A Lagrangian Approach to Transport of Momentum and Biomass in Aquatic Biological Systems

In recent years, a Lagrangian Coherent Structures (LCS) method was developed to identify boundaries between distinct kinematic regions in unsteady flows. Many fluid transport processes can be described in terms of these kinematic boundaries in the flow. The method has since been applied to many engineering, biological, and geological fluid systems, but primarily on transport of homogenous fluid mass. In this thesis, with emphases on aquatic biological transport systems, the LCS analysis is further developed to study momentum transport in animal locomotion and biomass transport in animal predation. Three independent studies are included in this thesis. In the first study, LCS analysis is used to identify the boundary of the vortex attached to the fin in sunfish pectoral fin locomotion. A potential flow, deformable body theory is used to describe the dynamics of the vortex. The hydrodynamic forces acting on the fin are evaluated from the linear momentum of the vortex itself and its added-mass. The quantification of instantaneous locomotive forces provides necessary information for studying complicated locomotive behaviors such as motion control and maneuvers. In the second study, the LCS analysis is applied to a numerically simulated undulatory swimming and shows existence of 'upstream fluid structures' that are invisible in Eulerian velocity/vorticity fields. These structures indicate the exact portion of fluid that interacts with the swimmer. A mass flow rate and a momentum flux are then defined. A metric for propulsive efficiency is established using the momentum flux, which can be used to measure and compare the efficiency of other engineering and natural propulsion systems. In the third study, a framework is developed to study transport of zooplankton prey in the feeding currents generated by a predator jellyfish. An equation of motion is proposed to describe the dynamics of prey in the flow. Then the concept of particle Lagrangian Coherent Structures (pLCS) is introduced to separate prey encounter regions from prey escape regions. The framework provides a mechanical basis for evaluating the predatory role of medusae in marine planktonic ecosystems. It can also be used to study transport and mixing in multiphase and granular flows in general.