Velocity inertial subrange model: Difference between revisions
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= 1.5 <ref name="Sreenivasan">{{Cite journal | = 1.5 <ref name="Sreenivasan">{{Cite journal | ||
|authors= K. R. Sreenivasan | |authors= K. R. Sreenivasan | ||
| | |journal_or_publisher= Phys. Fluids | ||
| | |paper_or_booktitle= On the universality of the Kolmogorov constant | ||
|year= | |year= 1995 | ||
|doi= 10.1063/1.868656 | |doi= 10.1063/1.868656 | ||
}}</ref>. Amongst the three direction, the spectra deviates by the constant <math>a_j</math>: | }}</ref>. Amongst the three direction, the spectra deviates by the constant <math>a_j</math> | ||
<ref name="Pope">{{Cite journal | |||
|authors= S.B Pope | |||
|journal_or_publisher= Cambridge Univ. Press | |||
|paper_or_booktitle= Turbulent flows | |||
|year= 2000 | |||
|doi= 10.1017/CBO9780511840531 | |||
}}</ref> | |||
: | |||
* In the longitudinal direction, i.e., the direction of mean advection (j=1), <math>a_1=\frac{18}{55}</math> | * In the longitudinal direction, i.e., the direction of mean advection (j=1), <math>a_1=\frac{18}{55}</math> | ||
* In the other directions <math>a_2=a_3=\frac{4}{3}a_1</math> | * In the other directions <math>a_2=a_3=\frac{4}{3}a_1</math> | ||
Revision as of 19:52, 11 November 2021
| Short definition of Velocity inertial subrange model |
|---|
| The inertial subrange separates the energy-containing production range from the viscous dissipation range. |
This is the common definition for Velocity inertial subrange model, but other definitions maybe discussed within the wiki.
{{#default_form:DefineConcept}} {{#arraymap:Velocity point-measurements, Velocity profilers|,|x||}}
Inertial subrange for steady-flows
This theoretical model predicts the spectral shape of velocities in wavenumber space.
<math>\Psi_{Vj}(\hat{k})=a_jC_k\varepsilon^{2/3}\hat{k}^{-5/3}</math>
Here <math>\hat{k}</math> is expressed in rad/m and <math>Vj</math> represents the velocities <math>V</math> in direction <math>j</math>. <math>C_k</math> is the empirical Kolmogorov universal constant of C = 1.5 [1]. Amongst the three direction, the spectra deviates by the constant <math>a_j</math> [2]
- In the longitudinal direction, i.e., the direction of mean advection (j=1), <math>a_1=\frac{18}{55}</math>
- In the other directions <math>a_2=a_3=\frac{4}{3}a_1</math>
Inertial subrange for flows influenced by surface waves
Need to add equations and figures from Lumley & Terray
Notes
- ↑ {{#arraymap:K. R. Sreenivasan|,|x|x|, |and}}. 1995. On the universality of the Kolmogorov constant. Phys. Fluids. doi:10.1063/1.868656
- ↑ {{#arraymap:S.B Pope|,|x|x|, |and}}. 2000. Turbulent flows. Cambridge Univ. Press. doi:10.1017/CBO9780511840531
