Experimental investigation of non-linear standing internal waves using combined density and velocity measurements

Abstract

To provide insight to the dynamics of weakly non-linear standing internal waves, the density and velocity fields are measured using combined planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques. A laboratory-scale apparatus was created to generate standing internal waves in a two-layer stratified system. Experimental results are presented for two configurations with a density jump of 1.1 kg/m\(^3\) and 1.5 kg/m\(^3\) (separately). The interface location, wave amplitude and period, interface thickness, convection transport terms, fluid velocity, shear strain rate, and vorticity are quantified and analyzed at fixed phases in the wave cycle. The comparison between the internal wave frequency computed from the experimental results and the dispersion relationship resulting from the theoretical third-order Stokes internal-wave solution confirms that the laboratory-generated waves demonstrate non-linear behavior. The interface detected from experimental PLIF images indicated that due to the non-linear effects, a steeper wave with a sharper-looking interface at anti-node locations was formed in comparison with the theoretical linear sinusoidal shape. Further, the magnitude of shear strain rate and vorticity computed from experimental PIV measurements had a sharp, non-linear increase along the interface compared to the one computed from the linear theory. This non-linear trend in shear strain rate and vorticity can lead to the generation of sharper interface and short-period (i.e., higher frequency) non-linear internal waves.