Isotropic turbulence: Difference between revisions
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A state whereby the velocity components and their derivatives are independent of direction. If this is not the case the turbulence is said to be [[anisotropic]]. | |||
The largest scale eddies of a turbulent flow contain the bulk of the turbulence kinetic energy of the flow. | The largest scale eddies of a turbulent flow contain the bulk of the turbulence kinetic energy of the flow. | ||
These eddies tend to be somewhat organized, and their shape and size reflect the physical boundaries and other characteristics of the flow. | These eddies tend to be somewhat organized, and their shape and size reflect the physical boundaries and other characteristics of the flow. The large eddies break down into smaller eddies through flow interactions and they eventually reach a size at which they tend to be isotropic – they do not have a preferred orientation and appear similar from all points of view. For isotropic turbulence, the irreversible rate of dissipation of the turbulence kinetic energy through viscous friction, ϵ, is related to the variance of any component of the (rate of) strain or the (rate of) shear, by<br> | ||
The large eddies break down into smaller eddies through flow interactions and they eventually reach a size at which they tend to be isotropic – they do not have a preferred orientation and appear similar from all points of view. | |||
For isotropic turbulence, the irreversible rate of dissipation of the turbulence kinetic energy through viscous friction, ϵ, is related to the variance of any component of the (rate of) strain or the (rate of) shear, by<br> | |||
<math> | <math> | ||
\begin{equation} | \begin{equation} | ||
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where <math>\partial u/\partial x</math> is any one of the three-components of strain, <math>\partial u/\partial z</math> is any one of the six components of shear, <math>\nu</math> is the kinematic viscosity, and the overline denotes a spatial average <ref>Taylor, G. I. (1935). Statistical theory of | where <math>\partial u/\partial x</math> is any one of the three-components of strain, <math>\partial u/\partial z</math> is any one of the six components of shear, <math>\nu</math> is the kinematic viscosity, and the overline denotes a spatial average <ref>Taylor, G. I. (1935). Statistical theory of turbulence. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 151(873), 421-444. </ref>. | ||
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The shear probe is designed to measure the variance of shear. | The shear probe is designed to measure the variance of shear. | ||
At the very smallest scales, viscosity dampens all motions and makes the flow spatially smooth and laminar. | At the very smallest scales, viscosity dampens all motions and makes the flow spatially smooth and laminar. --> | ||
Revision as of 06:28, 22 November 2021
| Short definition of Isotropic turbulence |
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| Turbulence properties are independent of direction |
This is the common definition for Isotropic turbulence, but other definitions maybe discussed within the wiki.
A state whereby the velocity components and their derivatives are independent of direction. If this is not the case the turbulence is said to be anisotropic.
The largest scale eddies of a turbulent flow contain the bulk of the turbulence kinetic energy of the flow.
These eddies tend to be somewhat organized, and their shape and size reflect the physical boundaries and other characteristics of the flow. The large eddies break down into smaller eddies through flow interactions and they eventually reach a size at which they tend to be isotropic – they do not have a preferred orientation and appear similar from all points of view. For isotropic turbulence, the irreversible rate of dissipation of the turbulence kinetic energy through viscous friction, ϵ, is related to the variance of any component of the (rate of) strain or the (rate of) shear, by
[math]\displaystyle{
\begin{equation}
\varepsilon =15\nu \overline{\left(\frac{\partial u}{\partial x} \right)^2} = \frac{15}{2} \nu \overline{\left(\frac{\partial u}{\partial z} \right)^2}
\label{eq:epsilon_1}
\end{equation}
}[/math]
where [math]\displaystyle{ \partial u/\partial x }[/math] is any one of the three-components of strain, [math]\displaystyle{ \partial u/\partial z }[/math] is any one of the six components of shear, [math]\displaystyle{ \nu }[/math] is the kinematic viscosity, and the overline denotes a spatial average [1].
- ↑ Taylor, G. I. (1935). Statistical theory of turbulence. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 151(873), 421-444.
