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Uncovering complex behavior in turbulence and sediment transport through simplified models
Although the dynamics of a turbulent fluid and of grains being transported downriver might not have much in common, it's the qualities they share that make them challenging subjects to study. Both contain many interacting components and nonlinearities, producing a chaotic, multi-scale, out-of-equilibrium system whose statistical properties are difficult to predict in a rigorous way. Furthermore, the range of temporal and spatial scales that they possess make direct numerical simulations of large systems (e.g. large Reynolds number flows or an alluvial channel) challenging and limited in scope. Because of this, an understanding of the system must be achieved through sensible approximations and simplifications of the full system. In this talk, I will introduce two open questions (1) the existence of sharp transitions of energy cascade directions in geophysical turbulence, and (2) the origins of intermittent statistics in sediment transport, and demonstrate the power that simplified models have in helping us uncover previously unattainable detail and understanding.