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Observations of the meridional circulation of the Sun, which plays a key rolein the operation of the solar dynamo, indicate that its speed varies with thesolar cycle, becoming faster during the solar minima and slower during thesolar maxima. To explain this variation of the meridional circulation with thesolar cycle, we construct a theoretical model by coupling the equation of themeridional circulation (the $\phi$ component of the vorticity equation withinthe solar convection zone) with the equations of the flux transport dynamomodel. We consider the back reaction due to the Lorentz force of thedynamo-generated magnetic fields and study the perturbations produced in themeridional circulation due to it. This enables us to model the variations ofthe meridional circulation without developing a full theory of the meridionalcirculation itself. We obtain results which reproduce the observational data ofsolar cycle variations of the meridional circulation reasonably well. We getthe best results on assuming the turbulent viscosity acting on the velocityfield to be comparable to the magnetic diffusivity (i.e. on assuming themagnetic Prandtl number to be close to unity). We have to assume an appropriatebottom boundary condition to ensure that the Lorentz force cannot drive a flowin the subadiabatic layers below the bottom of the tachocline. Our results aresensitive to this bottom boundary condition. We also suggest a hypothesis howthe observed inward flow towards the active regions may be produced.

A theoretical model of the variation of the meridional circulation with the solar cycle