Simulating the footprints of mixing in stratified fluids

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The majority of naturally occurring waters are density stratified for at least some portion of the year; stratification often separates the fluid into well-defined, nearly horizontal layers (e.g., warm water overlying cold) and in doing this changes the manner in which material is mixed and energy is distributed throughout the body of water. In a mid-sized lake on the Canadian shield, or in the coastal ocean, energetic motions may range in scale from multiple kilometers to sub-centimeter scales. Characterizing these motions is a challenge observationally, computationally and theoretically. The latter two are often coupled, and a large portion of the theoretical understanding of fluid motions in stratified fluids is built out of simplified, conceptual building blocks and is crucially dependent on high quality software to carry out simulations of the governing equations. Examples include coherent waves, called internal solitary-like waves, that transport material and energy over long distances without changing form and hydrodynamic instabilities, e.g., Kelvin-Helmholtz, Holmboe, that operate on small scales to mix the layers. The large scale motions' primary role in mixing is thus to set up conditions that are conducive to small scale instabilities. The proposed research program will extend the state of the art for simulations of internal wave induced mixing in stratified fluids to conditions more representative of the field (as opposed to the laboratory).  Particular areas of focus are: shoaling internal waves on shallow slopes, three dimensional wave-wave interactions, the effects of stratification due to heat and salt (i.e. double diffusive instability), and time dependent wave guides (e.g., due to radiative heating).  Stratified mixing due to heat and salt will be studied in the novel context of cave networks in the Yucatan, Mexico. The development of open source software will take place concurrently with scientific developments, and this software will be made available to the scientific community through github. Benefits to Canada will be accrued in three ways: 1) HQP will be trained in high performance computing and the application of this computing to scientific problems. Such individuals continue to be in short supply in both the public and private sectors, 2) high quality, open source software will be made available to the Canadian scientific community both with new tools and new scientific contexts, 3) novel process studies will test whether conclusions based on laboratory studies scale up to field scales. With a coastline that spans three extremely diverse oceans, a climate whose changes seem to accelerate each year, and economic interests that span the globe, Canada faces significant challenges in the coming decades. This proposal provides essential tools for an evidence-based approach to successfully tackling these challenges.