This paper uses five-dimensional nonlinear gyrokinetic Vlasov simulations to resolve how zonal flows exchange entropy with ion-temperature-gradient (ITG) and electron-temperature-gradient (ETG) turbulence. Separate entropy balances for zonal and nonzonal modes are coupled by a transfer function that kinetically generalizes Reynolds-stress production. A symmetrized triad transfer diagnostic identifies both participating Fourier modes and transfer direction. During ITG saturation, substantial entropy flows from nonzonal fluctuations into zonal modes and builds strong zonal flows. In the statistically steady state, direct transfer into the zonal component becomes weak; established zonal flows instead mediate transfer from heat-carrying, low-radial-wavenumber nonzonal modes toward higher-radial-wavenumber modes that contribute less transport, broadening the spectrum and regulating heat flux. Toroidal ETG turbulence behaves differently: interactions among low-wavenumber nonzonal modes dominate both saturation and steady transport, while zonal mediation remains weak for the parameters studied. The authors note that ETG regimes with weaker magnetic shear and stronger zonal flows may behave differently.
- Derived coupled gyrokinetic entropy balances for zonal and nonzonal fluctuations.
- Introduced a direction-resolving symmetrized triad entropy-transfer diagnostic.
- Identified transfer into zonal modes as a principal mechanism saturating the simulated ITG instability.
- Showed that steady ITG zonal flows redirect transport-carrying entropy toward higher radial wavenumbers.
- Distinguished this ITG pathway from nonzonal-dominated entropy transfer in the simulated ETG regime.