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A space–time integral minimisation method for the reconstruction of velocity fields from measured scalar fields

Published online by Cambridge University Press:  06 September 2018

Jurriaan J. J. Gillissen Open the ORCID record for Jurriaan J. J. Gillissen [Opens in a new window] ,
Alexandre Vilquin Open the ORCID record for Alexandre Vilquin [Opens in a new window] ,
Hamid Kellay ,
Roland Bouffanais Open the ORCID record for Roland Bouffanais [Opens in a new window]  and
Dick K. P. Yue Open the ORCID record for Dick K. P. Yue [Opens in a new window]
Jurriaan J. J. Gillissen*
Affiliation:
Center for Environmental Sensing and Modeling (CENSAM) IRG Singapore-MIT Alliance for Research and Technology (SMART) Centre, Science Drive 2, 117543Singapore
Alexandre Vilquin
Affiliation:
Laboratoire Ondes et Matière d’Aquitaine (UMR CNRS 5798), Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
Hamid Kellay
Affiliation:
Laboratoire Ondes et Matière d’Aquitaine (UMR CNRS 5798), Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
Roland Bouffanais
Affiliation:
Singapore University of Technology and Design, 8 Somapah Road, Singapore487372, Singapore
Dick K. P. Yue
Affiliation:
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
*
†Email address for correspondence: jurriaangillissen@gmail.com
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Abstract

Scalar image velocimetry (SIV) is the technique to extract velocity vectors from scalar field measurements. The usual technique involves minimising a cost functional, that penalises the deviation from the scalar conservation equation. This approach requires the measured scalar field to be sufficiently resolved and relatively noise free, such that space and time derivatives of the measured scalar field can be accurately evaluated. We quantify these requirements for a synthetic two-dimensional (2-D) turbulent flow field by evaluating the velocity reconstruction accuracy as a function of the temporal and spatial resolution and the noise level. We propose an improved SIV scheme, that reconstructs not only the velocity field but also the scalar field, which does not require approximating the space and time derivatives of the measured scalar field. Improved velocity reconstruction is demonstrated for the 2-D synthetic field. We furthermore apply the scheme to interferograms of the thickness field of a falling soap film, where 2-D turbulence is generated by an array of cylindrical obstacles. The statistics of the reconstructed velocity field are within 10 % of laser Doppler velocimetry measurements.

JFM classification

Mathematical Foundations: Mathematical Foundations Mathematical Foundations: Variational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 854 , 10 November 2018 , pp. 348 - 366
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Copyright
© 2018 Cambridge University Press 

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