Numerical investigation of spectrums of three-dimensional turbulent convection

The three-dimensional turbulent convectional flows of viscous and incompressible fluid in a rectangular parallelepiped numerically is simulated at heating from below. The horizontal boundaries are stress-free and isothermal. The calculated time spectrum of temperature pulsations at supercriticality is equal to 410 in centre of convective cell has a good agreement with experimental data for convection in cryogenic $He$. The Obukhov–Bolgiano spectra $k^{-11/5}$, $k^{-3}$ and $k^{-5}$ have been found for velocity pulsations. Also for temperature pulsations the Kolmogorov $k^{-5/3}$ and $k^{-2.4}$ are obtained. Such spectrums denote on temperature behavior as passive admixture and that dominant force for velocity is buoyancy.