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Beltrami Flows

Margetis, Alexander
http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1525299172164402

Abstract Details

2018, BS, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Our goal will be to find a weak solution to the Beltrami flow. A Beltrami flow in three-dimensional space is an incompressible (divergence free) vector field that is everywhere parallel to its curl. That is, curl(B) = λ B for some function. These flows arise naturally in many physical problems. In astrophysics and in plasma fusion Beltrami fields are known as force-free fields. They describe the equilibrium of perfectly conducting pressure-less plasma in the presence of a strong magnetic field. In fluid mechanics, Beltrami flows arise as steady states of the 3D Euler equations. Numerical evidence suggests that in certain regimes turbulent flows organize into a coherent hierarchy of weakly interacting superimposed approximate Beltrami flows. Given the importance of Beltrami fields, there are several approaches to proving existence of solutions, for instance use the calculus of variations, and use fixed point arguments. In this thesis we instead use a Hilbert space approach through the Lax-Milgram lemma.
Benjamin Jaye (Advisor)
Andrew Tonge (Committee Member)
Dexheimer Veronica (Committee Member)
Jeremy Williams (Committee Member)
23 p.
Applied Mathematics; Astrophysics
Beltrami Flows; Pressureless Fields; Plasma Fusion; Magnetic Field; Sun Corona; Finite Elements Method; Dirichlet; Neumann;

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Citations

  • Margetis, A. (2018). Beltrami Flows [Undergraduate thesis, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1525299172164402

    APA Style (7th edition)

  • Margetis, Alexander. Beltrami Flows. 2018. Kent State University, Undergraduate thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1525299172164402.

    MLA Style (8th edition)

  • Margetis, Alexander. "Beltrami Flows." Undergraduate thesis, Kent State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1525299172164402

    Chicago Manual of Style (17th edition)

ksuhonors1525299172164402
466
© 2018, some rights reserved.Creative Commons License Beltrami Flows by Alexander Margetis is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Kent State University Honors College and OhioLINK.