A Model for the Kinetic Energy Balance in Homogeneous Turbulence

We derive a two-equation model for the energy balance in statistically homogeneous turbulence. The present formulation is expressed in terms of the energy flux, unlike the classical approach, where the dissipation rate appears in the kinetic energy equation. This enables a unified description of both forced and decaying turbulence with a single set of model constants. The model also captures the time lag between the evolution of the kinetic energy and the dissipation rate. Reformulating the system as an equation for the dissipation rate further clarifies how non-equilibrium effects can be incorporated into existing turbulence models.