Turbulence kinetic energy

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


:<math>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}</math>