Taylor number#

Named after: Geoffrey Ingram Taylor (1886-1975).

$$\text{Ta} \stackrel{\text{def}}{=} \frac{\Omega^{2} L^{4}}{\nu^{2}} \sim \frac{\text{rotation}}{\text{viscous diffusion}}$$

Measures rotational forcing relative to viscous diffusion. It indicates when rotating shear flows become susceptible to Taylor-type instabilities.

Name	Symbol	SI units	Dimension
angular velocity	$\Omega$	$\mathrm{Hz}$	$\text T^{-1}$
characteristic length	$L$	$\mathrm{m}$	$\text L$
kinematic viscosity	$\nu$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$

Rotating instability

Range	Regime	Description
0 – 1	viscous dominated	Viscous diffusion damps rotational shear before strong inertial structures develop.
1 – 1700	rotation important	Rotation competes with viscous diffusion and can alter stability and momentum transport.
1700 – ∞	instability prone	Rotational forcing is strong enough that Taylor-like vortices or related instabilities may occur, depending on geometry.

Name	Symbol	SI units	Dimension
angular velocity	\(\Omega\)	\(\mathrm{Hz}\)	\(\text T^{-1}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)
kinematic viscosity	\(\nu\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)