Secondary mean motions arising in a buoyancy induced flow

Abstract The paper presents numerical calculations of the growth and non-linear interaction of two dimensional and transverse disturbances in a natural convection boundary layer flow adjacent to a vertical flat plate. We find that finite amplitude effects result in a double longitudinal mean secondary vortex system. At certain spanwise positions and, for particular phases of the primary wave, this highly organized longitudinal circulation causes an alternate spanwise thinning and thickening of the boundary region and resultant steepening and flattening of the base flow velocity profile. Measurements of the response of the flow to controlled two-dimensional streamwise disturbances, modulated by a transverse standing wave also show similar characteristics and that, in fact, the two disturbance features are and remain locked together at a small phase difference. Experimentally determined transition conditions thus correspond very closely to flows in which this analysis finds large vortex motions.