Coherent dynamics and turbulence dynamics in model geophysical flow

My Ph.D. study consists of three portions -- turbulence dynamics, coherent dynamics, and two newly developed analytic tools to probe turbulence dynamics and coherent dynamics in any generic flows. First, we study the turbulent dynamics in the model geophysical flow because the majority of fluid flows in nature and engineering applications are turbulent. Turbulent flows are distinct because they display a characteristic cascade of energy, which is typically described in an abstract way. My research recasts the turbulent energy cascade as a mechanical process so that, as with any energy flux, it can be interpreted as the result of the action of the turbulent stress against the rate of strain. Using the mechanical model and with the help of filter space techniques (FST), we define the efficiency of turbulence cascades based on the geometry of stress and rate of strain for the first time in the field. Moreover, our work reveals that the advection is a missing piece in the well- known "thinning mechanism". We find that excessive advection dampens the cascade efficiency by disrupting the delicate angle alignment between stress and rate of strain that is required to transfer energy. Additionally, we utilize FST to study decay turbulence. These works can eventually lead to new strategies for turbulence modeling. Second, transport phenomena are complicated but not random. Anyone who has observed ocean surface currents realizes that the flow appears to be composed of coherent motions that persist in time. Examples include eddies and jets that move in the flow for a longer time than the background flow. Such coherent structures are spatiotemporally compact regions of the flow that are thought to be important for determining mixing and transport. Geophysical flows can be well approximated as two-dimensional on large scales. And two-dimensional flows, in turn, are particularly prone to producing a range of coherent structures. However, how such structures interact with lateral boundaries such as coastlines, and bottom boundaries such as nonuniform bathymetry, is not well understood. A laboratory two-dimensional flow and Lagrangian coherent structure methods are used to study these questions. The research characterizes the different effects of canonical lateral boundary shapes and bottom bathymetry. Furthermore, we finds reduced transport across a bathymetric interface and describes this reduced transport in terms of the "porous transport barrier separating the two regions. The results can have implications in the siting of coastal facilities that must ensure the appropriate mixing for minimizing environmental impacts and benefit precise control to aquaculture. Third, I propose the two new tools which redefined what it means of coherence. Traditionally, coherent structures are perceived as spatiotemporally compact regions of the flow. By elegant redefinition, the coherent structures can tackle many more interesting and important engineering problems that include but are not limited to revealing information content in complex flows, effective compressing of flow data, recovering missing measurements, and connecting turbulent dynamics and kinematics. We redefine coherence based on linear predictability, i.e., perceiving coherent structures as regions that were highly predictable by knowing only a small subset of them. The research results in two tools: Linear Neighborhood (LN) and Dynamical Linear Neighborhood (DLN), which have shown promising results in the problems mentioned above

Advisor: Ouellette Nicholas (Nicholas Testroet)
Dabiri John O. (John Oluseun)
Fringer Oliver B. (Oliver Bartlett)