In this numerical study, we investigate natural convection in a two-dimensional square-section enclosure vibrating sinusoidally parallel to the applied temperature gradient in a zero-gravity field. The full Navier–Stokes equations are simplified with the Boussinesq approximation and solved by a finite difference method. Whereas the Prandtl number Pr is fixed to 7.1 (except for some test cases with Pr = 7.0, 6.8), the vibrational Rayleigh number Ra based on acceleration amplitude is varied from 1.0 × 104 to 1.0 × 105, and dimensionless angular frequency ω is varied from 1.0 × 100 to 1.0 × 103. In the tested range, time evolutions exhibit synchronous, 1/2-subharmonic and non-periodic responses, and flow patterns are characterized mainly by one- or two-cell structures. Flow-regime diagrams show considerable differences from results in a non-zero-mean-gravity field even at large acceleration amplitudes, and suggest that some parts of non-periodic-response regimes may be related to transitions between flow patterns. The amplitude of fluctuations in spatially averaged kinetic energy density K (equal to the difference between maximum and minimum kinetic energies over a cycle) tends to be large when fluid is stationary everywhere over some interval of time during each period, and has a peak when fluid begins to move continuously throughout one period. Such peaks are caused by impulsively started convection, and are not connected to resonant oscillations in a constant-gravity field.