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

Uber die Luminescenz des Luminols. VII. Die Wirkung von Fremdstoffzusatz auf die Luminolreaktion

Es wurde die Wirkung von Fremdstoffzusatz auf die Chemiluminiscenz des Luminols bei Anwesenheit von verschiedenen Katalysatoren mit komplex gebundenem Eisen untersucht. Die Fremdstoffe wirken loschend auf die Lumilnescenz, oder erhohen ihre maximale Helligkeit. Es konnte zwischen wahrer Inhibitorwirkung, Komplexbildung, Losungsmitteleinfluss und Elektrolytwirkung im Sinne der Bronstedschen Theorie unterschieden werden

A Desert Tortoise–Common Raven Viable Conflict Threshold

Since 1966, common raven (Corvus corax; raven) abundance has increased throughout much of this species’ Holarctic distribution, fueled by an ever-expanding supply of anthropogenic resource subsidies (e.g., water, food, shelter, and nesting substrate) to ecoregion specific raven population carrying capacities. Consequently, ravens are implicated in declines of both avian and reptilian species of conservation concern, including the California (USA) endangered and federally threatened Mojave desert tortoise (Gopherus agassizii; desert tortoise). While ravens are a natural predator of desert tortoises, the inter-generational stability of desert tortoise populations is expected to be compromised as annual juvenile survival is suppressed below 0.77 through a combination of raven depredation and other sources of mortality. To estimate the extent to which raven depredation suppresses desert tortoise recruitment within the Mojave Desert of California, we collected data from 274 variable-radius point counts, 78 desert tortoise decoy stations, and 8 control stations during the spring of 2020. Additionally, we complied a geodatabase of previously active raven nests, observed between 2013 and 2020. Raven density estimates from 4 monitoring areas ranged between 0.63 (eastern most) and 2.44 (western most) raven km-2 (95% CI: 0.35–1.14 and 1.33–4.48, respectively). We used a Bayesian shared frailty model to estimate the effects of raven density and distance to the nearest previously active raven nest on the annual “survival” of juvenile desert tortoise decoys (75-mm Midline Carapace Length), which we then converted into survival estimates for 0- to 10-year-old desert tortoises by adjusting exposure to reflect natural activity patterns. At the 1.72-km median distance from the nearest previously active raven nest, the estimated annual survival of desert tortoises decreased as raven density increased, ranging among conservation areas from 0.774 (eastern most) to 0.733 (western most). Accordingly, our model predicts that desert tortoise populations exposed to raven densities in excess of 0.89 raven km-2, at a distanc