Taylor microscale

The Taylor microscale, which is sometimes called the turbulence length scale, is a length scale used to characterize a turbulent fluid flow. This microscale is named after Geoffrey Ingram Taylor. The Taylor microscale is the intermediate length scale at which fluid viscosity significantly affects the dynamics of turbulent eddies in the flow. This length scale is traditionally applied to turbulent flow which can be characterized by a Kolmogorov spectrum of velocity fluctuations. In such a flow, length scales which are larger than the Taylor microscale are not strongly affected by viscosity. These larger length scales in the flow are generally referred to as the inertial range. Below the Taylor microscale the turbulent motions are subject to strong viscous forces and kinetic energy is dissipated into heat. These shorter length scale motions are generally termed the dissipation range. The Taylor microscale, which is sometimes called the turbulence length scale, is a length scale used to characterize a turbulent fluid flow. This microscale is named after Geoffrey Ingram Taylor. The Taylor microscale is the intermediate length scale at which fluid viscosity significantly affects the dynamics of turbulent eddies in the flow. This length scale is traditionally applied to turbulent flow which can be characterized by a Kolmogorov spectrum of velocity fluctuations. In such a flow, length scales which are larger than the Taylor microscale are not strongly affected by viscosity. These larger length scales in the flow are generally referred to as the inertial range. Below the Taylor microscale the turbulent motions are subject to strong viscous forces and kinetic energy is dissipated into heat. These shorter length scale motions are generally termed the dissipation range. Calculation of the Taylor microscale is not entirely straightforward, requiring formation of certain flow correlation function(s), then expanding in a Taylor series and using the first non-zero term to characterize an osculating parabola. The Taylor microscale is proportional to R e − 1 / 2 {displaystyle Re^{-1/2}} , while the Kolmogorov microscales is proportional to R e − 3 / 4 {displaystyle Re^{-3/4}} , where R e {displaystyle Re} is the integral scale Reynolds number. A turbulence Reynolds number calculated based on the Taylor microscale λ {displaystyle lambda } is given by R e λ = ⟨ v ′ ⟩ r m s λ ν {displaystyle Re_{lambda }={frac {langle mathbf {v'} angle _{rms}lambda }{ u }}} where ⟨ v ′ ⟩ r m s = ( v 1 ′ ) 2 + ( v 2 ′ ) 2 + ( v 3 ′ ) 2 {displaystyle langle mathbf {v'} angle _{rms}={sqrt {(v'_{1})^{2}+(v'_{2})^{2}+(v'_{3})^{2}}}} is the root mean square of the velocity fluctuations.The Taylor microscale is given as λ = 15 ν ϵ ⟨ v ′ ⟩ r m s {displaystyle lambda ={sqrt {15{frac { u }{epsilon }}}}langle mathbf {v'} angle _{rms}} where ν {displaystyle u } is the kinematic viscosity, and ϵ {displaystyle epsilon } is the rate of energy dissipation. A relation with turbulence kinetic energy can be derived as λ ≈ 10 ν k ϵ {displaystyle lambda approx {sqrt {10 u {frac {k}{epsilon }}}}}