A theoretical study is presented of convection in a horizontal fluid layer heated from below or above which is periodically accelerated in its plane. The analysis is based on Galerkin methods as well as on direct numerical simulations of the underlying Boussinesq equations.
Shaking in a fixed direction breaks the original isotropy of the layer. At onset of convection and at small acceleration, we find longitudinal rolls, where the roll axis aligns parallel to the acceleration direction. With increasing acceleration amplitude, a shear instability takes over and transverse rolls with the axis perpendicular to the shaking direction nucleate at onset. In the nonlinear regime, the longitudinal rolls become unstable against transverse modulations very close to onset which leads to a kind of domain chaos between patches of symmetry degenerated oblique rolls.
In the case of circular shaking, the system is isotropic in the time average sense, however, with a broken chiral symmetry. The onset of convection corresponds to the transverse roll case studied before with the roll axis selected spontaneously. With increasing Rayleigh number, a heteroclinic cycle is observed with the roll changing its orientation periodically in time. At even higher Rayleigh number, this heteroclinic cycle becomes chaotic similarly to the case of the Küppers–Lortz instability.