Intense turbulent convection in a horizontal plane liquid layer

Direct numerical simulation of turbulent convection in a horizontal liquid layer heated from below is performed within the framework of the nonstationary Navier—Stokes equations with the use of the Bubnov—Galerkin method. The main attention is given to calculations for superhigh supercriticalities. Computational burden is reduced by the use of the splitting method at each step of integration. Previously, the smallness of the residual arising from substitution of simulated results into the initial system of equations is demonstrated and the residual’s dependence on the number of reference functions and supercriticality is considered. A good agreement of the results obtained with the use of different numerical implementations of the Bubnov—Galerkin procedure is shown, in particular, for the stochastic processes corresponding to a low supercriticality and appearing with the formation of strange attractors close to a Mobius strip. The calculations were carried out for a wide range of supercriticality (from 1 to 34000). It is shown that simulations and experiment are in good qualitative agreement.     

A numerical analysis of the three-dimensional rayleigh-benard convection spectra

The problem of the incompressible liquid convection between two horizontal planes heated on the underside is considered in the three-dimensional statement. The horizontal boundaries are assumed to be free of tangential stresses and isothermal. The calculated temporal spectrum of the temperature pulsations at the convection cell center at a supercriticality of 410 agrees well with the experimental measurement result. The Bolgiano-Obukhov (BO), k ^−11/5, k ⁻³, and k ⁻⁵, were obtain for the velocity pulsations. The Kolmogorov spectra k ^−5/3 and k ^−2.4 were obtained for the temperature pulsations. The presence of clearly identified spectra in the convective flow under study allows this process to be characterized as developed turbulence.