A steady-state solution for the flow in the Boussineq approximation in a star

[fab13]

Hello,

I am trying desperately to find the solution indicated in this question :

If I compute the equations on the 3 axis, I can't get the flow to be directed along $\vec{e_y}$.

I have only :

$\dfrac{\partial v_{z}}{\partial t} = -\dfrac{1}{\rho_0}\dfrac{\partial \delta P}{\partial z}+\alpha g \delta T\quad(1)$

$\dfrac{\partial v_{x}}{\partial t} - 2\Omega_{z} v_{y}=0\quad(2)$

$\dfrac{\partial v_{y}}{\partial t} + 2\Omega_{z} v_{x}=0\quad(3)$

Anyone could see how to prove a flow directed along $\vec{e_{y}}$ for the steady solution of this equation ?

and with a gradient along $\vec{e_{z}}$ ?

Any help would be kind.

 

[stefan r]

There must be a flow along the y direction caused by the Coriolis force. The boussinesq approximation gives you buoyancy which fits with vertical flow. Use the given formula to partition total flow into the 2 perpendicular directions.

The solution to b should be in a few pages back in the textbook. I do not know what textbook you got that from. That wording of a question usually means the authors definition was in bold print or something similar. Also a likely test question so you might as well memorize that definition.