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.

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]

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

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 . 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