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.

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大纵横比下的剪切流及其抑制：不断增长的对流区的二维模拟

我们研究了当具有成分梯度的稳定分层流体从上方冷却时，不断增长的对流层中纬向流的发生和演变。这种配置允许在给定的模拟中研究大范围的瑞利数和对流区纵横比值的带状流。我们使用 Boussinesq 近似执行一系列二维 (2D) 模拟，其中计算域的纵横比介于 1 和 5 之间，并且 Prandtl 数 (Pr)$\mathrm{压力}=0.1$, 0.5, 1 和 7。对于纵横比为 1 的模拟，我们发现当对流层纵横比小于 2 时会出现纬向流，并且系统的演化取决于 Prandtl 数。为了$\mathrm{压力}\le 1$，流体经历对流传输的爆发，爆发之间的对流传输可以忽略不计。低 Pr 时爆发的幅度和频率较小，这表明爆发机制在 Pr 附近的狭窄范围内较强$\mathrm{压力}=1$正如在之前的热对流研究中所观察到的那样。为了$\mathrm{压力}=7$，流动的结构由倾斜的对流羽流组成，并且对流传输始终持续。在更广的域中，对流带的纵横比总是远大于2，并且不会出现带状流。这些结果证实并扩展到具有稳定成分梯度的流体先前关于热对流的发现。通过使用具有大纵横比的计算域可以避免带状流这一事实为对扩散界面的对流超调、层形成和传输特性进行二维研究提供了可能性。