  It is widely accepted that astrophysical magnetic fields are generated by
dynamo action. In many cases these fields exhibit organisation on a scale
larger than that of the underlying turbulent flow (e.g., the eleven-year solar
cycle). The mechanism for the generation of so-called large scale fields
remains an open problem. In cases where the magnetic Reynolds number ($Rm$) is
small, dynamo-generated fields are coherent but at (the astrophysically
relevant) high $Rm$, the fields are overwhelmed by small scale fluctuating
field. Recently Tobias and Cattaneo (2013) have shown that an imposed large
scale shear flow can suppress the small scale fluctuations and allow the large
scale temporal behaviour to emerge. Shear is also believed to modify the
electromotive force by introducing correlations between the flow and the field.
However in previous models at high $Rm$ the shear is often artificially imposed
or driven by an arbitrary body force. Here we consider a simple kinematic model
of a convective dynamo in which shear is self consistently driven by the
presence of a horizontal temperature gradient (resulting in a thermal wind) and
a rotation vector that is oblique to gravity. By considering a
$2.5$-dimensional system, we are able to reach high $Rm$ so that the dynamo
approaches the asymptotic regime where the growth rate becomes approximately
independent of $Rm$. We find the flows studied here to be excellent small-scale
dynamos, but with very little systematic behaviour evident at large $Rm$. We
attribute this to being unable to self-consistently generate flows with both
large (net) helicity and strong shear in this setup.
