Related papers: The evolution of three-dimensionally localized vor…
It is well-known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each…
In this paper, we investigate the long-time behavior of solutions to the two-dimensional Navier-Stokes equations with initial data evolving under the influence of the planar Couette flow. We focus on general perturbations, which may be…
The evolution of the large scale distribution of matter in the universe is often characterized by the density field. Here we take a complimentary approach and characterize it using the cosmic velocity field, specifically the deformation of…
In this work we are interested in extreme vortex states leading to the maximum possible growth of palinstrophy in 2D viscous incompressible flows on periodic domains. This study is a part of a broader research effort motivated by the…
We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g. the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The…
We present several new spatially localized equilibrium and traveling-wave solutions of plane Couette and channel flows. The solutions exhibit strikingly concentrated regions of vorticity that are flanked on either side by high-speed…
The deformation of two-dimensional vortex patches in the vicinity of fluid boundaries is investigated. The presence of a boundary causes an initially circular patch of uniform vorticity to deform. Sufficiently far away from the boundary,…
The coupled evolution of an eroding cylinder immersed in a fluid within the subcritical Reynolds range is explored with scale resolving simulations. Erosion of the cylinder is driven by fluid shear stress. K\'arm\'an vortex shedding…
An emerging long obstacle placed in a boundary layer developing under a free-surface generates a complex horseshoe vortex (HSV) system, which is composed of a set of vortices exhibiting a rich variety of dynamics. The present experimental…
The small vortex generation is a key issue of the mechanism for late flow transition and turbulence generation. It was widely accepted that small length vortices were generated by large vortex breakdown. According to our recent DNS, we find…
We investigate spatial and temporal cross-correlations between streamwise and normal velocity components in three shear flows: a low-dimensional model for vortex-streak interactions, direct numerical simulations for a nearly homogeneous…
The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a…
A phenomenological model is proposed for melting of a vortex lattice, based on screening of the elastic shear modulus by mobile or partially pinned dislocations. A first-order softening line is found and ends at a critical point beyond…
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…
We discuss friction-dominated vortex-string evolution using a new analytic model recently developed by the authors. By treating the average string velocity, as well as the characteristic lengthscale, as dynamical variables, we can provide a…
We employ the Gross--Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow's velocity exceeds a critical…
The study explores the development of the vortex line density in superfluids under thermal activation. This problem is of interest to both applied and fundamental research, and has been investigated by many authors in various aspects.…
An improved understanding of how vortices develop and propagate under pulsatile flow can shed important light on the mixing and transport processes including the transition to turbulent regime occurring in such systems. For example, the…
We present a numerical investigation of three-dimensional, short-wavelength linear instabilities in Kelvin-Helmholtz (KH) vortices in homogeneous and stratified environments. The base flow, generated using two-dimensional numerical…