Skip to main content Accessibility help

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

  • Jurriaan J. J. Gillissen (a1), Alexandre Vilquin (a2), Hamid Kellay (a2), Roland Bouffanais (a3) and Dick K. P. Yue (a4)...


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.


Corresponding author

Email address for correspondence:


Hide All
Auliel, M. I., Castro, F., Sosa, R. & Artana, G. 2015 Gravity-driven soap film dynamics in subcritical regimes. Phys. Rev. E 92 (4), 043009.
Brent, R. P. 2013 Algorithms for Minimization Without Derivatives. Courier Corporation.
Bruinsma, R. 1995 Theory of hydrodynamic convection in soap films. Physica A 216 (1–2), 5976.
Chomaz, J.-M. 2001 The dynamics of a viscous soap film with soluble surfactant. J. Fluid Mech. 442, 387409.
Corpetti, T., Héas, P., Mémin, E. & Papadakis, N. 2009 Pressure image assimilation for atmospheric motion estimation. Tellus A 61 (1), 160178.
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), 8097.
Greffier, O., Amarouchene, Y. & Kellay, H. 2002 Thickness fluctuations in turbulent soap films. Phys. Rev. Lett. 88 (19), 194101.
Gunzburger, M. D. 2003 Perspectives in Flow Control and Optimization. SIAM.
Kalnay, E. 2003 Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press.
Liu, T. & Shen, L. 2008 Fluid flow and optical flow. J. Fluid Mech. 614, 253291.
Papadakis, N. & Mémin, É. 2008 Variational assimilation of fluid motion from image sequence. SIAM J. Imaging Sci. 1 (4), 343363.
Pires, C., Vautard, R. & Talagrand, O. 1996 On extending the limits of variational assimilation in nonlinear chaotic systems. Tellus A 48 (1), 96121.
Polak, E. 1971 Computational Methods in Optimization: A Unified Approach. Academic.
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), 18691882.
Tikhonov, A. N. & Arsenin, V. Y. 1977 Solutions of Ill-Posed Problems. Winston.
Wu, X. L., Martin, B., Kellay, H. & Goldburg, W. I. 1995 Hydrodynamic convection in a two-dimensional Couette cell. Phys. Rev. Lett. 75 (2), 236239.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed