Abstract

We use Navier–Stokes-based linear models for wall-bounded turbulent flows to estimate large-scale fluctuations at different wall-normal locations from their measurements at a single wall-normal location. In these models, we replace the nonlinear term by a combination of a stochastic forcing term and an eddy dissipation term. The stochastic forcing term plays a role in energy production by the large scales, and the eddy dissipation term plays a role in energy dissipation by the small scales. Based on the results in channel flow, we find that the models can estimate large-scale fluctuations with reasonable accuracy only when the stochastic forcing and eddy dissipation terms vary with wall distance and with the length scale of the fluctuations to be estimated. The dependence on the wall distance ensures that energy production and energy dissipation are not concentrated close to the wall but are evenly distributed across the near-wall and logarithmic regions. The dependence on the length scale of the fluctuations ensures that lower wavelength fluctuations are not excessively damped by the eddy dissipation term and hence that the dominant scales shift towards lower wavelengths towards the wall. This highlights that, on the one hand, energy extraction in wall turbulence is predominantly linear and thus physics-based linear models give reasonably accurate results. On the other hand, the absence of linearly unstable modes in wall turbulence means that the nonlinear term still plays an essential role in energy extraction and thus the modelled terms should include the observed wall distance and length scale dependencies of the nonlinear term.

Highlights

  • When a flow passes over a solid wall it slows down to satisfy the no-slip boundary condition

  • We focus on applicability of the NS-based linear models to calculate the transfer function HL, eliminating the need for measured or numerically calculated data at the estimation locations for performing spectral linear stochastic estimation (SLSE)

  • We model the nonlinear term as a combination of eddy dissipation and white-in-time stochastic forcing terms

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Summary

Introduction

When a flow passes over a solid wall it slows down to satisfy the no-slip boundary condition. These fluctuations further increase the shear above the wall, increasing the mean shear stress at the wall (Adrian 2007) This has several important consequences, such as considerable increases in (i) the friction in transporting liquids through pipelines, (ii) the skin friction drag over aircraft and ships, and (iii) the dispersion of pollutants and the distribution of heat in the atmospheric boundary layer. The estimation of these fluctuations for either modelling or controlling their effects is of great significance (Smits & Marusic 2013). There is an increasing interest in estimating large-scale fluctuations because they (i) are easier to influence (Encinar & Jiménez 2019) and (ii) are dominant for engineering and environmental flows (Tomkins & Adrian 2005; Guala, Hommema & Adrian 2006; Smits, McKeon & Marusic 2011)

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