The effect of gravity on the generation and propagation of flows induced by thermoacoustic waves in an enclosure was numerically investigated. The compressible unsteady Navier-Stokes equations were solved by combining a flux-corrected transport algorithm for the convection terms and by a central differencing scheme for the viscous and conduction terms. In the simulations, the left wall of the enclosure is heated rapidly either in a spatially uniform or a nonuniform manner, whereas the right wall is held at the initial temperature of the gas., The upper and lower walls of the enclosure are insulated. At zero gravity, the spatially nonuniform beating generates a vortical flow in the enclosure, similar to that found in buoyancy-induced flows in a side-heated enclosure. For the conditions considered, the strength of the flows induced by the thermoacoustic waves is comparable to the flows induced by buoyancy.