LES-informed resolvent-based estimation of turbulent pipe flow

Abstract

A resolvent-based methodology is employed to obtain spatio-temporal estimates of turbulent pipe flow from low-rank probe measurements of wall shear-stress fluctuations. Direct numerical simulations (DNS) and large-eddy simulations (LES) of turbulent pipe flow at friction Reynolds number of 550 are used as databases. We consider a DNS database as the true spatio-temporal flow field, from which wall shear-stress fluctuations are extracted and considered as measurements. A resolvent-based estimator is built following our earlier work (Amaral et al. J. Fluid Mech., vol. 927, 2021, p. A17), requiring a model for the nonlinear (or forcing) terms of the Navier-Stokes equations system, which are obtained from another DNS database, as in our earlier work, and from a series of computationally cheaper LES databases with coarser grids; the underlying idea is that LES may provide accurate statistics of non-linear terms related to large-scale structures at a low computational cost. Comparisons between the DNS and the estimates indicate that sufficiently accurate results can be achieved with estimators built with statistics from LES with an order of magnitude less grid points than the DNS, with estimates closely matching the reference DNS results up to the buffer layer and reasonable agreement up to the beginning of the log layer.