Collaborative Research: Nonlinear Waves and Vorticity in Oceanic Flows

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1715082, Oliveras1715089, Curtis The investigators study the role of vorticity in three problems related to free-surface water waves in the ocean. Vorticity is a measure of the local rotation of a fluid. The investigators examine how eddies in fluids drive surface wave dynamics and how underwater currents that vary with depth affect nonlinear waves. They also study wind-driven waves and the effects of wind gusts. The first problem is related to the behavior of shoaling tsunamis in the presence of submerged eddies. The second leads to better understanding of the heights and velocities of surface waves over underwater currents, and can contribute to understanding how pollutants and micro-organisms propagate along underwater currents. The third helps explain how wind causes the formation of waves on the ocean surface. Undergraduate students participate in the research, and both investigators have records of engaging students from under-represented pools. The investigators study three separate topics regarding the influence of vorticity on free-surface water-waves: (1) how underwater eddies influence surface-wave dynamics, (2) how depth-varying currents exchange energy between density-stratified layers in the fully nonlinear regime, and (3) the development of a wind-wave generation model. These topics are approached through use of modified versions of the Unified Transform Method, a reformulation of Euler's equations of motion due to Ablowitz, Fokas, and Musslimani. The methods developed here are able to address a range of unexplored problems related to vorticity and depth-varying currents that are of interest to the fluid dynamics and oceanographic communities. For example, better understanding the stability of interfacial waves over depth-varying shear provides greater mathematical insight into the energy exchange between wind, currents, and waves beyond the linear regime. Undergraduate students participate in the research, and both investigators have records of engaging students from under-represented groups.