TY - JOUR

T1 - Large-scale circulations in a shear-free convective turbulence

T2 - Mean-field simulations

AU - Orian, G.

AU - Asulin, A.

AU - Tkachenko, E.

AU - Kleeorin, N.

AU - Levy, A.

AU - Rogachevskii, I.

N1 - Funding Information:
The authors benefited from stimulating discussions of various aspects of turbulent convection with A. Brandenburg, F. H. Busse, P. J. K€apyl€a, and S. Zilitinkevich. This research was supported in part by the Israel Ministry of Science and Technology (Grant No. 3-16516) and the PAZY Foundation of the Israel Atomic Energy Commission (Grant No. 122-2020).
Publisher Copyright:
© 2022 Author(s).

PY - 2022/10

Y1 - 2022/10

N2 - It has been previously shown [Elperin et al., "Formation of large-scale semi-organized structures in turbulent convection,"Phys. Rev. E 66, 066305 (2002)] that a non-rotating turbulent convection with nonuniform large-scale flows contributes to the turbulent heat flux. As a result, the turbulent heat flux depends explicitly not only on the gradients of the large-scale temperature, but also on the gradients of the large-scale velocity. This is because the nonuniform large-scale flows produce anisotropic velocity fluctuations, which modify the turbulent heat flux. This effect causes an excitation of a convective-wind instability and formation of large-scale semi-organized coherent structures (large-scale convective cells). In the present study, we perform mean-field numerical simulations of shear-free convection, which take into account the modification of the turbulent heat flux by nonuniform large-scale flows. We use periodic boundary conditions in horizontal direction as well as stress-free or no-slip boundary conditions in vertical direction. We show that the redistribution of the turbulent heat flux by the nonuniform large-scale motions in turbulent convection plays a crucial role in the formation of the large-scale semi-organized coherent structures. In particular, this effect results in a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale convective cells. We demonstrate that the convective-wind instability is excited when the scale separation ratio between the height of the convective layer and the integral turbulence scale is large. The level of the mean kinetic energy at saturation increases with the scale separation ratio. We also show that inside the large-scale convective cells, there are local regions with the positive vertical gradient of the potential temperature, which implies that these regions are stably stratified.

AB - It has been previously shown [Elperin et al., "Formation of large-scale semi-organized structures in turbulent convection,"Phys. Rev. E 66, 066305 (2002)] that a non-rotating turbulent convection with nonuniform large-scale flows contributes to the turbulent heat flux. As a result, the turbulent heat flux depends explicitly not only on the gradients of the large-scale temperature, but also on the gradients of the large-scale velocity. This is because the nonuniform large-scale flows produce anisotropic velocity fluctuations, which modify the turbulent heat flux. This effect causes an excitation of a convective-wind instability and formation of large-scale semi-organized coherent structures (large-scale convective cells). In the present study, we perform mean-field numerical simulations of shear-free convection, which take into account the modification of the turbulent heat flux by nonuniform large-scale flows. We use periodic boundary conditions in horizontal direction as well as stress-free or no-slip boundary conditions in vertical direction. We show that the redistribution of the turbulent heat flux by the nonuniform large-scale motions in turbulent convection plays a crucial role in the formation of the large-scale semi-organized coherent structures. In particular, this effect results in a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale convective cells. We demonstrate that the convective-wind instability is excited when the scale separation ratio between the height of the convective layer and the integral turbulence scale is large. The level of the mean kinetic energy at saturation increases with the scale separation ratio. We also show that inside the large-scale convective cells, there are local regions with the positive vertical gradient of the potential temperature, which implies that these regions are stably stratified.

UR - http://www.scopus.com/inward/record.url?scp=85140487469&partnerID=8YFLogxK

U2 - 10.1063/5.0110716

DO - 10.1063/5.0110716

M3 - Article

AN - SCOPUS:85140487469

SN - 1070-6631

VL - 34

JO - Physics of Fluids

JF - Physics of Fluids

IS - 10

M1 - 105121

ER -