The contribution of internal waves to the rate of tracer transport in the ocean is investigated using a multi-pronged approach that combines mathematical wave?mean interaction theory, physical modeling, numerical simulation, and comparison with observational field data. Specific topics to be studied include the vertical and horizontal mixing of tracers induced by breaking internal waves, the horizontal dispersion of tracers by non-breaking internal waves, and the structure and transport induced by waves generated by geostrophic flow over topography.
Intellectual merit The proposed research is timely and motivated firstly because of the current and increasing availability of high-resolution ocean data, and secondly because of the current dawning of an era of gravity-wave-permitting ocean models. In such models we can anticipate in the coming years the emergence of numerical gravity waves, albeit at the threshold of the model resolution. This research is anticipated to provide better guidance and an improved framework in which to interpret sub-mesoscale observations both in the field and in high-resolution numerical models. Investigating these issues also raises new mathematical research questions, for instance in the area of non-Gaussian wave theory. So this project is a conceptual two-way link between intertwining mathematical and geophysical research trajectories.
Broader impact Results from this theoretical study may feed into the future design of next-generation ocean forecasting systems for weather and climate, which is of great societal importance. On the educational side, training in advanced mathematics and applied science is paramount to the research elements of this proposal. The proposal includes training of a post-doctoral researcher and a PhD student as well as provision for merit-based stipends for advanced undergraduates interested in research experiences. Experience shows that such early research experiences on topics of fundamental importance can trigger an undergraduate's decision to apply for graduate school in mathematics or in another natural science.
Small scale waves can play an important role in the long term dynamics of the ocean. This is true not only for the surface gravity waves that are familiar to everyone, but also for their cousins in the ocean interior, which are called internal gravity waves. Just as the surface waves owe their existence to the density difference between water and air, their internal counterparts owe their existence to the gradual density stratification within the ocean, where the water at the sea floor is some 3% denser than the water near the surface. Because it is very hard to observe the deep ocean directly, say a mile deep below the sea surface, much less is known about oceanic internal waves than about surface waves. Here our project shed some more theoretical light on the dynamcis of these waves, and on how they can contribute to the dynamcis of the global ocean. One point of interest is the creation of vortices by dissipating internal waves. This seems a mysterious process, but it is analogous to the more familiar creation of rip currents by breaking surface waves on a beach. Our theory elucidates how fundamentally the same process might be going on at water depth several miles below the se surface. Another result of our project concerns the decomposition of data obtained from ship-based measurements into components associated with waves and vortices. In such measurements an instrument is towed at a fixed depth behind a ship and measurements of fluid velocity are taken continuously. The problem is then to figure out which part of the measured velocity field can be attributed to internal waves and which part can be attributed to vortices. Here we discovered a new method by which this distinction can be made almost exactly, which is surprising given the sparsity of data obtained along a single ship track. Our method makes clear the importance of small scale internal waves to the observed fields, which points into the importance of these nearly invisible, but very essential, forms of fluid motion.
