Mixing Dynamics in Double-Diffusive Convective Stratified Fluid Layers

Double-diffusive convection in a linearly stratified fluid in the presence of radiative cooling at the surface has been investigated experimentally and theoretically. The stratification strength, which was varied in the experiments, is characterized by the buoyancy frequency of a stable environment defined as N² = (g/ρ₀)/(dρ/d_z). The surface radiative cooling mimics buoyancy forcing incumbent at the surface of the ocean during the boreal winter months. The significant parameters governing the mixing dynamics for such a system were identified to be the Richardson number (Ri) and flux Rayleigh number (Ra_f). Controlled experiments were performed for Ri = 0–6, while maintaining a constant Ra_f = 2.58 x 10⁷. This indicates that the stratification strength N was changed while the cooling flux Q was fixed. The mixing and barrier layers were visualized using a commercial dye solution. The thickness of the mixing layer was quantified from the flow evolution images. It was found that the mixing layer decays exponentially with increase in the stratification strength owing to suppression of downward convective motion due to the buoyancy force. A similar trend was observed for the entrainment velocity. A scaling law was proposed as follows: Δ = CRi^–3/4, where Δ is the mixing layer depth and C is a constant. The experimental results were compared with theoretical analysis and reasonable agreement was found. The results would be useful in parameterizing the mixing and barrier layers in strongly stratified environments such as the Bay of Bengal.