Isotropic turbulence: Difference between revisions
No edit summary |
No edit summary |
||
| Line 13: | Line 13: | ||
\end{equation} | \end{equation} | ||
</math> <br> | </math> <br> | ||
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 | 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 turbulenc. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 151(873), 421-444. </ref>. | ||
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 20:35, 9 November 2021
| Short definition of Isotropic turbulence |
|---|
| Turbulence properties are independent of direction |
This is the common definition for Isotropic turbulence, but other definitions maybe discussed within the wiki.
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].
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.
- ↑ Taylor, G. I. (1935). Statistical theory of turbulenc. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 151(873), 421-444.
