  Solitary zonal structures have recently been identified in gyrokinetic
simulations of subcritical drift-wave (DW) turbulence with background shear
flows. However, the nature of these structures has not been fully understood
yet. Here, we show that similar structures can be obtained within a reduced
model, which complements the modified Hasegawa-Mima equation with a generic
primary instability and a background shear flow. We also find that these
structures can be qualitatively reproduced in the modified Hasegawa-Wakatani
equation, which subsumes the reduced model as a limit. In particular, we
illustrate that in both cases, the solitary zonal structures approximately
satisfy the same ''equation of state'', which is a local relation connecting
the DW envelope with the zonal-flow velocity. Due to this generality, our
reduced model can be considered as a minimum model for solitary zonal
structures in subcritical DWs.
