Related papers: Helicity within the vortex filament model
We comment on the paper by Van Gorder ["Motion of a helical vortex filament in superfluid ${}^4$He under the extrinsic form of the local induction approximation", Phys. Fluids 25, 085101 (2013)]. We point out that the flow of the normal…
Scroll waves exist ubiquitously in three-dimensional excitable media. It's rotation center can be regarded as a topological object called vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and even…
Superfluid helium is an intimate mixture of a viscous normal fluid, with continuous vorticity, and an inviscid superfluid, where vorticity is constrained to thin, stable topological defects. One mechanism to generate turbulence in this…
We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl. For a broad class of initial data sharing only the macroscopic…
This paper deals with the longstanding quest of the possible existence of finite-time singularities in the equations governing the dynamics of inviscid fluids, namely, Euler equations. Here, two contributions are brought for the case of…
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…
Recent studies of pseudo-plane ideal flow (PIF) reveal a ubiquitous presence of vortex alignment in both homogeneous and stratified fluids, and in both inertial and rotating reference frames as well. The exact solutions of a steady-state…
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…
In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows from Newtonian fluids to plasmas. Since…
Near absolute zero, superfluid liquid helium displays quantum properties at macroscopic length scales. One property, superfluidity, means flow with zero viscosity. Another property, the existence of a complex wavefunction, constrains the…
A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied to examine how the energy cascade is established and how this event could serve as a new test of LES turbulence models. This…
We consider the three-dimensional incompressible Euler equation \begin{equation*}\left\{\begin{aligned} &\partial_t \Omega+U \cdot \nabla \Omega-\Omega\cdot \nabla U=0 \\ &\Omega(x,0)=\Omega_0(x) \end{aligned}\right. \end{equation*} under…
Drain vortices are among the most common vortices observed in everyday life, yet their physics is complex due to the competition of vorticity's transport and diffusion, and the presence of viscous layers and a free surface. Recently, it has…
We consider a nonlinear model equation describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. In the present problem setting, we also take into account the effect of external flow. We prove the unique…
We analyze experimentally the shape of a long elastic filament rotating in a viscous liquid. We identify a continuous but sharp transition from a straight to an helical shape, resulting from the competition between viscous stresses and…
Here we show that under quantum reconnection, simulated by using the three-dimensional Gross- Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
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…
We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We prove the unique solvability of an initial-boundary value…
We study the behavior of vortex filaments subject to a uniform density of phase twist in oscillatory media described by the complex Ginzburg-Landau equation. The first instability is a supercritical Hopf bifurcation to stable propagating…