  Context. Mixing by convective overshooting has long been suggested to play an
important role for the amount of hydrogen available to nuclear burning in
convective cores of stars. The best way to model this effect is still debated.
Aims. We suggest an improved model for the computation of the dissipation rate
of turbulent kinetic energy which can be used in non-local models of stellar
convection and can readily be implemented and self-consistently used in 1D
stellar evolution calculations. Methods. We review the physics underlying
various models to compute the dissipation rate of turbulent kinetic energy,
{\epsilon}, in local and particularly in non-local models of convection in
stellar astrophysics. The different contributions to the dissipation rate and
their dependence on local stratification and on non-local transport are
analysed and a new method to account for at least some of these physical
mechanisms is suggested. Results. We show how the new approach influences
predictions of stellar models of intermediate-mass main-sequence stars and how
these changes differ from other modifications of the non-local convection model
that focus on the ratio of horizontal to vertical (turbulent) kinetic energy.
Conclusions. The new model is shown to allow for a physically more complete
description of convective overshooting and mixing in massive stars. Dissipation
by buoyancy waves is found to be a key ingredient which has to be accounted for
in non-local models of turbulent convection.
