Non-normality and small-scale statistics in a three-dimensional, separated shear flow
Author(s)
Bilbao-Ludena, Juan Carlos
Papadakis, George
Type
Journal Article
Abstract
We analyse the small-scale characteristics, such as enstrophy, total strain and
normality/non-normality, in the three-dimensional, separated flow around a NACA 0018
wing using direct numerical simulations. The angle of attack is 10◦ and the Reynolds
number (based on the chord length) is Rec = 5000. The role of non-normality is
investigated by performing Schur decomposition of the velocity gradient tensor. We also
apply the Schur decomposition to derive new expressions for the production of enstrophy
and total strain arising from the mean flow inhomogeneity. We focus on two sections of
the flow, across the recirculating zone and along the transitioning shear layer, and compare
our results with homogeneous isotropic turbulence (HIT). Within the recirculating region,
the non-normality index is approximately 0 (and close to the HIT value), indicating
almost equal normal and non-normal contributions. However, in the separating layer non normal effects strongly dominate, especially in the region of kinetic energy growth. Only
in the decay region do the values of the non-normality index gradually approximate
HIT values. The production of enstrophy due to vortex stretching is dominated by
the mixed (interaction) term, where normal strain stretches non-normal vorticity. The
same component also dominates the strain self-amplification term. The contributions of
different QR regions to the production terms are also examined. Production due to mean
strain rate is triggered upstream compared with production due to fluctuating strain fields.
normality/non-normality, in the three-dimensional, separated flow around a NACA 0018
wing using direct numerical simulations. The angle of attack is 10◦ and the Reynolds
number (based on the chord length) is Rec = 5000. The role of non-normality is
investigated by performing Schur decomposition of the velocity gradient tensor. We also
apply the Schur decomposition to derive new expressions for the production of enstrophy
and total strain arising from the mean flow inhomogeneity. We focus on two sections of
the flow, across the recirculating zone and along the transitioning shear layer, and compare
our results with homogeneous isotropic turbulence (HIT). Within the recirculating region,
the non-normality index is approximately 0 (and close to the HIT value), indicating
almost equal normal and non-normal contributions. However, in the separating layer non normal effects strongly dominate, especially in the region of kinetic energy growth. Only
in the decay region do the values of the non-normality index gradually approximate
HIT values. The production of enstrophy due to vortex stretching is dominated by
the mixed (interaction) term, where normal strain stretches non-normal vorticity. The
same component also dominates the strain self-amplification term. The contributions of
different QR regions to the production terms are also examined. Production due to mean
strain rate is triggered upstream compared with production due to fluctuating strain fields.
Date Issued
2025-05-10
Date Acceptance
2025-03-15
Citation
Journal of Fluid Mechanics, 2025, 1010
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Journal / Book Title
Journal of Fluid Mechanics
Volume
1010
Copyright Statement
© The Author(s), 2025. Published by Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Publication Status
Published
Article Number
A41
Date Publish Online
2025-05-09