Turbulent Convection Driven by a Constant Temperature Gradient

To better understand the nature of small-scale fluctuations and spectra in turbulent convection, we consider the theoretically interesting case of buoyancy driven thermal convection without boundary layers: that is we use numerical simulations to study the case of turbulent convection in a periodic box driven by a constant temperature gradient. High Rayleigh numbers are achieved using hyperviscous dissipation. The system develops constant heat flux via transport by a few strong ascending/descending jets. This heat flux is highly intermittent even at integral scales. Also, the heat flux depends only weakly on viscosity. We find that the scaling laws for spectra of temperature and velocity fluctuations are consistent with Kolmogorov scaling and inconsistent with Bolgiano-Obukhov scaling. At the level of spectra, the system is approximately locally isotropic. We also find that constant temperature gradient thermal convection exhibits a unique kind of intermittent structure in that scaling exponents of nth order moments of temperature differences saturate when n is large enough. A comparison is made between constant temperature gradient thermal convection and convection of a passive scalar with a constant scalar gradient. It is shown that at small scales the statistical properties of passive scalar convection are quite similar to that of thermal convection.