Density Perturbation and Energy Flux of Internal Waves from Velocity Data

Internal waves play a crucial role in ocean mixing, and density perturbation and energy flux are essential quantities to investigate the generation and propagation of internal waves. This paper presents a methodology for calculating density perturbation and energy flux of internal waves only using a velocity field that is based on linearized equations for internal waves. The method was tested by numerical simulations of internal waves generated by tidal flowing over a Gaussian topography in a stratified fluid. The density perturbations and energy fluxes determined using our method that only used velocity data agreed with density perturbations and energy fluxes determined by the equation of state based on temperature data. The mean relative error (MRE) and root mean square error (RMSE) between the two methods were lower than 5% and 10% respectively. In addition, an experiment was performed to exam our method using the velocity field measured by Particle Image Velocimetry (PIV), and the setup of the experiment is consistent with the numerical model. The results of the experiments calculated by the methods using PIV data were also generally equal to those of the numerical model.