Taylor vortex

Taylor vortices (after G. I. Taylor) are vortices formed in rotating Taylor-Couette flow when the Taylor number ($mathrm\{Ta\}$) of the flow exceeds a critical value $mathrm\{Ta\_c\}$.

For flow in which

:

instabilities in the flow are not present, i.e. perturbations to the flow are damped out by viscous forces, and the flow is steady. But, as the $mathrm\{Ta\}$ exceeds $mathrm\{Ta\_c\}$, axisymmetric instabilities appear. The nature of these instabilities is that of an exchange of stabilities (rather than an overstability), and the result is not turbulence but rather a stable secondary flow pattern that emerges in which large toroidal vortices form in flow, stacked one on top of the other. These are the Taylor vortices. While the fluid mechanics of the original flow are unsteady when $mathrm\{Ta\}>mathrm\{Ta\_c\}$, the new flow, called Taylor-Couette flow, with the Taylor vortices present, is actually steady until the flow reaches a large Reynolds number, at which point the flow transitions to unsteady "wavy vortex" flow, presumably indicating the presence of non-axisymmetric instabilities.

Rotating Couette flow is characterized geometrically by the two parameters

:$mu\; =\; Omega\_2\; /\; Omega\_1$

and

:$eta\; =\; R\_1\; /\; R\_2$

where the subscript "1" refers to the inner cylinder and the subscript "2" refers to the outer cylinder. The idealized mathematical problem is posed by choosing a particular value of $mu$, $eta$, and $mathrm\{Ta\}$. As $eta\; ightarrow\; 1$ and $mu\; ightarrow\; 1$ from below, the critical Taylor number is $mathrm\{Ta\_c\}\; simeq\; 1708$.