In problem 2, you will ¡­

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

is

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

is

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