According to the "Tid og sted" under GEF4500:
Avsluttende skriftlig eksamen
4. desember kl. 14:30 (3 timer).
* Store lesesal, gr. 2 Vilhelm Bjerknes hus
I've reserved room 5 from 1-3 pm on Monday. I guess that must be somewhere near room 7...
In problem 2, you will need an additional constraint at the wall. In addition to psi=0, also use the no-slip condition--- that v=d/dx psi=0
Note that the general solution to
d^4 psi/dx^4 - d/dx psi = 0
psi = c1 + c2 exp(x) + c3 exp(-x/2) cos(sqrt(3) x/2) + c4 exp(-x/2) sin(sqrt(3) x/2)
while the solution to;
d^4 psi/dx^4 + d/dx psi = 0
psi = c1 + c2 exp(-x) + c3 exp(x/2) cos(sqrt(3) x/2) + c4 exp(x/2) sin(sqrt(3) x/2)
In problem 3, it should read which profile is stable by Fjortofts if beta=0?
Also, the last profile SHOULD read:
U = 1/6 y^3 + 5/6 y
To evaluate Fjortoft's, set U_s equal to the value of U where d^2U/dy2 = 0
The argument in the exponential should have a minus sign in problem 1 on the 5th problem set.
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There's a problem downloading the class notes. I'm working on it...
Problem set 3: Assume that f=f_0 in problem 2 (so that df/dy=0).
There were two mistakes in problem 1 on problem set 2. The second order derivative should be with respect to t, not x, and below that it should be cos^3(t) rather than cos^3(x).
For psi0 and psi1, find only the particular solutions. Since we don't have boundary conditions, we ignore the homogeneous solutions.
Also: the sign on the RHS of equation 1 in problem 2 should be positive not negative.