Local turbulent kinetic energy balance
= Local turbulent kinetic energy balance
{title2=$\epsilon=P+B_0,\quad P=-\overline{u'w'}U_z$}
In stationary locally equilibrated turbulence, mean-shear production and buoyancy production balance viscous dissipation after transport terms are neglected. Stable buoyancy flux is negative and consumes part of the shear input. This approximation gives $\epsilon=u_*^3/(\kappa z)$ in a neutral logarithmic layer and $\epsilon\sim B_0$ in buoyancy-dominated free convection.