Identification of Lagrangian Coherent Structures Around Swimming Jellyfish from Experimental Time-Series Data

Author: Zhang, Zhonglin Johnny

Year: 2008

Degree: Senior thesis (Minor)

Advisors: Dabiri, John O.; Murray, Richard M.

Committee Member: Unknown, Unknown

Option: Aeronautics; Control and Dynamical Systems

DOI: 10.7907/KK45-ZV02

Abstract

The unique body kinematics of jellyfish embodies the most intriguing form of biological propulsion, which makes jellyfish a promising resource for developing new locomotion systems. Instead of the conventional Eulerian method, we take an unprecedented Lagrangian approach by tracking individual fluid particles around a swimming jellyfish over a finite time interval. Specifically, we utilize the Lagrangian coherent structures (LCS) in the flow field to investigate the flow characteristics around a jellyfish. LCS are separatrices or invariant manifolds, which separate the flow field into distinct regions. To locate the LCS in the flow, we employ the concept of the finite-time Lyapunov Exponent (FTLE), which measures the rate at which particles diverge from each other, and LCS are identified as the high-value ridges in the FTLE field. This method is implemented and validated by analysis on two-dimensional vortex dipole flow, two-dimensional experimental time-series data, and Hill’s vortex sphere. This method is expected to extract LCS from three-dimensional experimental time-series data.

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