Compound plasmonic vortex generation based on spiral nanoslits

In view of wide applications of structured light fields and plasmonic vortices, we propose the concept of compound plasmonic vortex and design several structured plasmonic vortex generators. This kind of structured plasmonic vortex generators consists of multiple spiral nanoslits and they can generate two or more concentric plasmonic vortices. Different from Laguerre–Gaussian beam, the topological charge of the plasmonic vortex in different region is different. Theoretical analysis lays the basis for the design of radially structured plasmonic vortex generators and numerical simulations for several examples confirm the effectiveness of the design principle. The discussions about the interference of vortex fields definite the generation condition for the structured vortex. This work provides a design methodology for generating new vortices using spiral nanoslits and the advanced radially structured plasmonic vortices is helpful for broadening the applications of vortex fields.     

Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier–Stokes equations

We present an iterative semi-implicit scheme for the incompressible Navier–Stokes equations, which is stable at CFL numbers well above the nominal limit. We have implemented this scheme in conjunction with spectral discretizations, which suffer from serious time step limitations at very high resolution. However, the approach we present is general and can be adopted with finite element and finite difference discretizations as well. Specifically, at each time level, the nonlinear convective term and the pressure boundary condition – both of which are treated explicitly in time – are updated using fixed-point iteration and Aitken relaxation. Eigenvalue analysis shows that this scheme is unconditionally stable for Stokes flows while numerical results suggest that the same is true for steady Navier–Stokes flows as well. This finding is also supported by error analysis that leads to the proper value of the relaxation parameter as a function of the flow parameters. In unsteady flows, second- and third-order temporal accuracy is obtained for the velocity field at CFL number 5–14 using analytical solutions. Systematic accuracy, stability, and cost comparisons are presented against the standard semi-implicit method and a recently proposed fully-implicit scheme that does not require Newton’s iterations. In addition to its enhanced accuracy and stability, the proposed method requires the solution of symmetric only linear systems for which very effective preconditioners exist unlike the fully-implicit schemes.     

Instanton solutions from Abelian sinh-Gordon and Tzitzeica vortices

We study the Abelian Higgs vortex solutions to the sinh-Gordon equation and the elliptic Tzitzeica equation. Starting from these particular vortices, we construct solutions to the Taubes equation with higher vortex number, on surfaces with conical singularities.We then, analyse more general properties of vortices on such singular surfaces and propose a method to obtain vortices on conifolds from vortices on surfaces of revolution. We apply our method to construct explicit vortex solutions on the Poincaré disk with a conical singularity in the centre, to which we refer as the “hyperbolic cone”.We uplift the Abelian sinh-Gordon and Tzitzeica vortex solutions to four dimensions and construct cylindrically symmetric, self-dual Yang–Mills instantons on a non-self-dual (nor anti-self-dual) 4-dimensional Kähler manifold with non-vanishing scalar curvature. The instantons we construct in this way cannot be obtained via a twistorial approach.     

On resistive nonlocal Josephson electrodynamics

New solutions of one-dimensional nonlocal Josephson electrodynamics are proposed that describe the steady and nonsteady Abrikosov-Josephson vortex states of the resistive model; these solutions are based on the superposition principle of the vortex structures whose properties are determined by the nonlinear interaction of the vortices. The stability of the current-voltage characteristic (1.13) is shown and the relaxation-oscillation mode of establishing the corresponding state is investigated. The laws governing the annihilation and dispersal of the interacting Abrikosov-Josephson vortices are examined. Zh. éksp. Teor. Fiz. 112, 1396–1408 (October 1997)     

Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams

We analyze the characterizations of the optical vortices generated by a multi-level achromatic spiral phase plate. The effective topological charge of the multi-level fractional spiral phase plate is expanded into Fourier series and the analytical formula of the relative intensity of each component is obtained. It is shown that the fractional part of the topological charge sharply reduces the purity of vortices. Using the 36 levels achromatic spiral phase plate, we can obtain a vortex beam with purity larger than 95% across a bandwidth exceeding 140 nm in the visible region of the spectrum.     

Vortex stretching and reconnection in a compressible fluid

Vortex stretching in a compressible fluid is considered. Two-dimensional (2D) and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices — “dressed" vortices (in analogy to “dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case — compressibility leads to defreezing of vortex lines in the fluid.     

Vortex patterns in quasi-two-dimensional flows of a viscous rotating fluid

A modified von Kármán problem that describes steady vortex flow in a rotating thin viscous fluid layer is solved. An analysis of the effect of bottom friction on the behavior of cyclonic and anticyclonic vortices at arbitrary values of the Rossby number is presented. Several anticyclonic flow patterns are examined. An approximate analytical solution obtained for steady flows is compared with numerical computations of a time-dependent problem. Experimental results on cyclonic and anticyclonic vortices in multiple-vortex quasi-turbulent flow are presented, and their interpretation based on the solution of the model problem is given.     

Self-oscillations in a jet flow and gaseous flame with strong swirl

Investigation results on unsteady flow dynamics in a gaseous jet flame with strong swirl, vortex breakdown, and precession of a vortex core obtained by panoramic optical methods are presented, as well as the results of theoretical analysis of the fastest growing modes of hydrodynamic instability. Characteristics of the most unstable self-oscillating mode in the initial region of the turbulent strongly swirling propane-air jet burning in the atmospheric air in the form of a lifted flame are determined. Analysis of data by principal component analysis and linear stability analysis revealed that evolution of the dominant self-oscillating mode corresponds to quasi-solid rotation with constant angular velocity of the spatial coherent structure consisting of a jet spiral vortex core and two spiral secondary vortices.     

Pattern formation and bistability in flow between counterrotating cylinders

In the Taykor-Coutte experiment on fluid flow counterrotating cylinders, there is a bicritical point where the onset of instabilities to Taylor vortex flow (a steady-state bifurcation) and spiral vortex flow (a Hopf bifurcation) meet. The nonlinear mode interactions near this bicritical point are analyzed, exploiting the role of symmetry in the bifurcation theory, and with emphasis of the relevance to experiments, for a range of raduis ratios 0.43 ≤η≤0.98. The mechanism of the pattern formation is elucidated, and several new flow patterns and transitions are predicted, including wavy vortices, bistability, hysteresis, and up to 7 quasiperiodic flows.     

A novel method of Newton iteration-based interval analysis for multidisciplinary systems

A Newton iteration-based interval uncertainty analysis method (NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary system into single disciplines and utilizes a Newton iteration equation to obtain the upper and lower bounds of coupled state variables at each iterative step. NI-IUAM only needs to determine the bounds of uncertain parameters and does not require specific distribution formats. In this way, NI-IUAM may greatly reduce the necessity for raw data. In addition, NI-IUAM can accelerate the convergence process as a result of the super-linear convergence of Newton iteration. The applicability of the proposed method is discussed, in particular that solutions obtained in each discipline must be compatible in multidisciplinary systems. The validity and efficiency of NI-IUAM is demonstrated by both numerical and engineering examples.     

Coherent structures and their stability in ion temperature gradient turbulence

Periodic arrays of large scale coherent vortices and their stability have been investigated, within the framework of /spl eta//sub i/ turbulence, using two-dimensional fluid simulation in slab geometry. These vortices, in combination with viscosity damping of small scales, contribute to the formation of a steady state in a system with linearly unstable modes. The steady state comprises of a few vortex convective turn over times and seems to be fairly robust. It has been recognized that a vortex chain, consisting of positive and negative vorticities, continues to move stably in the poloidal direction (along periodic direction). On the other hand, an initial isolated monopole vortex is unstable and leads to a long-lived stable dipolar structure after a few vortex turnover periods. A variety of simple collisional interaction processes among these coherent vortices have also been explored numerically.     

Solitary Wave Evolution of Optical Planar Vortices in Self-Defocusing Photorefractive Media

Solitary wave evolution of optical planar vortices in isotropie self-defoeusing photorefractive media is investigated in detail. We demonstrate that the formation of a planar vortex soliton intensively depends on the diameter and maximum intensity of the input vortex Seam. The exact solutions of planar vortex solitons are obtained due to the Petviashvili iteration method. It is found that, with the increasing soliton maximum intensity, the soliton core will be gradually diminished to a minimum value.     

Nonlinear vortex dynamics in open nonequilibrium systems with bulk mass loss and a generation mechanism for tornadoes and typhoons

Based on a general model of nonlinear vortex dynamics in open thermodynamically nonequilibrium systems with bulk or surface mass losses, an analysis is presented of the mechanism of generation of violent atmospheric vortices (tornadoes, typhoons, cyclones) associated with the formation of deep cloud systems by intense condensation of water vapor from moist air cooled below the dew point. Simple particular solutions to the Navier-Stokes equations are found that describe both axisymmetric and nonaxisymmetric incompressible vortex motions involving radial and vertical flows with viscous dissipation vanishing identically everywhere except for a thin shear layer at the boundary of the condensation region. It is shown that the nonlinear convective and local Coriolis forces generated by radial inflow in the presence of a background vorticity due to a global Coriolis force (the Earth’s rotation) accelerate the solid-body rotation in the vortex core either exponentially or in a nonlinear regime of finite-time blow-up. Due to updrafts, such a vortex is characterized by a strong helicity. This mechanism explains a number of observed properties and characteristics of the structure and evolution of tornadoes and typhoons. Upper estimates are found for the kinetic energies of violent atmospheric vortices. It is shown that increase in rotational kinetic energy of atmospheric vortices with constant vortex-core radii is consistent with energy and momentum conservation, because radial inflow continually supplies the required amount of rotational kinetic energy drawn from the ambient atmosphere to an open system.     

An efficient numerical method for the equations of steady and unsteady flows of homogeneous incompressible Newtonian fluid

In the present paper, we present some numerical methods to solve the equations of steady and unsteady flows, such as those in the microcirculatory bed and large blood vessels (arteries and veins), respectively. In the case of steady flows, the method does not need neither any boundary conditions on pressure nor any small parameter, and the main computation consists of solving some Poisson equations. In the case of unsteady flows, the scheme uses a consistent Neumann boundary condition for the pressure Poisson equation. At each time step, a Poisson and heat equation are solved for the pressure and each velocity component, respectively. The accuracy and efficiency of scheme are checked by a set of numerical tests.     

Vortices in a Josephson junction sandwiched between two superconducting waveguides

For a Josephson junction magnetically coupled to the superconducting waveguides enclosing it, solutions to the equation for the difference of the Cooper pair phases over the Josephson junction are found and the corresponding magnetic field values are calculated. Two gaps imposing an upper limit for the vortex velocity are found for free vortices (moving without dissipation). Existence conditions are found for fast vortices in the two high-velocity allowed regions. The dependence of the transport current on vortex velocity is established in cases where the current flows through the Josephson junction only or through the entire structure. A reverse current phenomenon is discovered in which vortices inside allowed velocity regions move opposite to the usual direction.     

Instability of surfactant solution flow in a Taylor cell

The hydrodynamic instability of surfactant solutions between two coaxial cylinders was investigated by using a laser-induced-fluorescence flow visualization technique to clarify the effect of drag-reducing additives on vortex formation in Taylor-Couette flow. The test fluids were Ethoquad O/12 surfactant solutions, which have a gel-like structure called “shear-induced structurer” (SIS). Photographs of the formation of Görtler vortices were taken and compared with these of tap water. In the Taylor number range of 1.2×10⁵≤Ta≤7.1×10⁵, tap water and 10 ppm surfactant solution flows consisted of Taylor vortices and much smaller Görtler vortices at the rotating inner wall. However, for 50 and 100 ppm surfactant solutions, Taylor vortices were not apparent and Görtler vortices were collapsed. Measurements of the wavelength of Görtler vortices lead to the conclusion that surfactant solutions have a stabilizing effect on Görtler instabilities. This effect depends on surfactant concentration and becomes considerable with increasing acceleration of the inner cylinder.     

Visualization of two-dimensional vortex flows in thin oscillating liquid films

A possibility of visualizing flows using random inhomogeneities of film thicknesses of different colors as particles for visualization is shown on an example of a vortex flow structure in an oscillating thin liquid film. Formation of vortex flows in a thin liquid film containing surface-active substances is investigated in experiments. The film is fixed horizontally along the edges of the cell vibrating in the vertical direction. Spatially homogeneous oscillations of the liquid film can excite different types of waves that generate two-dimensional vortex flows due to nonlinearity. We present results of experimental investigation of the structure of vortex flows in a thin film (0.5–10 μm) with rectangular boundaries. It has been revealed that, if the horizontal size of an inhomogeneous region is much smaller than the size of vortices, the inhomogeneities are transported by vortices and their interference pattern can be used for visualization of vortex flows.     

Vortex burst as a source of turbulence

An important issue in turbulence theory is to understand what kinds of elementary flow structures are responsible for the part of the turbulent energy spectrum described by Kolmogorov's celebrated k(-5/3) law. A model for such structure has been proposed by Lundgren [Phys. Fluids 25, 2193-2203 (1982)]] in the form of a vortex with spiral structure subjected to an axially straining field. We report experimental results of a vortex burst in a laminar-flow environment showing that this structure is responsible for a k(-5/3) part in the energy spectrum. If there are many experimental evidences of the existence of vortices with spiral structures in turbulent flows, it is the first time that such an elementary structure is experimentally shown to be responsible for the turbulent energy cascade.     

On the Incompressible Fluid Limit and the Vortex Motion Law of the Nonlinear Schrödinger Equation

The nonlinear Schr?dinger equation (NLS) has been a fundamental model for understanding vortex motion in superfluids. The vortex motion law has been formally derived on various physical grounds and has been around for almost half a century. We study the nonlinear Schr?dinger equation in the incompressible fluid limit on a bounded domain with Dirichlet or Neumann boundary condition. The initial condition contains any finite number of degree ± 1 vortices. We prove that the NLS linear momentum weakly converges to a solution of the incompressible Euler equation away from the vortices. If the initial NLS energy is almost minimizing, we show that the vortex motion obeys the classical Kirchhoff law for fluid point vortices. Similar results hold for the entire plane and periodic cases, and a related complex Ginzburg–Landau equation. We treat as well the semi-classical (WKB) limit of NLS in the presence of vortices. In this limit, sound waves propagate through steady vortices. Received: 1 December 1997 / Accepted: 27 June 1998     

Vortex pump for dilute bose-einstein condensates

The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed amount of vorticity can be added to the condensate in each cycle. In an adiabatic operation of this vortex pump, the appearance of vortices into the condensate is interpreted as the accumulation of a local Berry phase. Our design can be used as an experimentally realizable vortex source for possible vortex-based applications of dilute Bose-Einstein condensates.