In this work the role of Coriolis forces in the evolution of a two-dimensional thermally driven flow in a rotating enclosure of arbitrary geometry is discussed. Contrary to the claims made in some of the studies involving such class of flows that there is an active involvement of the these forces in the dynamics of the flow, it is shown that the Coriolis force does not play any role in the evolution of the velocity and temperature fields. This is theoretically demonstrated by recognizing the irrotational character of the Coriolis force in such class of flows. It is further shown that the presence of the irrotational Coriolis force affects only the pressure distribution in the rotating enclosure. The theoretical deductions apply quite generally to any geometry and thermal boundary conditions associated with the enclosure. The numerical results for the problem of two-dimensional thermally driven flow of air $(Pr=0.71)$ in a circular rotating enclosure provide direct evidence of the theoretical deductions.

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