Using 3-D weakly relativistic fluid equations, the dynamics for the plasma beat wave generated by two circularly polarized electromagnetic waves with Gaussian profiles are obtained. Unlike for the linear theory the authors find that there is a strong cross-field coupling between the longitudinal and radial electric field components of the beat wave resulting in a nonlinear phase change and energy transfer between these two components. The resulting beat wave structure is controlled more by this cross-field coupling than by the other nonlinear terms such as the nonlinear coupling to the laser beams with the result that the accelerating region of the plasma beat wave is much more resistive than previously calculated.