On the two-dimensional stability of the axisymmetric Burgers vortex

The stability of the axisymmetric Burgers vortex solution of the Navier–Stokes equations to two-dimensional perturbations is studied numerically up to Reynolds numbers, R=Gamma/2pinu, of order 104. No unstable eigenmodes for azimuthal mode numbers n=1,..., 10 are found in this range of Reynolds numbers. Increasing the Reynolds number has a stabilizing effect on the vortex

Structure and stability of non-symmetric Burgers vortices

We investigate, numerically and analytically, the structure and stability of steady and quasi-steady solutions of the Navier–Stokes equations corresponding to stretched vortices embedded in a uniform non-symmetric straining field, ([alpha]x, [beta]y, [gamma]z), [alpha]+[beta]+[gamma]=0, one principal axis of extensional strain of which is aligned with the vorticity. These are known as non-symmetric Burgers vortices (Robinson & Saffman 1984). We consider vortex Reynolds numbers R=[Gamma]/(2[pi]v) where [Gamma] is the vortex circulation and v the kinematic viscosity, in the range R=1[minus sign]104, and a broad range of strain ratios [lambda]=([beta][minus sign][alpha])/([beta]+[alpha]) including [lambda]>1, and in some cases [lambda][dbl greater-than sign]1. A pseudo-spectral method is used to obtain numerical solutions corresponding to steady and quasi-steady vortex states over our whole (R, [lambda]) parameter space including [lambda] where arguments proposed by Moffatt, Kida & Ohkitani (1994) demonstrate the non-existence of strictly steady solutions. When [lambda][dbl greater-than sign]1, R[dbl greater-than sign]1 and [epsilon][identical with][lambda]/R[double less-than sign]1, we find an accurate asymptotic form for the vorticity in a region 11. An iterative technique based on the power method is used to estimate the largest eigenvalues for the non-symmetric case [lambda]>0. Stability is found for 0[less-than-or-eq, slant][lambda][less-than-or-eq, slant]1, and a neutrally convective mode of instability is found and analysed for [lambda]>1. Our general conclusion is that the generalized non-symmetric Burgers vortex is unconditionally stable to two-dimensional disturbances for all R, 0[less-than-or-eq, slant][lambda][less-than-or-eq, slant]1, and that when [lambda]>1, the vortex will decay only through exponentially slow leakage of vorticity, indicating extreme robustness in this case

Control of an Active Suspension System as a Benchmark for Design and Optimization of Restricted Complexity Controllers

A benchmark problem for restricted complexity controller design is introduced. The objective is to design the lowest-order controller which meets the control specifications for an active suspension system. The input-output data of the plant are provided on the benchmark site and the final controllers are evaluated using the closed-loop data. Thirteen solutions proposed to solve the benchmark problem are briefly presented and classified in terms of methodology and compared with respect to their complexity and performance

Three-dimensional stability of Burgers vortices

Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex tubes observed in numerical simulations of three-dimensional turbulence. In this model, the velocity field is a two-dimensional perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number $Re = \Gamma/\nu$, where $\Gamma$ is the total circulation of the vortex and $\nu$ is the kinematic viscosity. The purpose of this paper is to show that Burgers vortex is asymptotically stable with respect to general three-dimensional perturbations, for all values of the Reynolds number. This definitive result subsumes earlier studies by various authors, which were either restricted to small Reynolds numbers or to two-dimensional perturbations. Our proof relies on the crucial observation that the linearized operator at Burgers vortex has a simple and very specific dependence upon the axial variable. This allows to reduce the full linearized equations to a vectorial two-dimensional problem, which can be treated using an extension of the techniques developped in earlier works. Although Burgers vortices are found to be stable for all Reynolds numbers, the proof indicates that perturbations may undergo an important transient amplification if $Re$ is large, a phenomenon that was indeed observed in numerical simulations.Comment: 31 pages, no figur

Detection of Voigt Spectral Line Profiles of Hydrogen Radio Recombination Lines toward Sagittarius B2(N)

We report the detection of Voigt spectral line profiles of radio recombination lines (RRLs) toward Sagittarius B2(N) with the 100-m Green Bank Telescope (GBT). At radio wavelengths, astronomical spectra are highly populated with RRLs, which serve as ideal probes of the physical conditions in molecular cloud complexes. An analysis of the Hn(alpha) lines presented herein shows that RRLs of higher principal quantum number (n>90) are generally divergent from their expected Gaussian profiles and, moreover, are well described by their respective Voigt profiles. This is in agreement with the theory that spectral lines experience pressure broadening as a result of electron collisions at lower radio frequencies. Given the inherent technical difficulties regarding the detection and profiling of true RRL wing spans and shapes, it is crucial that the observing instrumentation produce flat baselines as well as high sensitivity, high resolution data. The GBT has demonstrated its capabilities regarding all of these aspects, and we believe that future observations of RRL emission via the GBT will be crucial towards advancing our knowledge of the larger-scale extended structures of ionized gas in the interstellar medium (ISM)

Spectroscopy of η′\eta'-nucleus bound states at GSI and FAIR --- very preliminary results and future prospects ---

The possible existence of \eta'-nucleus bound states has been put forward through theoretical and experimental studies. It is strongly related to the \eta' mass at finite density, which is expected to be reduced because of the interplay between the $U_A(1)$ anomaly and partial restoration of chiral symmetry. The investigation of the C(p,d) reaction at GSI and FAIR, as well as an overview of the experimental program at GSI and future plans at FAIR are discussed.Comment: 7 pages, 3 figures; talk at the International Conference on Exotic Atoms and Related Topics (EXA2014), Vienna, Austria, 15-19 September 2014. in Hyperfine Interactions (2015

\b{eta}-delayed three-proton decay of 31Ar

The beta decay of 31Ar, produced by fragmentation of a 36Ar beam at 880 MeV/nucleon, was investigated. Identified ions of 31Ar were stopped in a gaseous time projection chamber with optical readout allowing to record decay events with emission of protons. In addition to \b{eta}-delayed emission of one and two protons we have clearly observed the beta-delayed three-proton branch. The branching ratio for this channel in 31Ar is found to be 0.07(2)%.Comment: 5 pages, 3 figures, submitted to Physical Rev.

Schottky mass measurements of heavy neutron-rich nuclides in the element range 70\leZ \le79 at the ESR

Storage-ring mass spectrometry was applied to neutron-rich $^{197}$Au projectile fragments. Masses of $^{181,183}$Lu, $^{185,186}$Hf, $^{187,188}$Ta, $^{191}$W, and $^{192,193}$Re nuclei were measured for the first time. The uncertainty of previously known masses of $^{189,190}$W and $^{195}$Os nuclei was improved. Observed irregularities on the smooth two-neutron separation energies for Hf and W isotopes are linked to the collectivity phenomena in the corresponding nuclei.Comment: 10 pages, 9 figures, 2 table