Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-19T11:26:49.740Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Auliel, M. I., Castro, F., Sosa, R. & Artana, G. 2015 Gravity-driven soap film dynamics in subcritical regimes. Phys. Rev. E 92 (4), 043009.Google Scholar
Brent, R. P. 2013 Algorithms for Minimization Without Derivatives. Courier Corporation.Google Scholar
Bruinsma, R. 1995 Theory of hydrodynamic convection in soap films. Physica A 216 (1–2), 59–76.Google Scholar
Chomaz, J.-M. 2001 The dynamics of a viscous soap film with soluble surfactant. J. Fluid Mech. 442, 387–409.Google Scholar
Corpetti, T., Héas, P., Mémin, E. & Papadakis, N. 2009 Pressure image assimilation for atmospheric motion estimation. Tellus A 61 (1), 160–178.Google Scholar
Corpetti, T., Heitz, D., Arroyo, G., Memin, E. & Santa-Cruz, A. 2006 Fluid experimental flow estimation based on an optical-flow scheme. Exp. Fluids 40 (1), 80–97.Google Scholar
Greffier, O., Amarouchene, Y. & Kellay, H. 2002 Thickness fluctuations in turbulent soap films. Phys. Rev. Lett. 88 (19), 194101.Google Scholar
Gunzburger, M. D. 2003 Perspectives in Flow Control and Optimization. SIAM.Google Scholar
Kalnay, E. 2003 Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press.Google Scholar
Liu, T. & Shen, L. 2008 Fluid flow and optical flow. J. Fluid Mech. 614, 253–291.Google Scholar
Papadakis, N. & Mémin, É. 2008 Variational assimilation of fluid motion from image sequence. SIAM J. Imaging Sci. 1 (4), 343–363.Google Scholar
Pires, C., Vautard, R. & Talagrand, O. 1996 On extending the limits of variational assimilation in nonlinear chaotic systems. Tellus A 48 (1), 96–121.Google Scholar
Polak, E. 1971 Computational Methods in Optimization: A Unified Approach. Academic.Google Scholar
Su, L. K. & Dahm, W. J. 1996 Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. I. Assessment of errors. Phys. Fluids 8 (7), 1869–1882.Google Scholar
Tikhonov, A. N. & Arsenin, V. Y. 1977 Solutions of Ill-Posed Problems. Winston.Google Scholar
Wu, X. L., Martin, B., Kellay, H. & Goldburg, W. I. 1995 Hydrodynamic convection in a two-dimensional Couette cell. Phys. Rev. Lett. 75 (2), 236–239.Google Scholar