Investigation of penetrative convection in stratified fluids through 3D-PTV

Abstract

Testing existing theories of flow and transport in stably stratified fluids when “penetrative convection” occurs requires experimental methods capable of fully three-dimensional descriptions of both the Eulerian velocity field and Lagrangian particle trajectories. Boundary layer experiments utilizing a photogrammetric three-camera three-dimensional Particle Tracking Velocimetry (3D-PTV) technique were performed on a laboratory model which simulated the evolution of the mixing layer in a stably stratified fluid body by heating a tank filled with water from below. A combination of image- and object space-based information was employed to establish the spatio-temporal correspondences between particle positions at consecutive time steps. An appropriate calibration procedure for the stereoscopic system provides the intrinsic and extrinsic parameters of the stereoscopic system to be used for determining the correspondence of points in the object or world reference frame and in the image reference frame. The photogrammetric principles used by 3D-PTV are described. First, the fundamental mathematical model of the collinearity condition and its extensions are explained. Then, the epipolar line intersection method built upon multicamera correspondences (structure-from-stereo) is discussed as well as the procedure of reconstruction of particle trajectories in a single step by conjunctly establishing the spatial and temporal correspondences between particle images. Tests on simulated data were performed as well as experimental data in order to ensure the method’s operability and robustness. The reconstructed velocity fields are compared to other laboratory investigations and field data.