Self-similar vortex reconnection

Irreversible Dynamics of Vortex Reconnections in Quantum Fluids

“…Finally note that in a recent work [19], it has been reported that vortex reconnections in Navier-Stokes also display a clear t 1/2 scaling, a coefficient A − ∼ 0.3 − 0.4 and the same time asymmetry A + > A − . Note that the Biot-Savart analytical calculations of reference [20] and the LIA based ones of [21], predict A − ∼ 0.47 and A − = 0.427 respectively, which are in agreement with our GP measurements. In what follows, we quantitatively relate the asymmetry in the distribution of the pre-factors with the irreversible energy transfer between the vortex-type and density/phase The simple linear theory neglecting the nonlinear term of the GP model [14,15], valid in the limit δ ± → 0, provides an insight into the dynamics of reconnecting parameters as the the order parameter can be found analytically.…”

Matching theory to characterize sound emission during vortex reconnection in quantum fluids

“…Following this seminal work, many numerical and theoretical studies were undertaken in the following decades. Many of those works focused on characterizing their rate of approach and separation, on the macroscopic angle between two reconnecting vortex filaments [6,[22][23][24][25][26][27][28], on the sound emission following a reconnection event [24,29], and on the evolution of the length of the filament and superfluid helicity throughout the Gray left and right triangles correspond to reconnections of free and trapped vortices respectively, from Galantucci et al [35].…”

“…Summarizing, in order to compute the differences before and after the reconnection in the incompressible energy and momentum of the superfluid, we use the theoretical description R ± 1,2 for the filaments given in Eqs. (27)(28)(29)(30). Namely, we use such parametrization when the distance is…”

“…The incompressible superfluid momenta density before and after reconnection can be therefore computed by using Eqs. (27)(28)(29)(30). Due to the particular symmetries of the reconnecting configuration, their expressions are rather simple.…”

Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state

“…Some of these solutions develop singularities [19,22,23], for instance forming sharp kinks at finite time. One application of such self-similarity in vortex filaments is to the dynamics of interacting filaments [24], including those near a vortex reconnection event [25]. However, the vortex filaments are derived in the zero-viscosity limit, and it is natural to wonder whether vortex dynamics in a viscous fluid modelled by Navier–Stokes equations could lead to blowup.…”