Time evolution for ω_rms²/2 (left axis and gray line) and vorticity growth terms (right axis and various colored lines for each term) for a non-isothermal run with R = 0.5 and forcing in acceleration form (and by construction its contribution to ⟨∂_tω²/2⟩ is zero). This plot zooms in on the beginning of the temporal evolution of all the terms until t ≃ 130 t_turn. However, the saturation regime does not present any relevant changes in time for more than 2000 t_turn, and no instability is reached. Both the 2ν⟨S∇lnρ ⋅ q⟩ and ⟨(j × b/ρ)⋅q⟩ terms are negligible and very close to 0, so this makes the total contribution of viscous forces, i.e., ⟨F_visc ⋅ q⟩, overlap with ν⟨q²⟩.