  The nonlinear dynamics of beta-induced Alfv\'en Eigenmodes (BAE) driven by
energetic particles (EP) in the presence of ion-temperature-gradient (ITG)
turbulence is investigated, by means of selfconsistent global gyrokinetic
simulations and analytical theory. A tokamak magnetic equilibrium with large
aspect ratio and reversed shear is considered. A previous study of this
configuration has shown that the electron species plays an important role in
determining the nonlinear saturation level of a BAE in the absence of
turbulence [A. Biancalani, et al., J. Plasma Phys. (2020)]. Here, we extend the
study to a turbulent plasma. The EPs are found modify the heat fluxes by
introducing energy at the large spatial scales, mainly at the toroidal mode
number of the dominant BAE and its harmonics. In this regime, BAEs are found to
carry a strong electron heat flux. The feed-back of the global relaxation of
the temperature profiles induced by the BAE, and on the turbulence dynamics, is
also discussed.
