Velocity inertial subrange model: Difference between revisions
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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 | 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 | = 1.5 <ref name="Sreenivasan">{{Cite journal | ||
|authors= K. R. Sreenivasan | |||
|journal= Phys. Fluids | |||
|papertitle= On the universality of the Kolmogorov constant | |||
|year= 1991 | |||
|doi= 10.1063/1.868656 | |||
}}</ref>. Amongst the three direction, the spectra deviates by the constant <math>a_j</math>: | |||
* 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 19:47, 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]:
- 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. 1991. {{{paper_or_booktitle}}}. {{{journal_or_publisher}}}. doi:10.1063/1.868656
