Numerical simulations of thermal convection on a hemisphere

Abstract

In this paper we present numerical simulations of two-dimensional turbulent convection on a hemisphere. Recent experiments on a half soap bubble located on a heated plate have shown that such a configuration is ideal for studying thermal convection on a curved surface. Thermal convection and fluid flows on curved surfaces are relevant to a variety of situations, notably for simulating atmospheric and geophysical flows. As in experiments, our simulations show that the gradient of temperature between the base and the top of the hemisphere generates thermal plumes at the base that move up from near the equator to the pole. The movement of these plumes gives rise to a two-dimensional turbulent thermal convective flow. Our simulations turn out to be in qualitative and quantitative agreement with experiments and show strong similarities with Rayleigh-Bénard convection in classical cells where a fluid is heated from below and cooled from above. To compare to results obtained in classical Rayleigh-Bénard convection in standard three-dimensional cells (rectangular or cylindrical), a Nusselt number adapted to our geometry and a Reynolds number are calculated as a function of the Rayleigh number. We find that the Nusselt and Reynolds numbers verify scaling laws consistent with turbulent Rayleigh-Bénard convection: Nu ∝ Ra 0.31 and Re ∝ Ra 1/2 . Further, a Bolgiano regime is found with the Bolgiano scale scaling as Ra −1/4 . All these elements show that despite the significant differences in geometry between our simulations and classical 3D cells, the scaling laws of thermal convection are robust.

Systems of intensive vertical vortices in turbulent atmosphere

“…Results of DNS of a thermal (Rayleigh-Bénard) convection on a hemisphere were reported in recent Ref. [23]. In this DNS a gradient of temperature between the heated equator and the pole creates a thermal convection with Rayleigh number Ra = 10 10 and Prandtl number P r = 7.…”

“…18 of the Ref. [23] and corresponds to a stationary state). The variable k in this figure is the spherical wavenumber.…”

Buoyancy driven distributed chaos and ensemble weather forecasting

“…18 of the Ref. [21] for the stationary state spectrum, Ra = 10 10 and P r = 7). The variable k is the spherical wavenumber.…”

“…Substituting the helicity correlation integral into Eq. (7) and using the dimensional considerations one obtains: (21) and then from the Eq. (19)…”

“…In a recent paper Ref. [21] results of a direct numerical simulation (DNS) of a Rayleigh-Bénard-like (thermal) convection on a hemisphere were reported. The system was heated at the equator and the gradient of temperature between the equator and the pole generates thermal plumes near the equator that move up from the equator zone toward the pole creating a thermal convection.…”