Ensembles in Urban Large Eddy Simulations with Changing Wind Direction

Abstract

Differences between time-averaged and ensemble-averaged wind are studied for the case of changing wind direction. We consider a flow driven by a temporally turning pressure gradient in both an idealized case of a staggered cube array and a realistic urban environment. The repeating structure of the idealized case allows us to construct a large ensemble of 3 240 members with a reasonable compute time. The results indicate that the use of plain time averaging instead of an ensemble average can severely reduce the accuracy of both the mean and variance. These errors are the largest when the averaging time is of the same order as the time scale associated with the turning. Utilizing Taylor diagrams, we show that a reasonable compromise between ensemble size and accuracy can be achieved by calculating the ensemble statistics from temporally averaged results with an averaging time that is clearly smaller than the characteristic time scale. This allows the use of reasonably-sized ensembles with 10-50 members. By applying this approach to the realistic urban geometry, we identify building wakes as the regions most severely affected by the incorrectly use of time averaging.