# At what critical Reynolds number does vortex shedding begin?

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.

Well this is leading me nowhere again.

This is what I think:

1.- Vortex shedding ocurrs at the NATURAL time scale (the time it takes the fluid to cross the obstacle).

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 (they are capable of travelling a longer distance that sound does in the natural time scale because of the extremely low viscidity) . Sufficiently far away of the obstacle, downstream, eddies are no longer in the obstacle's future cone.

At some some stage, the general properties of the fluid MUST change, in order of this nonsense (non-causality) not to happen. ASIK, in supersonic flows, shock waves are generated so that causality is not broken, so turbulence could have this same origin.

• In the lab reference frame speed of sound will be sum of fluid speed and sound speed in stationary fluid. – Deep Oct 21 '18 at 6:43