In: 

**"Fluid Dynamics", Chapter 3 (Turbulence), Section 26,** 

Landau and Lifchitz analyze the problem of the stability of a steady flow past a body of finite size.

The fluid is assumed to be incompressible and they reach the conclusion that perturbations that deviate from steady flows start to grow when a critical Reynolds number is reached (ASIK, this critical Reynolds number in unrelated to the $\mathbb{Re}_c$ at which the laminar flow becomes turbulent). 

They also deduce that the amplitude of the perturbation grows proportional to:
$$A\propto\sqrt{Re-Re_c}$$.

Would this be at the origin of vortex shedding?

What's the name of this critical Reynolds number?

How does this relate to Strouhal's number?

Thank you very much in advance.


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Well this is leading me nowhere again.

This is what I think:

 1. Vortex shedding introduces a NATURAL time scale.
 2. The speed of sound is the maximum velocity at which information travells 
    inside the fluid.
 3. Assume that the incoming fluid velocity increases: the natural time scale 
    decreases and viscidity decreases (eddies live longer) while the speed of 
    sound stays the same.
 4. **This situation is untenable**. At sufficiently long distances from the 
    obstacle (downstream), eddies become completely aloof of whatever is 
    happening upstream.