Observations of the quiet solar surface indicate that localised concentrations of vertical magnetic flux tend to accumulate in the convective downflows. Furthermore, there is some evidence to suggest that mesogranular boundaries are preferred locations for the formation of these flux concentrations. This implies that these magnetic fields are organised on scales that are larger than the granular scale. One possible explanation for the existence of quiet Sun magnetic features is that they are continuously regenerated by the near-surface convective motions. Motivated by this, we consider dynamo action in a local Cartesian model of convection in a compressible electrically conducting fluid. The horizontal scale of this domain is large enough to model mesoscale behaviour. Dynamo action occurs provided that the magnetic Reynolds number exceeds some critical value. In the kinematic regime the presence of mesogranules seems to be beneficial for dynamo action: compared to similar smaller aspect ratio calculations, we find higher kinematic growth rates for the magnetic energy, as well as a lower value for the critical magnetic Reynolds number. In the nonlinear regime the peak magnetic field strengths compare very favourably to observations, greatly exceeding the equipartition value at the surface, as observed in the quiet Sun. However, there is no evidence to suggest that the presence of mesogranules significantly increases the saturation level of the dynamo in this nonlinear regime, which (in the highest magnetic Reynolds number case) is comparable to that found in similar calculations in smaller domains.
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