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Preparation of Free-Surface Hyperbolic Water Vortices
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R Hänninen1, N Hietala1, H Salman2

  • 1Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland.

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|November 25, 2016
PubMed
Summary
This summary is machine-generated.

Researchers defined a Seifert framing for superfluid vortex filaments, introducing twist to recover kinetic helicity as a quadratic invariant. This method clarifies the quasi-classical limit of helicity in superfluids.

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Area of Science:

  • Fluid Dynamics
  • Quantum Fluids
  • Topological Fluid Mechanics

Background:

  • Kinetic helicity is a fluid dynamics invariant linked to vortex line topology.
  • Superfluid vorticity concentrates along filaments, but lacks a core structure, complicating helicity.
  • Standard helicity definitions fail to retain quadratic invariant properties in superfluids.

Purpose of the Study:

  • To redefine kinetic helicity for superfluid vortex filaments.
  • To recover the quadratic invariant properties of helicity in superfluids.
  • To explain the emergence of a quasi-classical helicity limit.

Main Methods:

  • Utilized a Seifert framing to define a spanwise vector for vortex filaments.
  • Introduced a twist component to the helicity definition.
  • Calculated internal twist using examples and related it to tangential velocity.

Main Results:

  • Recovered key properties of helicity as a quadratic invariant for superfluid vortex filaments.
  • Demonstrated that centreline helicity alone yields ambiguous results without twist.
  • Derived an internal twist angle equation similar to classical vortex tubes.

Conclusions:

  • A Seifert framing approach successfully reintroduces twist, restoring helicity's invariant properties in superfluids.
  • The method provides a clear understanding of how quasi-classical helicity arises from individual superfluid vortex filaments.