# Turbulence kinetic energy

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 $J/kg = m^2/s^2$.
$k \, \overset{\underset{\mathrm{def}}{}}{=} \, \frac{1}{2} \overline{u_i' u_i'} = \frac{1}{2} \left(\overline{u_x'^2} + \overline{u_y'^2} + \overline{u_z'^2} \right) = \frac{3}{2} \overline{u'^2}$