Course Outline
Fluid Dynamics
FLUID DYNAMICS
Parallel viscous flow
- Plane Couette flow, dynamic viscosity. Momentum equation and boundary conditions. Steady flows including Poiseuille flow in a channel. Unsteady flows, kinematic viscosity, brief description of viscous boundary layers (skin depth). [3]
Kinematics
- Material time derivative. Conservation of mass and the kinematic boundary condition. Incompressibility; streamfunction for two-dimensional flow. Streamlines and path lines. [2]
Dynamics
- Statement of Navier-Stokes momentum equation. Reynolds number. Stagnation-point flow; discussion of viscous boundary layer and pressure field. Conservation of momentum; Euler momentum equation. Bernoulli’s equation. Vorticity, vorticity equation, vortex line stretching, irrotational flow remains irrotational. [4]
Potential flows
- Velocity potential; Laplace’s equation, examples of solutions in spherical and cylindrical geometry by separation of variables. Translating sphere. Lift on a cylinder with circulation. Expression for pressure in time-dependent potential flows with potential forces. Oscillations in a manometer and of a bubble. [3]
Geophysical flows
- Linear water waves: dispersion relation, deep and shallow water, standing waves in a container, Rayleigh-Taylor instability. Euler equations in a rotating frame. Steady geostrophic flow, pressure as streamfunction. Motion in a shallow layer, hydrostatic assumption, modified continuity equation. Conservation of potential vorticity, Rossby radius of deformation. [4]
Appropriate books
- † D.J. Acheson Elementary Fluid Dynamics. Oxford University Press 1990
- G.K. Batchelor An Introduction to Fluid Dynamics. Cambridge University Press 2000
- G.M. Homsey et al. Multi-Media Fluid Mechanics. Cambridge University Press 2008
- M. van Dyke An Album of Fluid Motion. Parabolic Press
- M.G. Worster Understanding Fluid Flow. Cambridge University Press 2009
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