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We offer a unifying theory for turbulent purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, 2001) for Rayleigh--Benard turbulence and of Shishkina, Grossmann and Lohse (2016) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nondimensionalized, the Rayleigh--Roberts number) and the Prandtl number. The results of the theory are consistent with our direct numerical simulations.
An experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh numbers ($1.18
Convection over a wavy heated bottom wall in the air flow has been studied in experiments with the Rayleigh number $sim 10^8$. It is shown that the mean temperature gradient in the flow core inside a large-scale circulation is directed upward, that c
Direct numerical simulations are employed to reveal three distinctly different flow regions in rotating spherical Rayleigh-Benard convection. In the low-latitude region $mathrm{I}$ vertical (parallel to the axis of rotation) convective columns are ge
If a fluid flow is driven by a weak Gaussian random force, the nonlinearity in the Navier-Stokes equations is negligibly small and the resulting velocity field obeys Gaussian statistics. Nonlinear effects become important as the driving becomes stron
We present high-precision experimental and numerical studies of the Nusselt number $Nu$ as functions of the Rayleigh number $Ra$ in geostrophic rotating convection with domain aspect ratio ${Gamma}$ varying from 0.4 to 3.8 and the Ekman number Ek fro