Abstract
We present high-resolution direct numerical simulation studies of turbulent Rayleigh–Bénard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We have also investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory.
Highlights
IntroductionRecently the focus of direct numerical simulations (DNS) studies was shifted toward the bulk in a cubic convection cell [17] with a discussion of the scaling properties and statistics of the dissipation fields
In the present work we want to make a further step forward with direct numerical simulations (DNS) of RBC by resolving fine scales never accessed before, both in the bulk and boundary layers, in order to study the statistics of the gradient fields, their joint extreme events, the statistical effect of rare high-amplitude events as well as Rayleigh and Prandtl number variation
We find that the global measures of heat transport, such as Nusselt number, time-averaged temperature profiles and volume-averaged dissipation rates, are fairly insensitive to insufficient resolution, as long as the mean Kolmogorov length is resolved
Summary
Recently the focus of DNS studies was shifted toward the bulk in a cubic convection cell [17] with a discussion of the scaling properties and statistics of the dissipation fields It is well-known that the gradients of the turbulent fields are most sensitive to insufficient resolution. Superfine resolution simulations in isothermal box turbulence [23,24,25] and in turbulent shear flows [14] have led to some enlightening results on the distribution of the finest scales in such flows and their relation to the small-scale intermittency This intermittency is known to be coupled tightly to two highly fluctuating dissipation rates, one of the kinetic energy and the other of the thermal variance.
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