Analysis of Multipoint Correlations in Direct Numerical Simulation

TL;DR

This paper investigates the Markov properties of turbulent flow generated by DNS around an airfoil, revealing that turbulence structures can be modeled as stochastic processes, which advances understanding of turbulence modeling.

Contribution

It demonstrates the existence of Markov properties in turbulent flow near an airfoil, enabling stochastic modeling of turbulence structures based on DNS data.

Findings

Markov properties are present in turbulent flow near the airfoil.

Turbulence structures can be approximated by stochastic processes.

Limits of Gaussian Langevin processes are identified in the flow.

Abstract

We examine the Markov properties of the three velocity components of a turbulent flow generated by a DNS simulation of the flow around an airfoil section. The spectral element code Nektar has been used to generate a well resolved flow field around an fx79w-151a airfoil profile at a Reynolds number of Re=5000 and an angle of attack of {\alpha} = 12{\deg}. Due to a homogeneous geometry in the spanwise direction, a Fourier expansion has been used for the third dimension of the simulation. In the wake of the profile the flow field shows a von Karman street like behavior with the vortices decaying in the wake which trigger a turbulent field. Time series of the 3D flow field were extracted from the flow at different locations to analyze the stochastic features. In particular the existence of Markov properties in the flow have been shown for different cases in the surrounding of the airfoil. This is of basic interest as it indicates that fine structures of turbulence can be replaced by stochastic processes. Turbulent and Markovian scales are being determined in the turbulent field and limits of standard Gaussian Langevin processes are being determined by the reconstruction of a flow field in time and space.