View source for Velocity inertial subrange model

{{DefineConcept
|description=The inertial subrange separates the energy-containing production range from the viscous dissipation range.
|article_type=Fundamentals
|instrument_type=Velocity point-measurements, Velocity profilers
}}
== 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 (see Sreenivasan 1995 for a review on the universality of this constant). 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 other directions <math>a_2=a_3=\frac{4}{3}a_1</math> 

[[File:InertialSubrange.png]]

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== Inertial subrange for flows influenced by surface waves ==
Need to add equations and figures from Lumley & Terray

== Notes ==
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