RÉSUMÉ

We study the effect of shear on the line plumes in turbulent mixed convection (MC) and Rayleigh Bénard convection (RBC) for a decade range of near-wall Rayleigh numbers (2.3 × 10⁶ ≤ Ra_w ≤ 2.17 × 10⁹) and shear Reynolds numbers (802 ≤ Re ≤ 15000) for a Prandtl number range of 0.7 ≤ Pr ≤ 10.1 in air and water. Plumes are visualised in mixed convection in air by smoke while the plumes in RBC in water are detected from the planar PIV fields using the horizontal divergence criteria [Vipin K. and Puthenveettil B. A., ExHFT-8, Lisbon, 2013]. In addition to our planforms we measure the plume spacings from the planforms of Gilpin et al. [J. Heat Transfer 100, 71 (1978)], Pirozzoli et al. [J. Fluid Mech. 821, 482 (2017)] and by Blass et al. [arXiv:1904.11400 , physics.flu-dyn]. The mean plume spacing λ increase with increase in Re while they decrease with increase in Ra_w, in addition to being a function of Pr. We propose a common scaling law that captures this complex dependence of the mean plume spacing on Ra_w, Re and Pr, λ* = λ− λ_o = SZ_sh/D, where S = Re³/Ra_w is the shear parameter, Z_sh is the viscousshear length, D is a function of Pr and λ₀ the plume spacing in the absence of shear.