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.     

Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges

New quadrature formulas (QFs) for evaluating the singular integral (SI) of Cauchy type with unbounded weight function on the edges is constructed. The construction of the QFs is based on the modification of discrete vortices method (MMDV) and linear spline interpolation over the finite interval [−1,1]. It is proved that the constructed QFs converge for any singular point x not coinciding with the end points of the interval [−1,1]. Numerical results are given to validate the accuracy of the QFs. The error bounds are found to be of order O(h^α|lnh|) and O(h|lnh|) in the classes of functions H^α([−1,1]) and C¹([−1,1]), respectively.     

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.     

Energy Distribution in a Neutral Gas of Point Vortices

An analytical formula for the energy distribution of a neutral gas of point vortices is obtained. Good agreement with the numerical results of Campbell and O'Neil is found.     

Investigation of density ratio effects on normally injected cold jets into a hot cross flow

In this work, hydrodynamic effects of multiple squared cross-section cold jets inclined normally into a hot cross flow were computationally simulated using large eddy simulation (LES) approach. The finite volume method and the SIMPLE algorithm on a multi-block non-uniform staggered grid were applied. The jet into cross flow velocity ratio and the jet Reynolds number were 0.5 and 4,700, respectively. Simulations were performed for three different jets into cross flow temperature ratios, namely, 2, 1, and 0.5, corresponding to density ratios of 0.5, 1, and 2. The experimental and numerical results of Ajersch et al. (J. Turbomachinery 119(2), 330–342, 1997) at unit density ratio were used for validation purposes. The density ratio effects on the flow characteristics were investigated. It was shown that the density ratio has significant effects on the hydrodynamics of the jet into cross flow problems and even though the flow Mach number may be low, its effects due to temperature differences between the jet and the cross flow cannot be easily ignored.     

Topological Solutions in the Self-dual Chern–Simons–Higgs Theory in a Background Metric

In this Letter we show the existence of topological multi-vortex solutions in the self-dual Chern–Simons–Higgs theory in a background metric which interpolates flat spacetime and cylinder smoothly.     

Torsion,string tension,and topological origin of charge and mass

We consider the analogy between torsion line defects and vortex lines in a superconductor to suggest that the electric charge and masses of elementary particles may have a geometrical origin. Just as the field vanishes everywhere in a superconductor except along the vortex line, where the flux is confined, we have the torsion being concentrated only along the topological defects, giving rise to charge as well as mass. The mass is related to the string tension (c ²/G) and charge is connected with the gravitational permeability (G/c ²), both induced by torsion.