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.
Inertial subrange for steady-flows
This theoretical model predicts the spectral shape of velocities in wavenumber space.
[math]\displaystyle{ \Psi_{Vj}(\hat{k})=a_jC_k\varepsilon^{2/3}\hat{k}^{-5/3} }[/math]
Here [math]\displaystyle{ \hat{k} }[/math] is expressed in rad/m and [math]\displaystyle{ Vj }[/math] represents the velocities [math]\displaystyle{ V }[/math] in direction [math]\displaystyle{ j }[/math]. [math]\displaystyle{ 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]\displaystyle{ a_j }[/math] [2]
- In the longitudinal direction, i.e., the direction of mean advection (j=1), [math]\displaystyle{ a_1=\frac{18}{55} }[/math]
- In the other directions [math]\displaystyle{ 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
- ↑ K. R. Sreenivasan. 1995. On the universality of the Kolmogorov constant. Phys. Fluids. doi:10.1063/1.868656
- ↑ S.B Pope. 2000. Turbulent flows. Cambridge Univ. Press. doi:10.1017/CBO9780511840531
