The neutral wind field effects on the development of the equatorial plasma bubbles have been simulated by a two-dimensional time-dependent model similar to that developed by Zalessak and Ossakow. The results indicate that when there exists no neutral wind, any perturbation on the bottom-side of the ionosphere density profile will be amplified by the gravitational Rayleigh-Taylor (GRT) instability and an upwelling bubble will form as expected. When a zonal neutral wind field exists, the uplift velocity of the bubble will be enhanced by a uniform neutral wind, but suppressed by vertical shear of the wind field. Secondary structures called plumes will grow out from the side walls of the primary bubble if some secondary perturbation signal with vertical structure is seeded. We notice that patches and multiple plume structures have been observed in the mid-latitude and low-latitude ionosphere. So we have developed a two-dimensional local theory of the generalized GRT instability to calculate the growth rate of a small-scale perturbation signal in the vicinity of the primary bubble and found that the growth rate increases with time along with the growth of the bubble. It is proved that the irregularities generated by some of our simulations should be able to cascade into observable (e.g., by radar) turbulence: in a reasonable period of time after their generation Similar to the effect on the growth of the primary bubble, a strong uniform wind field may enhance the growth rate of a perturbation signal in the vicinity of the bubble, while a strong vertical wind shear will suppress the growth rate. The main point of this theory is that the growth rate of the GRT instability is controlled by the density gradients and the magnitudes of the velocity of the plasma motion, relative to the neutral wind in both directions. In addition, our simulations have proved that a seeding wave with phase velocity matching the background wind speed will generate the fastest growing bubble, disapproving the theory of spatial resonance.