A space-time integral minimisation method for the reconstruction of velocity fields from measured scalar fields.*

Scalar image velocimetry (SIV) reconstructs 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 scalar measurements to be sufficiently resolved and relatively noise free, such that space and time derivatives can be accurately evaluated. To alleviate these requirements, we propose an improved SIV scheme, which does not require evaluating the space and time derivatives of the measured scalar field. Improved velocity reconstruction is demonstrated for a two dimensional, synthetic field. We furthermore apply the scheme to interferograms of the thickness field of a turbulent soap film. The reconstructed velocity fluctuations are within 10 % of laser Doppler velocimetry measurements.