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Turbulence kinetic energy

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The turbulence kinetic energy, k, is the kinetic energy per unit mass of the turbulent fluctuations u_i' in a turbulent flow. The SI unit of k is J/kg = m^2/s^2.


k \, \overset{\underset{\mathrm{def}}{}}{=} \, \frac{1}{2} \overline{u_i' u_i'} = \frac{1}{2} \left(\overline{u_x'^2} + \overline{u_y'^2} + \overline{u_z'^2} \right) = \frac{3}{2} \overline{u'^2}
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