Velocity inertial subrange model: Difference between revisions

From Atomix
mNo edit summary
Line 15: Line 15:


[[File:InertialSubrange.png]]
[[File:InertialSubrange.png]]
<ref>This is not working, see {{cite journal|url=https://www.google.com |author= |date= |accessdate={{subst:#time:Y-m-d|now}}|title=Search}}</ref>


== Inertial subrange for flows influenced by surface waves ==
== Inertial subrange for flows influenced by surface waves ==

Revision as of 19:14, 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 (see Sreenivasan 1995 for a review on the universality of this constant). 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]

[1]

Inertial subrange for flows influenced by surface waves

Need to add equations and figures from Lumley & Terray

Notes

  1. This is not working, see . {{{year}}}. {{{paper_or_booktitle}}}. {{{journal_or_publisher}}}. doi:{{{doi}}}