Rotating non-Oberbeck--Boussinesq Rayleigh-Bénard convection in water

Abstract

Rotating Rayleigh-Bénard convection in water is studied in direct numerical simulations, where the temperature dependence of the viscosity, the thermal conductivity and the density within the buoyancy term is taken into account. In all simulations the arithmetic mean of the lowest and highest temperature in the system equals 40°C, corresponding to a Prandtl number of Pr = 4.38. In the non-rotational case the Rayleigh number Ra ranges from 107 to 1.16 × 109 and temperature differences Δ up to 70K are considered, whereas in the rotational case the Rossby number range from 0.05 ≤ Ro ≤ 10.0 is studied for Δ = 40K with the focus on Ra = 108. The non-Oberbeck-Boussinesq (NOB) effects in water are reflected in an up to 5.5K enhancement of the center temperature and in an up to 5% reduction of the Nusselt number. The top thermal and viscous boundary layer thicknesses increase and the bottom ones decrease, while the sum of the corresponding top and bottom thicknesses remains as in the classical Oberbeck-Boussinesq (OB) case. Rotation applied to NOB thermal convection reduces the central temperature enhancement. Under NOB conditions the top (bottom) thermal and viscous boundarylayers become equal for slightly smaller (larger) Rossby number than in the OB case. Furthermore, for rapid rotation the thermal bottom boundary layers become thicker than the top ones. The Nusselt number normalized by that in the non-rotating case depends similarly on Ro in both, the NOB and the OB cases. The deviation between the Nusselt number under OB and NOB conditions is minimal when the thermal and viscous boundary layers are equal.