Taylor-Couette instability

In 1901 M.Couete have done the foloween experience : a fluid was put between two centric cylinders. He then communicate a rotational velocity to the outside cylinder.

In 1923, G.Taylor make the same expewrience , but this time it was the inside cylinder witch was in motion. at the begining the fluid is rotationg with an orthoradial velocity. if we keep increasing the rotaional velocity of the inside cylinder, we notice that at a critical rotational velocity wc a componet of radial velocity is comunicated to the fluid. this is followed by an unsteady flow.

the distabilisator factor is the presence of radial velocity gradient witch create the centrifuge forces with an amplitude depending on the position of the fluid partical.

the viscosity is here a stabilisator factor wich tend to transforme the velocity field to uniform one.

the adimensional constant witch control the flow is the Taylor number and it represent the rate between the centrifuge forces and the viscous forces.

here are the expressions of the two forces acting on each partical.

Mechanism : the rotation of the interior cylinder give a rotational motion to fluid particals via the diffusion. So it's the closer particles to the itern cylinder wich wich have the highest momentum. these particles will have a radial motion oriented to the exterior under the centrifuge forces.