Direct numerical simulation of free and forced square jets

Direct numerical simulation (DNS) of incompressible, spatially developing square jets in the Reynolds number range of 500–2000 is reported. The three-dimensional unsteady Navier–Stokes equations are solved using high order spatial and temporal discretization. The objective of the present work is to understand the evolution of free and forced square jets by examining the formation of large-scale structures. Coherent structures and related interactions of free jets suggest control strategies that can be used to achieve enhanced spreading and mixing of the jet with the surrounding fluid. The critical Reynolds number for the onset on unsteadiness in an unperturbed free square jet is found to be 875–900 while it reduces to the range 500–525 in the presence of small-scale perturbations. Disturbances applied at the flow inlet cause saturation of KH-instability and early transition to turbulence. Forced jet calculations have been carried out using varicose perturbation with amplitude of 15%, while frequency is independently varied. Simulations show that the initial development of the square jet is influenced by the four corners leading to the appearance hairpin structures along with the formation of vortex rings. Farther downstream, adjacent vortices strongly interact leading to their rapid breakup. Excitation frequencies in the range 0.4–0.6 cause axis-switching of the jet cross-section. Results show that square jets achieve greater spreading but are less controllable in comparison to the circular ones.     

Spatial relation between fluctuating wall pressure and near-wall streamwise vortices in wall bounded turbulent flow

A new view of the spatial relation between fluctuating wall pressure and near-wall streamwise vortices (NWSV) is proposed for wall bounded turbulent flow by use of the direct numerical simulation (DNS) database. The results show that the wall region with low pressure forms just below the strong NWSV, which is mostly associated with the overhead NWSV. The wall region with high pressure forms downstream of the NWSV, which has a good correspondence with the downwash of the fluids induced by the upstream NWSV. The results provide a significant basis for the detection of NWSV.     

Dynamic Stability and Instability of Pinned Fundamental Vortices

We study the dynamic stability and instability of pinned fundamental ±1 vortex solutions to the Ginzburg–Landau equations with external potential in ℝ². For sufficiently small external potentials, there exists a perturbed vortex solution centered near each non-degenerate critical point of the potential. With respect to both dissipative and Hamiltonian dynamics, we show that perturbed vortex solutions which are concentrated near local maxima (resp. minima) are orbitally stable (resp. unstable). In the dissipative case, the stability is in the stronger “asymptotic” sense. The research of S. Gustafson partially supported by a grant from NSERC. The research of F. Ting on this paper was supported by NSERC under grant N298724.     

Effects of the induced birefringence in photorefractive crystals on speckle optical vortices

In this work, we show that it is possible to change the properties of an optical vortex formed in a speckle pattern by the control of an external electric field applied to a sillenite-type photorefractive material in a non-holographic configuration. To show it, a scheme that allows the recovering of both, the polarization state and the phase distribution of an optical field was implemented. Changes in the polarization state of the light in the neighborhood of the vortex were observed with the application of an external electric field. Likewise, changes in the phase structure around the vortex and displacements of the vortices themselves were measured. These displacements have a fairly linear dependence on the applied field to the photorefractive crystal. Experimental results are qualitatively explained with the theoretical treatment of non-holographic recording in photorefractive crystals.     

Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation

This paper evaluates the performance of a point-diffraction interferometer for closed-loop adaptive optics. A point-diffraction interferometer was built using a modified Mach-Zehnder set-up. The system was used in closed-loop using a SLM to implement a square, 12 × 12, piston-only segmented corrector with a stroke of ±π. Its performance was tested for the case of atmospheric turbulence aberrations. The investigation showed, through simulation and experiment, that the point-diffraction interferometer worked in closed-loop operation in both uniform intensity and scintillated aberrations. Its robustness in the presence of phase discontinuities makes it a promising option for wavefront sensing in strong scintillation.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.      

Coherence properties of a Bose-Einstein condensate in an optical superlattice

We study the effect of a one dimensional optical superlattice on the superfluid properties (superfluid fraction, number squeezing, dynamic structure factor) and the quasi-momentum distribution of the Mott-insulator. We show that due to the secondary lattice, there is a decrease in the superfluid fraction and the number fluctuation. The dynamic structure factor which can be measured by Bragg spectroscopy is also suppressed due to the addition of the secondary lattice. The visibility of the interference pattern (the quasi-momentum distribution) of the Mott-insulator is found to decrease due to the presence of the secondary lattice. Our results have important implications in atom interferometry and quantum computation in optical lattices.     

Self-dual Chern–Simons Vortices on Bounded Domains

In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point.     

On the invariant measures for the two-dimensional euler flow

It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy.