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