Mathematical modeling, immersed boundary simulation, and experimental validation of the fluid flow around the upside-down jellyfish Cassiopea xamachana

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Last Modified
  • March 21, 2019
Creator
  • Hamlet, Christina
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • The jellyfish has been the subject of extensive research in the areas of ecology, biomechanics, fluid dynamics and engineering. Previous mathematical and experimental studies of the flows generated by jellyfish focused primarily on swimming mechanisms. Recently, the fluid dynamics of feeding from currents generated during swimming has been considered. In this study the benthic lifestyle of the upside- down jellyfish Cassiopea xamachana was capitalized upon to explore the fluid dynamics of feeding uncoupled from swimming. A two-dimensional mathematical model was developed to capture the fundamental characteristics of the motion of the unique concave bell shape. Given the prominence of the oral arm array, this structure was included and modeled as a porous layer that perturbs the flow generated by bell contractions. The immersed boundary method was used to solve the fluid-structure interaction problem. Parameter sweeps were used to explore numerically the effects of changes in pulse dynamics and the properties of the oral arms independently. Velocity fields obtained from live organisms using digital particle image velocimetry were used to validate the numerical simulations of the model. Parameter sweeps were used to explore the effects of scaling and to compare the model to a more traditional bell-only model. The effects of low-velocity background flow, neighboring jellyfish, and synchronous and asynchronous pulsing were also examined. The presence of the prominent porous layer structure in the field of flow increased the flux of new fluid from along the substrate to the bell. A consistent pattern of flow across the porous layer across a wide range of background flow patterns. The numerical simulations showed that pauses between bell expansion and the next contraction altered fluid flow over the bell and through the oral arms. Studies of the effects of neighboring models showed that spacing and relative size of individuals changed flow rates substantially. These substantial changes could explain so-called hitchhiking behavior observed in smaller or weakened jellyfish.
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  • In Copyright
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  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics."
Advisor
  • Miller, Laura
Degree granting institution
  • University of North Carolina at Chapel Hill
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Place of publication
  • Chapel Hill, NC
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  • Open access
Date uploaded
  • March 18, 2013

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