Random field reconstruction of inhomogeneous turbulence. Part II: Numerical approximation and simulation

A novel random field model or the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities in terms of stochastic Fourier-type integrals has recently been introduced and analyzed by the authors. This article concerns the numerical discretization and implementation of the model and discusses its key features by means of numerical simulations. We present a suitable discretization scheme that combines a randomized quadrature method for stochastic integrals with a local linearization of the non-uniform advection of the turbulent structures by the mean flow. The convergence of the scheme towards the continuous model is verified analytically. Moreover, we describe an efficient algorithmic implementation that allows for flexible local evaluations of the simulated turbulence field. The main features of the model are illustrated by a variety of simulation results, each highlighting specific aspects such as the influence of the inhomogeneous model parameters on the generated fluctuations, spatio-temporal ergodicity properties under inhomogeneous flow conditions, and the validity of Kolmogorov's two-thirds law in dependence on the local turbulence Reynolds number.