Dynamical Oceanography. Part II: Wave Dynamics

Robert O. Reid

• Contents
• The Hydrodynamic Problem
  • Basic hydrodynamic and thermodynamic equations
  • Equations of state for a binary fluid
    • Dry air
    • Pure water
    • Thermal stability and neutral surfaces
  • Boundary conditions for a non-diffusive, inviscid, non-heat conducting fluid
    • Fixed, impermeable boundary
    • Free surface, kinematic condition
    • Free surface, dynamic condition for zero surface tension and no viscosity
  • Linearized problem relative to a basic state of rest for an inviscid, non-diffusive, non-conducting fluid
    • Basic state of rest
    • Linearized perturbations
    • Associated energy equation
  • Linearized problem relative to a basic state with velocity shear and tilted density surfaces
    • Perturbation equations
    • Associated perturbation energy equation
• Fluid Wave Dynamics - Linear Theory
  • Some general wave kinematics
    • Wave modulation and group velocity
    • An alternate interpretation of group speed
    • A dispersive wave train
    • Space-time evolution of a resolved, progressive, plane wave group of variable wave number
    • Special cases
      • Non-dispersive wave group
      • Centered disturbances
      • Short gravity waves
      • Capillary waves
      • Short waves near the minimum group speed
      • Dispersion of a plane Tsunami wave
• Very Low Frequency Waves ()
  • Basic Equations
  • Separation of Variables
  • Gravity Modes for f Constant
  • Quasi-Geostrophic Modes (Rossby Waves)
    • The Quasi-Geostrophic Vorticity Equation
    • Rossby Modes for Constant Beta
    • Rossby Dispersion Diagram
    • Energetics of Rossby Waves
  • Reflection of Rossby waves
  • Vertically propagating Rossby waves
    • Simple plane wave solutions for N constant
• Forced Quasi-Geostrophic Disturbances
  • Steady state circulation
  • Modified Sverdrup regime with bathymetry
  • Steady state circulation
  • Modified Sverdrup regime with bathymetry
• Gravitational and Inertial Oscillations of a Parcel in a Stratified Fluid in Geostrophic Balance
  • Simple oscillatory solutions for , s = 0
  • General coupled oscillations
  • Unstable solutions
  • Neutral stratification
  • Strong stratification
  • Sample illustrations of parcel paths
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