title: Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer.
abstract: Thermal instability in a horizontal Newtonian liquid layer with rigid boundaries is investigated in the presence of vertical quasiperiodic forcing having two incommensurate frequencies omega1 and omega2. By means of a Galerkin projection truncated to the first order, the governing linear system corresponding to the onset of convection is reduced to a damped quasiperiodic Mathieu equation. The threshold of convection corresponding to quasiperiodic solutions is determined in the cases of heating from below and heating from above. We show that a modulation with two incommensurate frequencies has a stabilizing or a destabilizing effect depending on the frequencies ratio omega=omega2/omega1. The effect of the Prandtl number in a stabilizing zone is also examined for different frequency ratios.
authors.affiliation: University Hassan II Aïn-Chock, Faculty of Sciences, Laboratory of Mechanics, Casablanca, Morocco.
authors.forename: Taoufik
authors.initials: T
authors.lastname: Boulal
authors.forename: Saïd
authors.initials: S
authors.lastname: Aniss
authors.forename: Mohamed
authors.initials: M
authors.lastname: Belhaq
authors.forename: Richard
authors.initials: R
authors.lastname: Rand