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Quantum fluids: space curves on vortex rings

Rudge, Kaleigh
; 
Strong, Scott
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2021
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Keywords
Jacobi elliptic functions
 space curves
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Reuleaux 2021
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Reuleaux_2021_Rudge_Strong_Quantum-Fluids.pdf
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https://hdl.handle.net/11124/178552
 https://doi.org/10.25676/11124/178552
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Abstract
Vortex filaments are a fundamental structure in fluid dynamics for transferring energy and are crucial in the understanding of how quantum turbulent structures settle. Building these geometric vortex lines can be performed by using Jacobi elliptic functions to piece together hoops on an elliptical curve in space. In this article we will discuss the geometry of these space curves. We will start with the static elliptical track with the hoop, and introduce the use of the Jacobi elliptic functions in the parameterized planes. Then we will observe the curve in space to discuss the curvature and torsion features of the curve. Finally, we will look at the vortex line in a unit parameterization case to further discuss our results.
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