Limiting regimes of turbulent horizontal convection. Part 2. Large Prandtl numbers

Abstract

Horizontal convection at large Rayleigh and Prandtl numbers is studied experimentally in a regime up to seven orders of magnitude larger in terms of Rayleigh numbers than previously achieved. To reach Rayleigh numbers up to $10^{17}$ , the horizontal density gradient is generated using differential solutal convection by a differential input of salt and fresh water controlled by diffusion in a novel experiment in which the zero-net mass flux of water is ensured through permeable membranes. This set-up allows us to accurately measure the Nusselt number in solutal convection by carefully controlling the amount of salt water exchanged through the membranes. Combined measurements of density and velocity across more than five orders of magnitude in Rayleigh numbers show that the flow transitions from the Beardsley & Festa (J. Phys. Oceanogr., vol. 2, issue 4, 1972, pp. 444–455), Shishkina & Wagner (Phys. Rev. Lett., vol. 116, issue 2, 2016, 024302) regime to the Chiu-Webster et al. (J. Fluid Mech., vol. 611, 2008, pp. 395–426) regime and frames the present results within the scope of Shishkina et al. (Geophys. Res. Lett., vol. 43, issue 3, 2016, pp. 1219–1225), and the theory of Part 1 (Passaggia & Scotti, vol. 997, 2024, J. Fluid Mech., A5). In particular, we show that, even for large Prandtl numbers, the circulation eventually clusters underneath the forcing horizontal boundary, leaving a stratified core without motion. Finally, the previous regime diagrams (Hughes & Griffiths, Annu. Rev. Fluid Mech., vol. 40, 2008, pp. 185–208; Shishkina et al., Geophys. Res. Lett., vol. 43, issue 3, 2016, pp. 1219–1225) are extended by combining the present results at high Prandtl numbers, the results at low Prandtl numbers of Part 1, together with previous results from the literature. This work sets a new picture of the transition landscape of horizontal convection over six orders of magnitude in Prandtl number and sixteen orders of magnitude in Rayleigh number.