We study in detail, solving the Bogoliubov-de Gennes equations, the magnetic field, supercurrent and order parameter profiles originated by a solenoid or magnetic whisker inserted in a type-II superconductor. We consider solutions of different vorticities, n, in the various cases. The results confirm the connection between the vorticity, the internal currents and the boundstates in a self-consi...

In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow vorticity and boundary circulation in flows with vortex sheet initial data. We formulate our results for flows outside a finite number of smooth obstacles. Our po...

Wavetrain modulations upon arbitrary vertically sheared currents were thoroughly studied by Benny and his group. If the Benny asymptotic expansion becomes invalid for the range of small values of vorticity the present work is focusing upon, then it has to be shown and explained what is wrong with the Benny expansion. The same question applies to Jonhson (1976) results. The dependence of the cub...

A control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number. To do this it is necessary to include the conservation of angular momentum. The mean vorticity increases from zero as the cube of Froude number minus one, and, in dimensionless form, approaches a constant at large Froude number. Digital particle imaging v...

In [C2], Chemin shows that solutions of the Navier-Stokes equations in R for an incompressible fluid whose initial vorticity lies in L ∩ L∞ converge in the zero-viscosity limit in the L–norm to a solution of the Euler equations, convergence being uniform over any finite time interval. In [Y2], Yudovich assumes an initial vorticity lying in L for all p ≥ p0, and establishes the uniqueness of sol...

In the following, we prove new regularity results for two-dimensional steady periodic capillary water waves with vorticity, in the absence of stagnation points. Firstly, we prove that if the vorticity function has a Hölder-continuous first derivative, then the free surface is a smooth curve and the streamlines beneath the surface will be real analytic. Furthermore, once we assume that the vor...

This paper demonstrates that analytical solutions to the steady two-dimensional Euler equations possessing all the qualitative properties of multipolar vortices observed experimentally and numerically can be constructed using the theory of algebraic curves and quadrature domains. The solutions consist of a finite set of line vortices superposed on finite-area patches of uniform vorticity. By wa...

the present study aimed to investigate two numerical solutions of the navier-stokes equations. for this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...

In this note we prove that the finite time blow-up of classical solutions of the 3-D homogeneous incompressible Euler equations is controlled by the Besov space, Ḃ0 ∞,1, norm of the two components of the vorticity. For the axisymmetric flows with swirl we deduce that the blow-up of solution is controlled by the same Besov space norm of the angular component of the vorticity. For the proof of th...

In two dimensions, vorticity is materially conserved in an invisicid environment. Additionally, if the fluid is nondivergent, the velocity field can be determined from a solution to the Poisson equation relating velocity and vorticity. Vortex methods translate these well-known facts as well as the ability to capture the time evolution of Lagrangian particles into a method of representing the fl...