We investigate the onset and evolution of zonal flows in a growing convective layer when a stably stratified fluid with a composition gradient is cooled from above. This configuration allows the study of zonal flows for a wide range of values of the Rayleigh number and aspect ratio of the convection zone within a given simulation. We perform a series of two-dimensional (2D) simulations using the Boussinesq approximation with aspect ratio of the computational domain between 1 and 5 and Prandtl number (Pr) $\mathrm{Pr}=0.1$, 0.5, 1, and 7. For simulations with aspect ratio of one we find that zonal flows appear when the aspect ratio of the convective layer is smaller than 2, and the evolution of the system depends on the Prandtl number. For $\mathrm{Pr}\le 1$, the fluid experiences bursts of convective transport with negligible convective transport between bursts. The magnitude and frequency of the bursts are smaller at low Pr, which suggests that the bursting regime is stronger in a narrow range around $\mathrm{Pr}=1$ as observed in previous studies of thermal convection. For $\mathrm{Pr}=7$, the structure of the flow consists of tilted convective plumes, and the convective transport is sustained at all times. In wider domains, the aspect ratio of the convective zone is always much larger than 2, and zonal flows do not appear. These results confirm and extend to fluids with stable composition gradients previous findings on thermal convection. The fact that zonal flows can be avoided by using computational domains with large aspect ratios opens up the possibility of 2D studies of convective overshoot, layer formation, and transport properties across diffusive interfaces.

• Received 1 March 2021
• Accepted 21 July 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.074502