On the use of full particle trajectories and vorticity transport for dense velocity field reconstruction

A procedure is proposed to reconstruct the instantaneous velocity field from full particle trajectories in a data assimilation framework that includes the vorticity transport equation. The technique is christened as time-segment assimilation (TSA). The work addresses the common problem of low seeding concentration in 3D experiments, usually leading to limited spatial resolution. In the present study the measurement fidelity and spatial resolution are increased by considering finite time-segments as a whole for instantaneous velocity reconstruction. The use of a time-segment for velocity field reconstruction from measurement data extends previously proposed data assimilation techniques that consider only instantaneous measurement data (e.g. VIC+ and FlowFit), to use finite measurement time-segments. The assessment with sinusoids indicates lower errors due to modulation. However, the appearance of a range of amplified peaks is not fully understood. In the case of a simulated turbulent boundary layer measurement more vortical structures are recovered when a longer time-segment is used for the velocity field reconstruction.