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?

Thank you very much in advance.