521 ADV FLUID MECH II Winter 2003Hwk 4 (Due Apr 1)1. Examine a viscous version of the Rayleigh problem by examining the deformation rate a mode shape when turning a half-filled jar of honey (or the equivalent) up-side down. Compare to deformation when jar is only rotated by 90 degrees. Describe a strategy for getting the honey out ASAP.
2. Add different horizontal velocities to the upper and lower fluids in the Rayleigh problem. Make sure the Rayleigh problem is recovered if the velocities goes to zero and the Kelvin-Helmholz problem is obtained when g=0.
3. Formulate the problem for Marangoni convection in a liquid layer.
4. Describe a hydrodynamic stability problem of your interest in 2 pages or less. Indicate the basic state, the instability mechanism, and set up the problem. Give any previous results.