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.

<math>\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>\Psi_{Vj}(\hat{k})</math>. Large-scale turbulence anisotropy in low energy flow may alter the expected spectral shape

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 . 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>

Inertial subrange for flows influenced by surface waves

Need to add equations and figures from Lumley & Terray