A low-storage method consistent with second-order statistics for time-resolved databases of turbulent channel flow up to Reτ=5300

Wall-bounded flows play an important role in numerous common applications, and have been intensively studied for over a century. However, the dynamics and structure of the logarithmic and outer regions remain controversial to this date, and understanding their dynamics is essential for the development of effective prediction and control strategies, and for the construction of a complete theory of wall-bounded flows. Recently, the use of time-resolved direct numerical simulations of turbulent flows at high Reynolds numbers has proved useful to study the physics of wall-bounded turbulence, but a proper analysis of the logarithmic and outer layers requires simulations at high Reynolds numbers in large domains, making the storage of complete time series challenging. In this paper a novel low-storage method for time-resolved databases is presented. This approach reduces the storage cost of time-resolved databases by storing filtered flow fields that target the large and intermediate scales, while retaining all the information needed to fully reconstruct the flow at the level of filtered flow fields and complete second-order statistics. This is done by storing also the filtered turbulent stresses, allowing to recover the exact effect of the small scales on the large and intermediate scales. A significant speed-up of the computations is achieved, first, by relaxing the numerical resolution, which is shown to affect only the dynamics close to the wall, but not the large scales stored in the database, and, second, by exploiting the computing power and efficiency of GPU co-processors using a new high-resolution hybrid CUDA-MPI code. This speed-up allows running for physically meaningful times to capture the dynamics of the large scales. The resulting temporally resolved large-scale database of a turbulent channel flow up to Reτ=5300, in large boxes for long times, is briefly introduced, showing significant indicators of large-scale dynamics with characteristic times of the order of up to eight eddy turnover times.