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Linear-model-based estimation in wall turbulence: Improved stochastic forcing and eddy viscosity terms

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Gupta, V 
Madhusudanan, A 
Wan, M 
Illingworth, SJ 
Juniper, MP 


jats:pWe 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.</jats:p>



turbulent boundary layers, turbulence modelling

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Journal of Fluid Mechanics

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Cambridge University Press (CUP)


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This work was supported by the National Natural Science Foundation of China (grant nos. 91752201, 12002147 and 12050410247), the Shenzhen Science and Technology Innovation Committee (KQTD20180411143441009), the Department of Science and Technology of Guangdong Province (grant nos. 2019B21203001 and 2020B1212030001) and the Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou (GML2019ZD0103). We acknowledge support from the Centers for Mechanical Engineering Research and Education at MIT and SUSTech, as well as from the Center for Computational Science and Engineering at SUSTech. AM and SJI are grateful for the financial support of the Australian Research Council.