Three-dimensional thermal convection in a cubic cavity heated from one wall and chilled from its opposite wall in the terrestrial-gravity and zero-gravity fields with and without a sinusoidal modulation is investigated numerically. The gravity and its modulation are parallel to the temperature gradient. An incompressible fluid with Prandtl number Pr= 7.1 (water) is considered and hence the Boussinesq approximation is used. The gravity-modulation parameters are a vibrational Rayleigh number Ra-eta and a non-dimentional gravity-modulation frequency omega. Here the authors report a novel 'trident' flow structure in laminar and steady thermal convection, which consists of a point-symmetric pair of three-pronged flows, namely, three ascending streams and three descending streams in the cube. This flow structure is stable and persistent in the sense that it is observed in all three situations: a stationary cube under the terrestrial gravity, an oscillating cube under the terrestrial gravity, and an oscillating cube under zero gravity. A POD analysis confirmed this observation. Tested parameters are Rayleigh number Ra = 8.0 x 10(4) in the terrestrial-gravity field without the gravity modulation or Ra = 1.0 x 10(4) ; and the gravity modulation in the terrestrial-gravity field Ra-eta = 1.0 x 10(5) and omega = 5.0 in the terrestrial-gravity field and Ra-eta = 1.1 x 10(5) and omega = 5.0 in the zero-gravity field. (C) 2019 Elsevier Ltd. All rights reserved.