We study drift/Rossby wave turbulence described by the large-scale limit of the Charney–Hasegawa–Mima equation. We define the zonal and meridional regions as and respectively, where is in a plane perpendicular to the magnetic field such that kx is along the isopycnals and ky is along the plasma density gradient. We prove that the only types of resonant triads allowed are and . Therefore, if the spectrum of weak large-scale drift/Rossby turbulence is initially in Z it will remain in Z indefinitely. We present a generalised Fjørtoft’s argument to find transfer directions for the quadratic invariants in the two-dimensional -space. Using direct numerical simulations, we test and confirm our theoretical predictions for weak large-scale drift/Rossby turbulence, and establish qualitative differences with cases when turbulence is strong. We demonstrate that the qualitative features of the large-scale limit survive when the typical turbulent scale is only moderately greater than the Larmor/Rossby radius.