ME245 Oceanic and Atmospheric Waves- UC Berkeley
























1.     Introduction: Propagating waves, Group Speed, Phase Speed, Conservation relations.


2.     Governing Equations: Mass, Momentum and Energy equations, Boundary conditions


3.     Surface Waves

o    Governing Equations, Dispersion Relation, Energy and Energy Propagation

o    The Initial Value Problem- The Method of Stationary Phase

o    Waves in Slowly Varying Media: Ray Theory

o    Gravity, Capillary and Capillary-Gravity Waves

o    Long wave approximation,

o    Some Nonlinear Aspects: KdV equation, Nonlinear Schrodinger Equation


4.     Pressure Waves

o    Basic Physics of Acoustic Waves, Bulk Modulus, Sound Speed

o    Reflection at a Solid Boundary, Snell's law

o    Plane Waves in a Channel

o    Scattering in a Discontinuity

o    Slowly Varying Medium


5.     Internal Gravity Waves

o    Discussion of Interfacial Waves

o    Governing Equations for Continuous Stratified Fluids, Dispersion Relation, Normal Modes

o    Internal Waves Reflection

o    Focusing of internal waves and internal wave attractors

o    WKB approximation and Atmospheric Modes

o    Vertical propagation - steady flow and the radiation condition

o    Lee waves in Compressible fluid


6.     Shallow Water Dynamics

o    Laplace's Tidal Equation

o    Shallow Water Equations with Rotation

o    Seiches in Enclosed Basins

o    Edge Waves and Coastal Seiches

o    Inertial-internal gravity waves, Sverdrup and Poincare Waves

o    Channel Modes and Kelvin Waves

o    Waveguide Modes

o    Geostrophic motion, Rossby and Planetary Waves

o    Equatorial beta-Plane and Equatorial Waves


7.     Topographic Effects

o    Bottom-Trapped Waves

o    Continental Shelf Waves

o    Coastal-Trapped Waves






  • Recommended Reading

  • Sutherland, B.R., Internal Gravity Waves, 2010,  ISBN-13: 978-0521839150.
    Pedlosky, J., Waves in the Ocean and Atmosphere: Introduction to Wave Dynamics, 2003, ISBN-13: 978-3642055645.
    Kundu, P. K. et al. Fluid Mechanics. 5th ed., 2011. ISBN: 978-0123821003.
    Yih, C. Fluid Mechanics: A Concise Introduction to the Theory. West River Press, 1988. ISBN: 9780960219001.
    Lighthill, James. Waves in Fluids. New York, NY: Cambridge University Press, 2001. ISBN: 9780521010450.
    Whitham, G. B. Linear and Nonlinear Waves. New York, NY: Wiley-Interscience, 1999. ISBN: 9780471359425.
    Defant, A. Physical Oceanography, Vol. I & II. 1961, Pergamon Press, ISBN-13: 978-0750645522.
    Gill, A. E. Atmosphere-Ocean Dynamics. Academic Press 1982, ISBN-13: 978-0122835223.
    Krauss, W.  Methods and Results of Theoretical Oceanography. Vol. I   Gebruder Borntraeger 1973 ISBN-13: 978-3443010010.
    LeBlond, P. H., and Mysak, L. A. Waves in the Ocean. Elsevier 1978, ISBN 9780444419262.

    Pedlosky, J. Geophysical Fluid Dynamics. 2nd ed. New York, NY: Springer Verlag, 1992. ISBN: 9780387963877.
    MIroposky Y.Z. and Shishkina, O.D., Dynamics of Internal Gravity Waves in the Ocean, 2001, ISBN-13: 978-9048156924.