Estimates of the Strouhal number from numerical models of convection

We determine the Strouhal number (hereafter St), which is essentially a nondimensional measure of the correlation time, from numerical calculations of convection. We use two independent methods to estimate St. Firstly, we apply the minimal tau-approximation (MTA) on the equation of the time derivative of the Reynolds stress. A relaxation time is obtained from which St can be estimated by normalising with a typical turnover time. Secondly, we calculate the correlation and turnover times separately, the former from the autocorrelation of velocity and the latter by following test particles embedded in the flow.We find that the Strouhal number is in general of the order of 0.1 to 1, i.e. rather large in comparison to the typical assumption in the mean-field theories that St ≪ 1. However, there is a clear decreasing trend as function of the Rayleigh number and increasing rotation. Furthermore, for the present range of parameters the decrease of St does not show signs of saturation, indicating that in stellar convection zones, where the Rayleigh numbers are much larger, the Strouhal number may indeed be significantly smaller. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)