  Numerical simulations of a thin layer of turbulent flow in stably stratified
conditions within the Boussinesq approximation have been performed. The
statistics of energy transfer among scales have been investigated for different
values of control parameters: thickness of the layer and density
stratification. It is shown that in a thin layer with a quasi-two-dimensional
phenomenology, stratification provides a new channel for the energy transfer
towards small scales and reduces the inverse cascade. The role of vortex
stretching and enstrophy flux in the transfer of kinetic energy into potential
energy at small scales is discussed.
