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Problem 7 - Solve this by approximation as follows 7.2.1...

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Problem 7 7.1 Rederive the convective cell linear normal modes, as was done in class and in the notes, from the Navier Stokes equations. Thus, you will not obtain omega = 0 any more. Does the mode oscillate? damp? 7.2 Rederive the sound wave dispersion using the full Navier-Stokes equations, ie, including both viscosity and thermal conduction. (in the last homework, we did only viscosity). Use Eq 3a of Topic 4 for the pressure/temperature equation. You will find a 3d order equation in omega.
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Unformatted text preview: Solve this by approximation as follows: 7.2.1 First, LOOK for a mode with omega ~ kc_s, ie the sound frequency. LOOK means scale the terms assuming omega ~ kc_s and identify the big and small terms. Then, find omega_0 and then omega_1, by perturbation. State how the viscosity and thermal conduction affect the sound wave. 7.2.2 Next, LOOK for a mode with omega << kc_s, ie below the sound frequency. Find the lowest order nonzero omega in this case. This is the entropy mode....
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