Related papers: On taming Moffatt-Kimura vortices of doom in the v…
To address the possible occurrence of a Finite-Time Singularity (FTS) during the oblique reconnection of two vortex rings, Moffatt-Kimura (MK) (J. Fluid Mech., 2019a; J. Fluid Mech., 2019b) developed a simplified model based on the…
We present experimental and theoretical results on formation of quantum vortices in a laser beam propagating in a nonlinear medium. Topological constrains richer than the mere conservation of vorticity impose an elaborate dynamical behavior…
We theoretically investigate the properties of ultra-cold dipolar atoms in radially coupled, concentric annular traps created by a potential barrier. The non-rotating ground-state phases are investigated across the superfluid-supersolid…
The goal of this article is to present -- in a cohesive, and somewhat self-contained fashion -- several recent results revealing an experimentally, numerically, and mathematical analysis-supported \emph{geometric scenario} manifesting…
This article presents a comprehensive analysis of the formation and dissipation of vortices within chaotic fluid flows, leveraging the framework of Sobolev and Besov spaces on Riemannian manifolds. Building upon the Navier-Stokes equations,…
We study spontaneous-symmetry-broken phase-separated vortex lattice in a weakly interacting uniform rapidly rotating binary Bose superfluid contained in a quasi-two-dimensional circular or square bucket. For the inter-species repulsion…
The decay of quantum vortex rings in counterflow regimes, visualized in Helium II with the help of solid hydrogen particles trapped to their cores, has been a puzzling issue within the usual description of superfluid vortex dynamics,…
The aim of these notes is to present in a comprehensive and relatively self-contained way some recent developments in the mathematical analysis of two-dimensional viscous flows. We consider the incompressible Navier-Stokes equations in the…
In this technical note, we demonstrate the robustness of our numerical scheme of vorticity iteration in dealing with the dipole-wall interaction at small viscosity, with emphasis on mesh convergence, boundary vorticity as well as wall…
It is well known that an inverse turbulent cascade in a finite ($2 \pi \times 2 \pi$) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial…
This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point…
A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution…
The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been…
We study a dissipative extension of vortex-binary motion in a doubly periodic fluid domain. The underlying conservative system admits an exact integrable reduction to a single complex relative coordinate. Dissipation is introduced via a…
As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier--Stokes equations in the half-plane $R^2_+$ with no-slip boundary condition and point vortices as initial data. We focus on the paradigmatic…
A controllable soft solid is realised in vortex matter in a type II superconductor. The two-dimensional unit cell area can be varied by a factor of $10^4$ in the solid phase, without a change of crystal symmetry offering easy exploration of…
We introduce a numerical strategy to study the evolution of 2D water waves in the presence of a plunging jet. The free-surface Navier-Stokes solution is obtained with a finite but small viscosity. We observe the formation of a surface…
In quantum gases, weak links are typically realized with externally imposed optical potentials. We show that, in rotating binary condensates, quantized vortices in one component form hollow channels that act as self-induced weak links for…
To produce a vortex, a torque must be applied to the fluid. In viscous fluids, the torques that produce turbulent vortices result from the loss of symmetry of the stress tensor, once the viscous friction exceeds the shear stress resistance…
Vortex shedding by a swimming sphere in a viscous incompressible fluid is studied for surface modulation characterized by a superposition of dipolar and quadrupolar, as well as for quadrupolar and octupolar displacements, varying…