Abstracts - KTH Mechanics

172
Lagrangian (physical) analysis of coherent vortical structures
D. Doorly ∗ ,I.Motazavi † , and S. Sherwin ∗
One of the most helpful techniques to study two and three-dimensional vortex
dynamics is the identification of the Coherent structures (CS). Coherent structures
generally refer to the organised and concentrated rotational patterns within the flow
and are a useful way to characterise flow evolution in time. An important feature
of coherent structures identification is the reduction of a vector flow field into scalar
quantity. Typically a specific isocontour value, or cutoff, of the scalar quantity is then
chosen to identify the coherent structures. Whilst the original definitions 1 , 2 defined
exact values for the cutoff in numerical practise the cutoff value is varied to eliminate
numerical noise.
In this work, we focus on the Lagrangian (physical) interpretation of a Coherent
Structure (CS). A more physical understanding of the λ2 criterion suggested by Jeong
and Hussain can be gained by considering the motion of two adjacent points in a
plane. Here, we shall show that if we ignore contributions from unsteady the strain
and rotational tensor then the λ2 criterion can be interpreted as requiring the inner
product of the displacement between two material points with the acceleration of the
two points, i.e.
∆x · ∆ ′′
x < 0 (1)
where the superscript prime denote time differentiation. When λ2 < 0weshall
demonstrate that this can be interpreting as equivalent to requiring that the inner
product (1) is satisfied for all points in one plane containing the point of interest.
Then, we study the cutoff (λ2) choice for a CS and its effect on the identification
procedure extending previous research 3 to three-dimensional flows. The results show
that the exact application of the vortex identification approaches can generate noisy
vorticity configurations 4 . Ranges of choice of cut-off values are extensively studied
for laminar (Re = 100) and transitional (Re = 500) external and internal flows.
As a procedure for choosing an appropriate cut-off the proportion of the enstrophy
captured within the λ2 coherent structure to the total enstrophy within the global
flow domain is studied. We see that an appropriate value of λ2 permits to capture the
coherent vortices. Larger or smaller cut-off values, either generate large noise or miss
the main informations on vortical structures. We propose that numerical application
of the λ2 to coherent structure identification criterion should be used in conjunction
with an enstrophy capture analysis to determine a valid range of cut-off values.
∗ Department of Aeronautics, Imperial College London, London, SW7 2BY, UK.
† MAB UMR 5466, Université Bordeaux 1 and INRIA, 351 cours de la Libération, F-33405 Talence.
1 Joeng and Hussain, J. Fluid Mech. 285, 69 (1995).
2 Weiss, Physica D 48, 273 (1991).
3 Creusé andMortazavi,Europ. J. Mech. B/Fluids 20, 603 (2001).
4 Miliou, Mortazavi and Sherwin Comptes Rendus Acad. Sc. 333, 211 (2005).