Taylor number

In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about an axis, relative to viscous forces. In 1923 Geoffrey Ingram Taylor introduced this quantity in his article on the stability of flow. The typical context of the Taylor number is in characterization of the Couette flow between rotating colinear cylinders or rotating concentric spheres. In the case of a system which is not rotating uniformly, such as the case of cylindrical Couette flow, where the outer cylinder is stationary and the inner cylinder is rotating, inertial forces will often tend to destabilize a system, whereas viscous forces tend to stabilize a system and damp out perturbations and turbulence. On the other hand, in other cases the effect of rotation can be stabilizing. For example, in the case of cylindrical Couette flow with positive Rayleigh discriminant, there are no axisymmetric instabilities. Another example is a bucket of water that is rotating uniformly (i.e. undergoing solid body rotation). Here the fluid is subject to the Taylor-Proudman theorem which says that small motions will tend to produce purely two-dimensional perturbations to the overall rotational flow. However, in this case the effects of rotation and viscosity are usually characterized by the Ekman number and the Rossby number rather than by the Taylor number.