Descripción: The nonlinear conditions for the development of helical vortex filaments in a circular tube are considered. The helical flow is assumed to be irrotational, except in a vortex filament of infinitesimal core area. By introducing an appropriate image for this helical vortex filament, the boundary condition on the material frontier is satisfied. By assuming an axisymmetric flow upstream and imposing the conservation laws, a dependence between the helix pitch and the nonlinear amplitude of the helical vortex developed downstream is obtained. Our results show that only helical flows with the pitch in a certain range of values are allowed. The dependence of this range on the swirl ratio and on the tube cross section is considered. We discuss the usefulness of the nonlinear analysis of the allowed flows to explain experimental results and to complement the usual linear study of stability. © 1999 American Institute of Physics.

Descripción: We present a parametric space study of the decay of turbulence in rotating flows combining direct numerical simulations, large eddy simulations, and phenomenological theory. Several cases are considered: (1) the effect of varying the characteristic scale of the initial conditions when compared with the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect of helicity (correlation between the velocity and vorticity); (3) the effect of Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial conditions. Initial conditions include the Taylor-Green vortex, the Arn'old-Beltrami-Childress flow, and random flows with large-scale energy spectrum proportional to k4. The decay laws obtained in the simulations for the energy, helicity, and enstrophy in each case can be explained with phenomenological arguments that consider separate decays for two-dimensional and three-dimensional modes and that take into account the role of helicity and rotation in slowing down the energy decay. The time evolution of the energy spectrum and development of anisotropies in the simulations are also discussed. Finally, the effect of rotation and helicity in the skewness and kurtosis of the flow is considered. © 2011 American Institute of Physics.

Descripción: We examine long-time properties of the ideal dynamics of three-dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases, the results agree with the isotropic predictions stemming from statistical mechanics. No accumulation of excitation occurs in the large scales, although, in the dissipative rotating case, anisotropy and accumulation, in the form of an inverse cascade of energy, are known to occur. We attribute this latter discrepancy to the linearity of the term responsible for the emergence of inertial waves. At intermediate times, inertial energy spectra emerge that differ somewhat from classical wave-turbulence expectations and with a trace of large-scale excitation that goes away for long times. These results are discussed in the context of partial two dimensionalization of the flow undergoing strong rotation as advocated by several authors. © 2011 American Physical Society.

Descripción: The use of plasma actuators is a recent technology that imposes a localized electric force that is used to control air flows. A suitable representation of actuation enables to undertake plasma actuators optimization, to design flow-control strategies, or to analyse the flow stabilization that can be attained by plasma forcing. The problem description may be clearly separated in two regions. An outer region, where the fluid is electrically neutral, in which the flow is described by the Navier-Stokes equation without any forcing term. An inner region, that forms a thin boundary layer, where the fluid is ionized and electric forces are predominant. The outer limit of the inner solution becomes the boundary condition for the outer problem. The outer problem can then be solved with a slip velocity that is issued from the inner solution. Although the solution for the inner problem is quite complex it can be contoured proposing pseudo-empirical models where the slip velocity of the outer problem is determined indirectly from experiments. This pseudo-empirical model approach has been recently tested in different cylinder flows and revealed quite adapted to describe actuated flow behaviour. In this work we determine experimentally the influence of the duty cycle on the slip velocity distribution. The velocity was measured by means of a pitot tube and flow visualizations of the starting vortex (i.e. the induced flow when actuation is activated in a quiescent air) have been done by means of the Schlieren technique. We also performed numerical experiments to simulate the outer region problem when actuation is activated in a quiescent air using a slip velocity distribution as a boundary condition. The experimental and numerical results are in good agreement showing the potential of this pseudo-empirical model approach to characterize the plasma actuation.

Descripción: The Kelvin-Helmoltz instability (KH) with formation of vortices appears in a wide variety of terrestrial, interplanetary, and astrophysical contexts. We study a series of iterated rolled-up coherent plasma structures (15) that flow in the equatorial Earth's boundary layer (BL), observed on October 24, 2001. The data were recorded during a 1.5 hour-long Wind crossing of the BL at the dawn magnetospheric flank, tailward of the terminator (X≈-13 RE). The interplanetary magnetic field (IMF) was radially directed, almost antiparallel to the magnetosheath (MS) flow. This configuration is expected to be adverse to the KH instability because of the collinearity of field and flow, and the high compressibility of the MS. We analyze the BL stability with compressible MHD theory using continuous profiles for the physical quantities. Upstream, at near Earth sites, we input parameters derived from an exact MHD solution for collinear flows. Further downtail at Wind position we input measured parameters. The BL is found KH unstable in spite of unfavorable features of the external flow. On the experimental side, the passage of vortices is inferred from the presence of low density - hot plasma being accelerated to speeds higher than that of the contiguous MS. It is further supported by the peculiar correlation of relative motions (in the bulk velocity frame): cold-dense plasma drifts sunward, while hot-tenuous plasma moves tailward. This event differs from many other studies that reported BL vortices under strongly northward IMF orientations. This is a case of KH vortices observed under an almost radial IMF, with implicit significance for the more common Parker's spiral fields, and the problem of plasma entry in the magnetosphere.

Descripción: We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 61443 points and three different configurations on grids of 40963 points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity. © 2013 American Physical Society.

Descripción: We examine the decomposition of forced Taylor-Green and Arn'old-Beltrami-Childress (ABC) flows into coherent and incoherent components using an orthonormal wavelet decomposition. We ask whether wavelet coefficient thresholding based on the Donoho-Johnstone criterion can extract a coherent vortex signal while leaving behind Gaussian random noise. We find that no threshold yields a strictly Gaussian incoherent component, and that the most Gaussian incoherent flow is found for data compression lower than that achieved with the fully iterated Donoho-Johnstone threshold. Moreover, even at such low compression, the incoherent component shows clear signs of large-scale spatial correlations that are signatures of the forcings used to drive the flows. © 2012 American Institute of Physics.

Descripción: We study the intermittency properties of the energy and helicity cascades in two 15363 direct numerical simulations of helical rotating turbulence. Symmetric and antisymmetric velocity increments are examinedas well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and nonintermittentwhereas the direct cascade of helicity is highly intermittent. Furthermorethe study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at very small scales in the flow. Finallywe observe the juxtaposition in space of strong laminar and persistent helical columns next to time-varying vortex tanglesthe former being associated with the self-similarity of energy and the latter with the intermittency of helicity. © 2010 American Institute of Physics.

Descripción: The dynamic behavior of the anode-arc-root at the nozzle surface of a plasma torch was experimentally investigated in this work. A gas (N2) vortex-stabilized non-transferred arc torch with a thoriated tungsten rod (2wt %) cathode (3.2 mm diameter) and a coaxial anode (5 mm diameter, 30 mm length) was used in the experiment. By using a sweeping Langmuir probe in floating condition, the voltage of the plasma jet outside the nozzle was inferred. Arc voltage waveforms were also obtained. Data have been obtained for an arc current of 100 A and a gas flow rate of 30 Nl min-1. A typical sawtooth shape (i.e., restrike mode) (with a fluctuating level of ≈ ± 25 %) and a dominant frequency of ≈ 6.5 kHz was observed in the arc voltage waveforms, which is attributed to anode-arc-root movements along the anode surface followed by a restrike at a certain point close to the cathode. By performing a time correlation between the probe and arc voltage oscillograms together with simple estimations, the amplitude of the movement of the arc-root along the anode surface as well its velocity were inferred.

Descripción: We investigate the relaxation of a strongly turbulent fluid to metastable states, in times much shorter than the dissipation time scale. Several simulations of decaying two-dimensional Navier-Stokes flows were performed, which show the relaxation to organized states dominated by coherent vortex structures of length scales comparable to the size of the system. In the case of periodic boundary conditions, the organized state is characterized by a strong correlation between vorticity and stream function, the second of which satisfies a sinh-Poisson equation quite accurately. However, in the case of free-slip boundary conditions the relaxed state does not display any significant correlation between its vorticity and its stream function. Notwithstanding, in both cases the role of nonlinearities is found to be essential even at these late stages of the evolution. However, we show that even severe truncations of a few (short wave number) nonlinearly coupled Fourier modes provide an accurate description of the long-term dynamics of the fluid. Therefore the dynamics of the flow in these metastable states is somewhere in between a strong turbulent regime and a (mostly linear) dissipative relaxation stage. © 1996 The American Physical Society.