Time averaging, hierarchy of the governing equations, and the balance of turbulent kinetic energy

We discuss a connection between governing equations, constitutive theory, and closure problem for atmospheric boundary layer. Such a connection is of prime importance in building algorithms for numerical simulations. We consider averaging in time and its relation to the Boussinesq approximation of the governing equations. We introduce a notion of instantaneous turbulent kinetic energy and derive a new balance equation for its material derivative.