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12.802

Waves, Instability and Turbulence at Small Scales

3-0-9 units · Graduate

Covers basic concepts of wave motion, flow instability, and turbulence in rotating and stratified fluids with emphasis on small scales. Presents wave properties, including the dispersion relation, phase and group velocities, and wave kinematics, and uses these concepts to study the dynamics of surface and internal gravity waves, Poincare waves, Kelvin waves, and topographic waves. Includes flow instability. Explores general concepts of linear instability in small-scale stratified shear flows (Rayleigh and Kelvin-Helmholtz instabilities); examines non-rotating stratified turbulence resulting from these instabilities. Also discusses wave-mean flow interaction, hydraulic control, the entrainment assumption, and the interpretation of microstructure observations.

Spring 2008 · Wave Motion in the Ocean and the Atmosphere

Topics

  • Waves
  • Slowly varying media: ray theory
  • Surface gravity waves
  • Energy equation
  • Initial value problem — homogeneous medium
  • Internal waves
  • WKB theory for internal gravity waves — non rotating case
  • Internal waves modified by rotation — unbounded fluid
  • The oceanic wave guide: normal modes of a stratified, rotating fluid
  • Unbounded domain — non rotating reflection from a solid boundary
  • Laplace tidal equations on the sphere
  • Shallow water equations with rotation — Poincaré waves
  • The Kelvin wave
  • Rossby or planetary waves
  • Reflection and energetics of Rossby waves
  • The equatorial wave guide
  • The shelf problem and edge waves
  • Coastal trapped waves
  • Quasi-geostrophic potential vorticity equation in a stratified atmosphere
  • Energetics with a mean flow for the ocean and atmosphere
  • Topographically forced, steady Rossby waves with a zonal flow in an isothermal atmosphere
  • Waves with a mean flow — ocean

Readings

  • Pedlosky, Joseph. Waves in the Ocean and Atmosphere Introduction to Wave Dynamics . New York, NY: Springer-Verlag, 2003, p. 260. ISBN: 9783540003403.
    Listed reading
  • Gill, Adrian. Atmosphere-Ocean Dynamics . New York, NY: Academic Press, 1982, p. 662. ISBN: 9780122835223.
    Listed reading
Spring 2004 · Wave Motions in the Ocean and Atmosphere

Topics

  • Basics
  • Boussinesq
  • Available Potential Energy
  • Internal Gravity Waves
  • Surface Forced IGW’s
  • Curvilinear Coordinates
  • Pressure-like Coordinates
  • Surface Waves
  • Shallow Water Equations
  • Thermodynamics
  • Laplace Tidal Equations
  • Laplace Tidal Equations (LTE)
  • Hough Functions
  • Laplace Tidal Equations (VSE)
  • Equatorial Beta Plane
  • Rotating Waves in a Channel
  • Leewaves in Compressible Fluid
  • Quasigeostrophy
  • WKB Approx. and Atmospheric Modes
  • Eady Problem

Readings

  • Kundu, P. K. Fluid Mechanics . 3rd ed. San Diego, CA: Academic Press, 2004. ISBN: 9780121782535.
    Listed reading
  • Yih, C. Fluid Mechanics: A Concise Introduction to the Theory . Ann Arbor, MI: West River Press, 1988. ISBN: 9780960219001.
    Listed reading
  • Pedlosky, J. Geophysical Fluid Dynamics . 2nd ed. New York, NY: Springer Verlag, 1992. ISBN: 9780387963877.
    Listed reading
  • Jeffreys, H. Cartesian Tensors . New York, NY: Cambridge University Press, 1931. ISBN: 9780521091916.
    Listed reading
  • Lighthill, James. Waves in Fluids . New York, NY: Cambridge University Press, 2001. ISBN: 9780521010450.
    Listed reading
  • Whitham, G. B. Linear and Nonlinear Waves . New York, NY: Wiley-Interscience, 1999. ISBN: 9780471359425.
    Listed reading

Prerequisites & course information

Prereq: 12.800 or permission of instructor Acad Year 2027-2028: Not offered Acad Year 2028-2029: G (Spring) 3-0-9 units

Sources