Identification of very large scale structures in the boundary layer over large roughness elements

Laurent Perret,Franck Kerhervé

doi:10.1007/s00348-019-2749-7

Abstract

The dynamics of a turbulent boundary layer developing over a cube array is investigated based on stereoscopic PIV measurements performed in a boundary layer wind tunnel. The fluctuating streamwise velocity component $$u'$$ is analyzed via the recently introduced Spectral Proper Orthogonal Decomposition method (S-POD). A modification of the definition of the spatial S-POD modes is proposed so that they are orthonormal to each other. This results in spatio-temporal modes which reflect the statistical organization of the most energetic structures both in space and time. It is first demonstrated that the first S-POD modes of $$u'$$ correspond to large-scale elongated coherent structures of low or high momentum. The existence of very large scale structures whose length spans several boundary layer thickness is demonstrated, in agreement with the recent similar findings for flows over smooth wall. These structures are found to be non-negligible contributors to the Reynolds shear stress and the turbulent kinetic energy. Their relationship with the smaller scales of the flow is investigated via the computation of joint third-order statistics and is shown to be of non-linear nature.

Highlights

During the past few years, very large scale motions (VLSMs) in turbulent boundary layers over smooth walls have received renewed attention from the research community
The Spectral Proper Orthogonal Decomposition method (S-proper orthogonal decomposition (POD)) acts as a band-pass filter applied to the bi(t), the width of which varying from +∞ (Nf = 0, equivalent to the classical POD) to the narrowest possible one, dictated by the particle image velocimetry (PIV) sampling of the flow (Nf = +∞, equivalent to the Fourier transform)
A high-Reynolds number boundary layer flow developing over large roughness elements representative of the urban canopy has been investigated via the use of the recently introduced spectral POD (Sieber et al 2016)

Summary

Introduction

During the past few years, very large scale motions (VLSMs) in turbulent boundary layers over smooth walls have received renewed attention from the research community. Common features of the VLSMs found in wallbounded flows are that they consist of elongated low- and high-speed regions relative to the mean flow populating the logarithmic and outer layers (Hutchins and Marusic 2007). Their streamwise extent scales with boundary layer thickness and can reach several times (Guala et al 2011).

Methods

Results

Conclusion