Large-scale instabilities in a nonrotating turbulent convection

Abstract

A theoretical approach proposed in Phys. Rev. E 66, 066305 (2002) is developed further to investigate formation of large-scale coherent structures in a non-rotating turbulent convection via excitation of a large-scale instability. In particular, the convective-wind instability that causes formation of large-scale coherent motions in the form of cells, can be excited in a shear-free regime. It was shown that the redistribution of the turbulent heat flux due to non-uniform large-scale motions plays a crucial role in the formation of the coherent large-scale structures in the turbulent convection. The modification of the turbulent heat flux results in strong reduction of the critical Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the excitation of the convective-wind instability. The large-scale convective-shear instability that results in the formation of the large-scale coherent motions in the form of rolls stretched along imposed large-scale velocity, can be excited in the sheared turbulent convection. This instability causes the generation of convective-shear waves propagating perpendicular to the convective rolls. The mean-field equations which describe the convective-wind and convective-shear instabilities, are solved numerically. We determine the key parameters that affect formation of the large-scale coherent structures in the turbulent convection. In particular, the degree of thermal anisotropy and the lateral background heat flux strongly modify the growth rates of the large-scale convective-shear instability, the frequencies of the generated convective-shear waves and change the thresholds required for the excitation of the large-scale instabilities. This study elucidates the origins of the large-scale circulations and rolls in the atmospheric convective boundary layers and the meso-granular structures in the solar convection.

Large-scale patterns in Rayleigh–Bénard convection

“…Our main aim is to return to the question with which we closed a previous report on large scales of convection [21]: is there a natural scale to which the convective patterns tend when they are not inhibited by the geometry of the container? Some indication of the existence of a saturation scale is provided by the work of Cattaneo et al [18], Rincon et al [26] and Elperin et al [14]. Here we further explore this topic and consider a series of numerical simulations of Rayleigh-Bénard convection at several moderately large values of the Rayleigh number and for values of the aspect ratio ranging up to a ratio of horizontal to vertical domain size of about 38.…”

“…These structures have approximately circular horizontal cross-sections with diameters comparable to the boundary layer thickness and they typically traverse the full body of the fluid [1,2]. When the aspect ratio of the container is moderately large (horizontal domain size of about 4 to 6 times the layer depth) the plumes are found to congregate into patterns associated with large-scale circulations that have been studied experimentally [3][4][5][6][7][8][9][10], analytically [11][12][13][14] and numerically [15][16][17][18][19][20][21][22][23]. The dependence of the properties of turbulent convection and of large-scale circulations on aspect * Corresponding author.…”

Transition phenomena in unstably stratified turbulent flows

“…A mean-field theory [4,35,36] has been proposed to explain the formation of coherent structures in turbulent convection. It is known from laboratory experiments and numerical simulations [7,14,15,21] that the coherent structures in Rayleigh-Bénard turbulent convection are not driven by the turbulent Reynolds stresses associated with the tilting plumes at the upper and the lower horizontal walls.…”

Effect of large-scale coherent structures on turbulent convection

“…[14,42,43]. According to this theory a redistribution of the turbulent heat flux due to non-uniform largescale motions plays a crucial role in the formation of the large-scale coherent structures in turbulent convection.…”

“…A convective-wind instability in the shear-free turbulent convection causes the large-scale motions in the form of cells. In the sheared convection, the large-scale instability results in an excitation of convective-shear waves, and the dominant coherent structures in the sheared convection are rolls [14,42,43].…”