Accelerations in water waves by extended particle image velocimetry

Abstract

Particle image velocimetry (PIV) measures instantaneous velocity across an extended area of flow by recording the motion of tracers suspended in and moving with the fluid. This principle is extended to the measurement of higher moments of the velocity field (acceleration) by recording the velocity field at two separate time instants using two cameras, viewing the same region of flow. Planar illumination of large areas within a hydrodynamic flow is achieved using a scanned argon ion laser beam and individual velocity measurements are made by cross-correlating image pairs acquired with a cooled, frame-straddling camera. A high-speed acousto-optic modulator is used to shut off the CW laser after two scans of the flow have been captured by the first camera. The modulator switches the beam back on for the second velocity measurement after a programmed delay. Synchronization of the cameras and beam modulator with the scanning beam system is achieved with a purpose-built multi-channel synchronizer device and operated from an integrated modular tree-based acquisition and processing software system. The extended PIV system is employed to measure the velocities and accelerations in periodic waves in a precise laboratory wave tank. A complementary theoretical description of Stokes waves provides a comparison with the measurements. The theoretical model is very precise, with an error term being less than 0.5% relative to the primary wave for the conditions of the experiments. The purpose is to test the measurement system and to judge the accuracy of the wave experiments under realistic and controllable conditions in the laboratory. Good agreement between the experiments and theory is found. The relative accuracy of the present experiments and measurements may be quantified in terms of the standard deviation due to an ensemble of measurements. In the best case, we find a relative standard deviation of 0.6% for the velocity measurements and 2% for the accelerations. It is indicated that such an accuracy may be generally achieved by appropriately choosing the size of the field of view.