1
$\begingroup$

The transition from laminar flow to turbulent flow is usually told interms of Reynolds numbers. The Reynolds number is $Re=UL/\nu$ where $U$ is the speed, $L$ is dimensional length and $\nu$ is the viscosity. Even if we say the Reynold's number tells us whether the flow is turbulent or not, I have never seen a unique $Re$ that differentiates laminar from turbulence. My question is then, is the cause of turblence perfectly known? is it velocity, length or viscosity that highly determines the flow condition? Is there a unique Reynold's number that separates laminar flow from turbulent?

$\endgroup$
3
$\begingroup$

We know the general cause for turbulence: it is that inertial effects (mass wanting to keep going in the direction that it's going) grow so large that viscous effects cannot contain the system in the laminar flow regime anymore. When those viscous effects cannot slow down a whole chunk of fluid, they are forces acting off-center on a mass: hence they create angular momentum and vortices.

A dimensionless representation of this is captured in the so-called Reynolds number, as you note, but no, the "laminar-to-turbulent" transition does not occur at the same Reynolds number in all geometries. This is due to an even more fundamental problem: Reynolds numbers are fundamentally incomparable between geometries; they depend on some convention about how to specify the "length" parameter of a certain geometry, and that convention is not just a human choice, but it also cannot be compared across different geometries.

We can perhaps hope that people start renormalizing their Reynolds numbers so that the laminar-to-turbulent switch always happens over a well-defined range, perhaps fixing the numbers based on the "infinite planar flow about an infinitely long cylinder" Reynolds numbers -- but this is not very likely to happen in the near future.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy