Experiments in Fluids

, 58:140 | Cite as

Coupling temporal and spatial gradient information in high-density unstructured Lagrangian measurements

  • Jaime G. WongEmail author
  • Giuseppe A. Rosi
  • Amirreza Rouhi
  • David E. Rival
Research Article


Particle tracking velocimetry (PTV) produces high-quality temporal information that is often neglected when computing spatial gradients. A method is presented here to utilize this temporal information in order to improve the estimation of spatial gradients for spatially unstructured Lagrangian data sets. Starting with an initial guess, this method penalizes any gradient estimate where the substantial derivative of vorticity along a pathline is not equal to the local vortex stretching/tilting. Furthermore, given an initial guess, this method can proceed on an individual pathline without any further reference to neighbouring pathlines. The equivalence of the substantial derivative and vortex stretching/tilting is based on the vorticity transport equation, where viscous diffusion is neglected. By minimizing the residual of the vorticity-transport equation, the proposed method is first tested to reduce error and noise on a synthetic Taylor–Green vortex field dissipating in time. Furthermore, when the proposed method is applied to high-density experimental data collected with ‘Shake-the-Box’ PTV, noise within the spatial gradients is significantly reduced. In the particular test case investigated here of an accelerating circular plate captured during a single run, the method acts to delineate the shear layer and vortex core, as well as resolve the Kelvin-Helmholtz instabilities, which were previously unidentifiable without the use of ensemble averaging. The proposed method shows promise for improving PTV measurements that require robust spatial gradients while retaining the unstructured Lagrangian perspective.

Supplementary material

348_2017_2427_MOESM1_ESM.mp4 (8.7 mb)
Supplementary material 1 (mp4 8874 KB)
348_2017_2427_MOESM2_ESM.mp4 (7.5 mb)
Supplementary material 2 (mp4 7690 KB)
348_2017_2427_MOESM3_ESM.mp4 (7.5 mb)
Supplementary material 3 (mp4 7730 KB)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringQueen’s UniversityKingstonCanada
  2. 2.Department of Mechanical EngineeringThe University of MelbourneParkvilleAustralia

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