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 maybe discussed within the wiki.

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Inertial subrange for steady-flows

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

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

Sketch of velocity power density spectrum in log-log space. The inertial subrange's -5/3 slope is highlighted. The vertical axis represents ${\mathrm{\Psi }}_{Vj}(\hat{k})$. 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