Resonant standing internal waves in a basin filled with two liquids separated by a pycnocline

Combined theoretical and quantitative experimental study of resonant internal standing waves in a pycnocline between two miscible liquids in a narrow rectangular basin is presented. The waves are excited by a cylinder that harmonically oscillates in the vertical direction. A linear theoretical model describing the internal wave structure that accounts for pycnocline thickness, the finite wavemaker size and dissipation is developed. Separate series of measurements were performed using shadowgraphy and time-resolved particle image velocimetry. Accurate density profile measurements were carried out to monitor the variation of the pycnocline parameters in the course of the experiments; these measurements were used as the input parameters for the model simulations. The detected broadening of the pycnocline is attributed mainly to the presence of the waves and leads to the variation of the wave structure. The complex spatio-Temporal structure of the observed internal wavefield was elucidated by carrying band-pass filtering in the temporal domain. The experiments demonstrate the coexistence of multiple spatial modes at the forcing frequency as well as the presence of the internal wave system at the second harmonic of the forcing frequency. The results of the theoretical model are in good agreement with the experiments.