Natural convection boundary layer in a stably stratified medium: Stability, transition and turbulence

Abstract

The three-dimensional linear stability, oblique transition and turbulence of a vertical natural convection boundary layer immersed in a stably stratified medium (vertical buoyancy layer) at a constant Prandtl number of 0.71 are investigated using numerical simulations. For linear instabilities, buoyancy and viscosity do not always destabilise the laminar flow but, depending on the Reynolds number, have a non-trivial influence on the linear growth of disturbances. Further, certain three-dimensional oblique wave instabilities have comparable growth rates to two-dimensional instabilities. These three-dimensional oblique waves can cause the vertical buoyancy layer to transition to turbulence without two-dimensional waves. This O-type transition in vertical buoyancy layers drastically differs from that observed in canonical wall-bounded flows. In vertical buoyancy layers, depending on the wavenumber of the initial oblique waves, the flow can transition by forming streaks, two-dimensional waves or a combination of the two. In contrast, canonical wall-bounded flows always transition by forming streaks. At sufficiently high Reynolds numbers, the flow becomes turbulent and new scaling laws are proposed for the turbulent mean flow and the one-point second-order turbulence statistics. The statistical turbulent structure of vertical buoyancy layers is investigated using two-dimensional correlations and one-dimensional energy spectra. It is demonstrated that large-scale streamwise elongated motions (eddies having length scales comparable to the outer length scale of the flow) populate the outer layer of the vertical buoyancy layer, exhibiting coherence across the entire thickness of the boundary layer. Finally, a theory and a phenomenological model are proposed to predict the relative scaling of longitudinal structure functions of streamwise velocity fluctuations. It is shown that the energy of the large-scale eddies is related to the intermittent dissipation field, implying that the large-scale and small-scale eddies are related. The developed theory is not limited to vertical buoyancy layers but is valid for shear-dominated turbulence in general.