Velocity inertial subrange model

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 may be discussed within the wiki.

Inertial subrange for steady-flows

This theoretical model predicts the spectral shape of velocities in wavenumber space.

${\Psi }_{Vj}(\hat{k})=a_j{C}_k{\epsilon }^{2/3}{\hat{k}}^{-5/3}$

Sketch of velocity power density spectrum in log-log space. The inertial subrange's -5/3 slope is highlighted. The vertical axis represents ${\Psi }_{Vj}(\hat{k})$. Large-scale turbulence anisotropy in low energy flow may alter the expected spectral shape

Here $\hat{k}$ is expressed in rad/m and $Vj$ represents the velocities $V$ in direction $j$. $C_k$ is the empirical Kolmogorov universal constant of C = 1.5 . Amongst the three direction, the spectra deviates by the constant $a_j$:

• In the longitudinal direction, i.e., the direction of mean advection (j=1), $a_1=\frac{18}{55}$
• In the other directions $a_2=a_3=\frac{4}{3}{a}_1$

Inertial subrange for flows influenced by surface waves

Need to add equations and figures from Lumley & Terray