Direct numerical simulation of turbulence in an internally heated convective fluid layer and implications for statistical modelling

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Abstract
Direct numerical simulations (DNS) are reported for the convection in an internally heated convective fluid layer which is bounded by rigid isothermal horizontal walls at equal temperature. The simulations for a fluid Prandtl number of seven cover seven distinct internal Rayleigh numbers in the range 105 ≤ RaI ≤ 109. From the numerical database the changes of convective patterns and dynamics for increasing RaI , i.e. increasing turbulence intensity, are analysed. To support the development and improvement of statistical turbulence models for this special type of convection, turbulence data for mean and fluctuating temperature and velocities are provided. For the simulation with RaI = 108 budgets of turbulence kinetic energy k and vertical turbulent heat flux are presented. In addition, closure assumptions commonly used in statistical turbulence models are tested against the DNS data. It is found that the turbulent diffusive transport of k and is strongly underestimated by standard models. The modelling of the turbulent heat fluxes by a turbulent Prandtl number approach is totally inadequate for internally heated convection. Instead, a second moment closure for is required.