Related papers: Gradient catastrophe and flutter in vortex filamen…
Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic system of quasi-linear PDEs of the first order. Dispersionless…
Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment and…
We explore the generation of extreme wave events in mechanical metamaterials using the regularization of the gradient catastrophe theory developed by A. Tovbis and M. Bertola for the nonlinear Schr\"odinger equation. According to this…
A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for…
The Rayleigh capillary instability of a cylindrical interface between two immiscible fluids is one of the most fundamental in fluid dynamics. As Plateau observed from energetic considerations and Rayleigh clarified through hydrodynamics,…
Flutter instability in an infinite medium is a form of material instability corresponding to the occurrence of complex conjugate squares of the acceleration wave velocities. Although its occurrence is known to be possible in elastoplastic…
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…
A semiclassical wave-packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock wave phenomenon. The…
We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we…
We studied the stability of linear vortex filaments in 3-dimensional (3D) excitable media, using both analytical and numerical methods. We found an intrinsic 3D instability of vortex filaments that is diffusion-induced, and is due to the…
The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales--from the largest scales where energy is injected, down to the smallest scales where…
A qualitatively different manifestation of the Rayleigh instability is demonstrated, where, instead of the usual extended undulations and breakup of the liquid into many droplets, the instability is localized, leading to an isolated…
We simulate the head-on collision between vortex rings with circulation Reynolds numbers of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The simulation fidelity is established with integral metrics…
In this paper, we study the evolution of a vortex filament in an incompressible ideal fluid. Under the assumption that the vorticity is concentrated along a smooth curve in $\mathbb{R}^3$, we prove that the curve evolves to leading order by…
The process of breaking of inviscid incompressible flows along a rigid body with slipping boundary conditions is studied. Such slipping flows are compressible, which is the main reason for the formation of a singularity for the gradient of…
We present the results of smoothed particle hydrodynamic simulations investigating the evolution and fragmentation of filaments that are accreting from a turbulent medium. We show that the presence of turbulence, and the resulting…
Two-dimensional Euler flows, in the plane or on simple surfaces, possess a material invariant, namely the scalar vorticity normal to the surface. Consequently, flows with piecewise-uniform vorticity remain that way, and moreover evolve in a…
A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes the breakdown of a Fermi sea to disconnected parts with multiple Fermi points. We…
The present work discusses about a possible physical interpretation of the occurrence of turbulence in a dynamic fluid with mathematical modeling and computer simulation. Here turbulence is defined to be a phenomenon of random velocity…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…