This course covers physical principals fundamental to the study of the oceans; the equations of motion for rotating fluids; circulation theorem and conservation of potential vorticity; scale analysis; boundary conditions; surface gravity waves; rotation effects in homogeneous oceans. Prerequisites: OCE 541 or equivalent, fluid mechanics and partial differential equations. Cr. 3.

Outline:

• Governing equations (Dr. Pettigrew)
  • equations of motion; rotational effects; mass conservation equation; density equation; circulation and vorticity; vorticity equation, potential vorticity; kinetic and potential energy; mechanical energy equations; turbulent mixing

   

• Scales of motion (Dr. Pettigrew)
  • a coordinate system for planetary scale motions; f-plane and b-plane; importance of rotation and Rossby number; importance of stratification; Boussinesq approximation and hydrostatic approximation; importance of friction and Ekman number

   

• Adjustment under gravity (Dr. Xue)
  • surface gravity waves; short-wave and long-wave approximations

   

• Linear barotropic waves (Dr. Xue)
  • shallow water equation; tides and related; the Rossby adjustment problem; conservation of potential vorticity for a shallow homogeneous layer; Kelvin wave; Inertia-gravity waves; quasigeostrophic theory; planetary Rossby waves; topographic Rossby waves; waves in a shear flow; barotropic instability

   

• Wind forced motions (Dr. Pettigrew)
  • Ekman layer; Ekman transport and Ekman pumping; bottom friction (velocity structure and bottom boundary layer); spin-down by bottom friction

   

• Large-scale ocean circulation (Dr. Xue)
  • a simple model of mid-latitude circulation and Sverdrup relation; westward intensification and western boundary currents 

Text:

Cushman-Roisin: Introduction to Geophysical Fluid Dynamics, Prentice Hall

Gill: Atmosphere-Ocean Dynamics, Academic Press