On the use of finite mixtures to improve the physical interpretation of a ground vortex flow

Laser-Doppler measurements of the velocity characteristics of a ground vortex flow resulting from the collision of a wall jet with a boundary layer are analyzed using advanced statistical tools, namely finite mixtures of probability density functions. These are determined by the best fitting to experimental results using a Bayesian approach based on a Markov Chain Monte Carlo (MCMC) algorithm. This approach takes into account eventual multimodality and heterogeneities in velocity field distributions. Therefore, it provides a more complete information about heterogeneous velocity distributions and its corresponding characteristic velocities and turbulent fluctuations. The ground vortex flow investigated is generated by a wall jet-to-boundary layer velocity ratio of 2. The results evidence how finite mixtures are able to reconstruct the measured probability distribution in the form of a mathematical probability density function. This allows to improve the physical interpretation of the ground vortex flow through quantifying its complex structure, which is particularly relevant to VSTOL aircraft flows. Namely, identify the separation point oscillation region, and the enlargement of the region comprising the effect of collision between wall jet and boundary layer in planes moving away from the wall. Also, in the collision zone, following a conventional statistical analysis, the rms velocity fluctuation (u′) appears to be overestimated for the horizontal component due to the measured velocity range oscillating between positive and negative values. The results evidence how U‾ and u′ provide an idea of the flow dynamics, but their use is limited and an important amount of information associated with the highly curved flow complexity is lost. This prevents distinguish the magnitude of velocity fluctuations according to the flow direction, and the endorsement of anisotropy near the collision region, justifying the possibility of being numerically simulated.