A new approach to understanding fluid mixing in process-study models of stratified fluids

Well established energy-based methods of quantifying diapycnal mixing in process-study numerical models are often used to provide information about when mixing occurs, and how much mixing has occurred. However, describing how and where this mixing has taken place remains a challenge. Moreover, methods based on sorting the density field struggle with under resolution and uncertainty as to the definition of the reference density when bathymetry is present. Here, an alternative method of understanding mixing is proposed. Paired histograms of user selected variables (which we abbreviate USP) are employed to identify mixing fluid, and are then used to display regions of fluid in physical space that are undergoing mixing. Here, two case studies are presented to showcase this method: shoaling internal solitary waves and a shear instability in cold water influenced by the nonlinearity of the equation of state. For the first case, the USP method identifies differences in the mixing processes associated with different internal solitary wave breaking types, including differences in the horizontal extent and advection of mixed fluid. For the second case, the method is used to identify how density, and passive tracers are mixed within the core of the asymmetric cold-water Kelvin-Helmholtz instability.