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Detection of vortical structures in sparse Lagrangian data using coherent-structure colouring

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Abstract

In this study, vortical structures are detected on sparse Shake-The-Box data sets using the Coherent-Structure Colouring (CSC) algorithm. The performance of this Lagrangian approach is assessed by comparing the CSC-coloured tracks with the baseline vorticity field. The ability to extract vortical structures from sparse data is accessed on two Lagrangian particle tracking data sets: the flow past an Ahmed body and a swirling jet flow. The effects of two normalized parameters on the identification of vortical structures were defined and studied: the mean track length and the mean inter-particle distance. The accuracy of the vortical-structure detection problem through CSC is shown to improve with decreasing inter-particle distance values, whereas little dependence on the mean track length is observed at all. Overall, the CSC algorithm showed to yield accurate detection of coherent structures for inter-particle distances smaller than 15% of the characteristic dimension of the structure. However, the results quickly deteriorate for sparser Lagrangian data.

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Abbreviations

\(\overline{r}_{ij}\) :

Mean distance between the i-th and j-th tracks

\(r_{ij}\) :

Instantaneous distance between the i-th and j-th tracks

\(R_{x,y}\) :

Cross-correlation between x and y

\(\lambda\) :

Average inter-particle distance

L :

Track length

\(\overline{V}\) :

Mean particle velocity

\(\vert V \vert\) :

Mean flow velocity

D :

Characteristic length of the flow

\(\omega\) :

Vorticity field

\(\mathcal {A}\) :

Adjacency matrix

\(\mathcal {L}\) :

Laplacian matrix

\(\mathcal {D}\) :

Degree matrix

T :

Temporal track length

t :

flow time

\(a_{ij}\) :

Components of the second-order tensor \(\mathcal {A}\)

\(d_{ij}\) :

Components of the second-order tensor \(\mathcal {D}\)

X :

Eigenvector of the maximum eigenvalue \(\xi _{max}\)

\(\xi\) :

Eigenvalues of the spectral-clustering problem

\(x_i\) :

Components of the first-order tensor X

\(\psi\) :

Eulerian field

\(\phi\) :

Function of formalized parameters

C :

Particle concentration, \([N/D^d] | d =2, 3\)

l :

Mean radius of large-scale structures

\(\tau\) :

Mean characteristic period of large-scale structures, \(\tau =l/V_T\)

\(V_T\) :

Mean tangential velocity of large-scale structures

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Acknowledgements

DER acknowledges support from the NATO Science for Peace and Security programme.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada

    F. A. C. Martins & D. E. Rival

  2. Department of Aerodynamics, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands

    A. Sciacchitano

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  1. F. A. C. Martins
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  3. D. E. Rival
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Correspondence to D. E. Rival.

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Martins, F.A.C., Sciacchitano, A. & Rival, D.E. Detection of vortical structures in sparse Lagrangian data using coherent-structure colouring. Exp Fluids 62, 69 (2021). https://doi.org/10.1007/s00348-021-03135-5

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