相关论文: Helicity, Topology and Kelvin Waves in reconnectin…
The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of…
A new algebraic method for computing helicity is developed, by discovering a relationship between helicity of fluid mechanics and algebraic polynomial invariants of knot theory. We have constructed a topological invariant…
We numerically study the evolution of a small turbulent region of quantised vorticity in superfluid helium, a regime which can be realised in the laboratory. We show that the turbulence achieves a fluctuating steady-state in terms of…
Kinetic helicity (hereafter helicity) is defined by the correlation between the velocity and the flow-aligned vorticity. Helicity, as well as energy, is an inviscid invariant of the hydrodynamic equations. In contrast to energy, a measure…
For certain families of fluid flow, a new conserved quantity -- stream-helicity -- has been established.Using examples of linked and knotted streamtubes, it has been shown that stream-helicity does, in certain cases, entertain itself with a…
Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be…
Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main…
The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the…
Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of…
We consider the reconnection of two untwisted, linked quantised vortex rings in a Bose-Einstein condensate. We show that the reconnection is capable of transferring helicity, from the links present in the initial configuration, to a…
Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by…
The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental…
Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to the recombination in polymer physics and…
Knots and links are fundamental topological objects play a key role in both classical and quantum fluids. In this research, we propose a novel scheme to generate torus vortex knots and links through the reconnections of vortex rings…
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical…
In superfluid helium, vorticity is quantized and constrained on line-like phase singularities, called quantum or quantized vortices. By visualizing the motion of sub-micron frozen particles in superfluid $^{4}$He, we directly observe for…
An overview is given of the helicity of the velocity field (``kinetic'' helicity to distinguish it from the ``magnetic'' helicity used in magnetohydrodynamics, astrophysics, and solar physics; or simply \emph{helicity} in this Chapter) and…
Helicity, a measure of the linkage of flux lines, has subtle and largely unknown effects upon dynamics. Both magnetic and hydrodynamic helicity are conserved for ideal systems and could suppress nonlinear dynamics. What actually happens is…
In this paper, the Kelvin wave and knot dynamics are studied on three dimensional smoothly deformed entangled vortex-membranes in five dimensional space. Owing to the existence of local Lorentz invariance and diffeomorphism invariance, in…
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent…