Geophysical Fluid Dynamics Syllabus
Fall 2001
-
Introduction to fluids
- Mathematical
review: scalars, vectors and tensors
- Physical properties
of fluids
- Kinematics
- The primitive
equations
- Boundary conditions
- Vorticity and
circulation
- Energetics
- Dynamic similarity
- Idealized
viscous flows: convection with vorticity
- Wave kinematics
1. Introduction to Fluids
- Definition of a fluid
- Contrasting solids and fluids
- Intermolecular forces
- Air: microscopic properties
- Air: need for a macroscopic approach
- The continuum hypothesis
- The perfect gas law
2. Mathematical Review
- Distinguishing vectors from scalars
- Cartesian coordinates in several notations
- Review of scalar and vector operations
- Introducing tensors
- Scalar differentiation
- Vector differentiation
- Scalar integration
- Vector integration
- Integral differentiation (Leibnitz)
3. Physical Properties
of Fluids
- Forces acting on fluids
- Stress tensor in a fluid at rest
- Pressure as momentum flux in a perfect gas
- Physical mechanism of viscosity in a perfect gas
4. Kinematics
- Lagrangian and
Eulerian descriptions of the flow
- Acceleration: local and advective rates of change
- Moving a parcel: translation, divergence,
deformation and vorticity
- Strain rate and rotation tensors
- Vorticity and the rotation
tensor
- Following the flow: streamlines and
trajectories; streamfunction
- Bernoulli integral on a streamline
- Vortex kinematics
5. Review of the Primitive
Equations
- Conservation of mass: The continuity equation
- Newton's second law applied to fluids: The
Navier Stokes equation
- Expression for the stress tensor in a moving fluid
- Effects of rotation: Coriolis and
Centrifugal
"forces"
- The first law of thermodynamics
- The equation of state
6. Boundary Conditions
- Inviscid, non-conducting ("dry water")
- Viscous ("wet water")
- Conducting
- Boundaries at infinity
- Summary table
7. Vorticity and Circulation
- Definitions of vorticity and
circulation
- Relation between circulation and vorticity
- Bjerknes' circulation theorem
- Kelvin's circulation
theorem
- Vorticity constructs: vortex lines, vortex
sheets, vortex tubes,...
- Helmholtz vortex theorems
- Vorticity equation in tensor form
- Taylor-Proudman theorem
- Ertel's theorem and potential vorticity
- Helmholtz' theorems: application to the smoke ring experiment
8. Energetics
- Kinetic energy equation
- Potential energy equation
- Mechanical energy equation
- First law of thermodynamics
- Second law of thermodynamics
- Energy transfers
9. Dynamic similarity
- Dimensional analysis and dynamic similarity
- Nondimensionalization of the equations
- Buckingham's Pi theorem
- Oft sighted non-dimensional parameters
10. Idealized Viscous
Flows: Convection with Vorticity 
- Vortex ring in ambient environment
- Jet out of a nozzle
- Buoyant plume
- Jet into cross flow
- Buoyant plume in cross flow
11. Wave Dynamics
- Surface gravity waves
- Dispersion relation
- Group velocity and energetics: wave train kinematics
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Last Updated: 16 August 2001.