# Taylor number

﻿
Taylor number

In fluid dynamics, the Taylor number is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about a vertical axis, relative to viscous forces. 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 in the case 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.

There are various definitions of the Taylor number which are not all equivalent, but most commonly it is given by

:$mathrm\left\{Ta\right\}=frac\left\{4Omega^2 R^4\right\}\left\{ u^2\right\}$

where $Omega$ is a characteristic angular velocity, $R$ is a characteristic linear dimension perpendicular to the rotation axis, and $u$ is the kinematic viscosity.

In the case of inertial instability such as Taylor-Couette flow,the Taylor number is mathematically analogous to the Rayleigh number which characterizes the strength of buoyant forces relative to viscous forces in convection. When the former exceeds the latter by a critical ratio, convective instability sets in. Likewise, in various systems and geometries, when the Taylor number exceeds a critical value, inertial instabilities set in, sometimes known as Taylor instabilities, which may lead to Taylor vortices or cells.

Taylor refers to the British physicist Geoffrey Ingram Taylor (1886-1975).

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• 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 :mathrm{Ta}mathrm{Ta c} …   Wikipedia

• Taylor Swift (album) — Taylor Swift Studio album by …   Wikipedia

• Taylor Hanson — Background information Birth name Jordan Taylor Hanson Born March 14, 1983 (1983 03 14 …   Wikipedia

• Taylor Swift (album) — Taylor Swift Album par Taylor Swift Sortie 24 octobre 2006 (édition normale) 6 novembre 2007 (édition deluxe) Enregistrement 2006 Durée 40:48 (é …   Wikipédia en Français

• Taylor KO Factor — is a commonly used mathematical approach for evaluating the stopping power of hunting cartridges. The term KO is an acronym for Knock Out. The Taylor KO Factor (TKOF) is a figure of merit that allows hunters to compare bullets with respect to… …   Wikipedia

• Taylor Woodrow Construction — Limited (TWC) is the general construction subsidiary of Taylor Wimpey plc. It is the only UK division of the Group still trading under the Taylor Woodrow brand name.HistoryTaylor Woodrow Construction was formed in 1937. [ [http://www.taylorwimpey …   Wikipedia

• Taylor dispersion — is an effect in fluid mechanics in which a shear flow can increase the effective diffusivity of a species. Essentially, the shear acts to smear out the concentration distribution in the direction of the flow, enhancing the rate at which it… …   Wikipedia

• Taylor Park — is an area of land located in the area of Norden in the Metropolitan Borough of Rochdale, Greater Manchester, England. It was originally made into a park because it is situated on a mine shaft for the mine that used to be in operation in the… …   Wikipedia

• Taylor Booth — Taylor L. Booth (d. October 20, 1986) was a mathematician specialized in automata theory.One of his fundamental works is Sequential Machines and Automata Theory (1967). It is a wide ranging book meant for specialists, written for both theoretical …   Wikipedia

• Number Sense (UIL) — Number Sense is one of several academic events sanctioned by the University Interscholastic League. It is also a competition held by the Texas Math and Science Coaches Association, using the same rules as the UIL. It is one of the UIL s oldest… …   Wikipedia

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.