tide potential
    • The time variation of the tidal forces
  • Conservative force field
  • Geopotential
  • Configuration of level surfaces on the Earth
    • The sea level reference geoid
    • Changes in the reference geoid associated with variations in the angular speed of the earth
  • Geometrical spacing of the equigeopotential surfaces in the sea and the air
  • Dynamic height and dynamic depth
  • Relative velocity in a moving coordinate system
  • Rate of change of a vector in a moving coordinate system
  • Relative and absolute acceleration
  • Geostrophic acceleration
  • Other accelerations related to the earth's motion
• Fluid Density and Hydrostatic Pressure
  • A fluid defined
    • A fluid mixture
  • Isotropy of hydrostatic pressure
  • Fluid density defined
  • The hydrostatic equation
    • Units of pressure
  • Quasi-hydrostatic conditions
  • Homogeneous fluid
  • Barotropic fluid
  • Baroclinic fluid
  • The two-layer model
    • Slopes of the isobaric surfaces in a two-layer barotropic fluid
  • Relation between isobaric slopes and isopycnal slopes in a baroclinic fluid
  • The equation of state for sea water
  • Isobaric slopes in terms of the field of temperature and salinity
  • Potential density and sigma-t
  • Hydrostatic stability
• The Fundamental Equations of Hydro-Thermo-Dynamics of a Real Fluid
  • The Four Basic Principles
  • Fluid Velocity
  • The Equation of Continuity
  • The Continuity of Salt
  • Advective and Non-Advective Transport
  • Non-Conservative Constituents
  • Conservation of Momentum: The Equations of Absolute Motion
  • Symmetry of the viscous stress tensor
  • Equation of relative motion on the rotating earth
  • Generation and dissipation of mechanical energy
  • Conservation of total energy
  • The first law of thermodynamics
  • A special case of the first law
  • Temperature and entropy-the Kelvin hypothesis
  • A more general form of the Kelvin hypothesis for pure fluids
  • Gibbs' extension of the Kelvin hypothesis to fluid mixtures
  • Evaluation of the equations of state for gases
  • Some further consequences of the Kelvin hypothesis
  • The second law of thermodynamics
  • The integral form of the second law
    • Extension of equations for mixtures to more than two constitutents
    • Free energy function
    • Mixture of ideal gases
  • Some direct consequences of the second law in regard to the behavior of the entropy function
  • Boundary conditions for the flux of salt and the kinematic condition in the presence of evaporation
  • Boundary condition on the temperature or heat flux at the surface
  • Boundary condition on the stress
  • Summary of fundamental relations
• Some Special Laws of Non-Advective Transfer of Properties
  • Fourier's law of heat conduction
  • Diffusion
  • Viscous stresses
  • Diffusion-drag theory
• References
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