A physics-enabled flow restoration algorithm for sparse PIV and PTV measurements

The gaps and noise present in particle image velocimetry (PIV) and particle tracking velocimetry (PTV) measurements affect the accuracy of the data collected. Existing algorithms developed for the restoration of such data are only applicable to experimental measurements collected under well-prepared laboratory conditions (i.e. where the pattern of the velocity flow field is known), and the distribution, size and type of gaps and noise may be controlled by the laboratory set-up. However, in many cases, such as PIV and PTV measurements of arbitrarily turbid coastal waters, the arrangement of such conditions is not possible. When the size of gaps or the level of noise in these experimental measurements become too large, their successful restoration with existing algorithms becomes questionable. Here, we outline a new physics-enabled flow restoration algorithm (PEFRA), specially designed for the restoration of such velocity data. Implemented as a 'black box' algorithm, where no user-background in fluid dynamics is necessary, the physical structure of the flow in gappy or noisy data is able to be restored in accordance with its hydrodynamical basis. The use of this is not dependent on types of flow, types of gaps or noise in measurements. The algorithm will operate on any data time-series containing a sequence of velocity flow fields recorded by PIV or PTV. Tests with numerical flow fields established that this method is able to successfully restore corrupted PIV and PTV measurements with different levels of sparsity and noise. This assessment of the algorithm performance is extended with an example application to in situ submersible 3D-PTV measurements collected in the bottom boundary layer of the coastal ocean, where the naturally-occurring plankton and suspended sediments used as tracers causes an increase in the noise level that, without such denoising, will contaminate the measurements.