Rayleigh-Benard (RB) convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimension (2D) RB convection and the other one three-dimension (3D) RB convection with a rotating axis parallel to the plate. We explore the parameter range of Rayleigh numbers Ra from $10^7 to $10^9$ and Prandtl numbers $Pr$ from $1$ to $100$. We show that zonal flow, which was observed, for example, by Goluskin emph{et al}. emph{J. Fluid. Mech.} 759, 360-385 (2014) for $Gamma=2$, is only stable when $Gamma$ is smaller than a critical value, which depends on $Ra$ and $Pr$. With increasing $Gamma$, we find a second regime in which both zonal flow and different convection roll states can be statistically stable. For even larger $Gamma$, in a third regime, only convection roll states are statistically stable and zonal flow is not sustained. For the 3D simulations, we fix $Ra=10^7$ and $Pr=0.71$, and compare the flow for $Gamma=8$ and $Gamma = 16$. We demonstrate that with increasing aspect ratio $Gamma$, zonal flow, which was observed for small $Gamma=2pi$ by von Hardenberg emph{et al}. emph{Phys. Rev. Lett.} 15, 134501 (2015), completely disappears for $Gamma=16$. For such large $Gamma$ only convection roll states are statistically stable. In between, here for medium aspect ratio $Gamma = 8$, the convection roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2D case.
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