Results of an experimental study on the solidification and convection of a ternary solution of H$_2$O–CuSO$_4$–Na$_2$SO$_4$ when cooled from a vertical side boundary are presented. Cooling and crystallization at a sidewall result in the formation of horizontal gradients of composition and temperature which are restricted to thin boundary layers adjacent to the solid. The dynamics of the buoyancy-induced flows in the compositional and thermal boundary layers is shown to depend critically on the morphology of the growing solid as well as on the density changes in the fluid released on solidification. In a ternary system, the possibility of a density reversal in the residual fluid as a second component solidifies leads to a wide range of possible behaviours. Three broad regimes are identified and the flows which arise in two of these are studied in detail; the behaviour in the third regime can be inferred from these results. When the thermal and compositional boundary layers are both heavy and flow to the base of the tank (regime I), the evolution of the interior fluid is shown to be initially quantitatively similar to that arising from thermal convection only. Slow compositional changes in the interior only later result in a number of double-diffusive effects. When the compositional and thermal buoyancies in the boundary layers are opposed (regimes II and III), a unidirectional downflow, counterflow and upflow are all observed at various stages of the experiment. The onset and duration of these different flows is shown to depend on the ratio of compositional to thermal buoyancies, the relative fluxes in the boundary layers, and the crystal morphology. The effect of surface roughness for the particular ternary system investigated is quantified by measuring its effect on the fluxes in the boundary layers, which allows the modification of existing theories to predict the conditions under which the different boundary layer dynamics arise.