Energy release in the solar atmosphere from a stream of infalling prominence debris

Recent high-resolution and high-cadence EUV imaging has revealed a new phenomenon, impacting prominence debris, where prominence material from failed or partial eruptions can impact the lower atmosphere, releasing energy. We report a clear example of energy release and EUV brightening due to infalling prominence debris that occurred on 2011 September 7-8. The initial eruption of material was associated with an X1.8-class flare from AR11283, occurring at 22:30 UT on 2011 September 7. Subsequently, a semi-continuous stream of this material returned to the solar surface with a velocity v > 150 km/s, impacting a region remote from the original active region between 00:20 - 00:40 UT on 2011 September 8. Using SDO/AIA, the differential emission measure of the plasma was estimated throughout this brightening event. We found that the radiated energy of the impacted plasma was L_rad ~10^27 ergs, while the thermal energy peaked at ~10^28 ergs. From this we were able to determine the mass content of the debris to be in the range 2x10^14 < m < 2x10^15 g. Given typical promimence masses, the likely debris mass is towards the lower end of this range. This clear example of a prominence debris event shows that significant energy release takes place during these events, and that such impacts may be used as a novel diagnostic tool for investigating prominence material properties.Comment: Accepted by AstroPhysical Journal Letters, 6 pages, 5 figure

The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex

Copyright © 1999 Cambridge University Press. Published version reproduced with the permission of the publisher.The response of a Gaussian vortex to a weak time-dependent external strain field is studied numerically. The cases of an impulsive strain, an on–off step function, and a continuous random strain are considered. Transfers of enstrophy between mean and azimuthal components are observed, and the results are compared with an analogous passive scalar model and with Kida's elliptical vortex model. A ‘rebound’ phenomenon is seen: after enstrophy is transferred from mean to azimuthal component by the external straining field, there is a subsequent transfer of enstrophy back from the azimuthal component to the mean. Analytical support is given for this phenomenon using Lundgren's asymptotic formulation of the spiral wind-up of vorticity. Finally the decay of the vortex under a continuous random external strain is studied numerically and compared with the passive scalar model. The vorticity distribution decays more slowly than the scalar because of the rebound phenomenon

The spiral wind-up of vorticity in an inviscid planar vortex

Copyright © 1998 Cambridge University Press. Published version reproduced with the permission of the publisher.The relaxation of a smooth two-dimensional vortex to axisymmetry, also known as `axisymmetrization', is studied asymptotically and numerically. The vortex is perturbed at t = 0 and differential rotation leads to the wind-up of vorticity fluctuations to forma spiral. It is shown that for infinite Reynolds number and in the linear approximation, the vorticity distribution tends to axisymmetry in a weak or coarse-grained sense: when the vorticity field is integrated against a smooth test function the result decays asymptotically as t−λ with λ = 1 + (n2 + 8)1/2, where n is the azimuthal wavenumber of the perturbation and n ≥1. The far-field stream function of the perturbation decays with the same exponent. To obtain these results the paper develops a complete asymptotic picture of the linear evolution of vorticity fluctuations for large times t, which is based on that of Lundgren (1982)

Nonlinear equilibration of a dynamo in a smooth helical flow

Copyright © 1997 Cambridge University Press. Published version reproduced with the permission of the publisher.We investigate the nonlinear equilibration of magnetic fields in a smooth helical flow at large Reynolds number Re and magnetic Reynolds number Rm with Re >> Rm >> 1. We start with a smooth spiral Couette flow driven by boundary conditions. Such flows act as dynamos, that is are unstable to growing magnetic fields; here we disregard purely hydrodynamic instabilities such as Taylor-Couette modes. The dominant feedback from a magnetic field mode is only on the mean flow and this yields a simplified `mean-flow system' consisting of one magnetic mode and the mean flow, which we solve numerically. We also obtain the asymptotic structure of the equilibrated fields for weakly and strongly nonlinear regimes. In particular the field tends to concentrate in a cylindrical shell where all stretching and differential rotation is suppressed by the Lorentz force, and the fluid is in solid-body motion. This shell is bounded by thin diffusive layers where the stretching that maintains the field against diffusive decay is dominant

Can feedback from the jumbo CD market improve bank surveillance?

Banks and banking

Could a CAMELS downgrade model improve off-site surveillance?

The Federal Reserve’s off-site surveillance system includes two econometric models that are collectively known as the System for Estimating Examination Ratings (SEER). One model, the SEER risk rank model, uses the latest financial statements to estimate the probability that each Fed-supervised bank will fail in the next two years. The other component, the SEER rating model, uses the latest financial statements to produce a “shadow” CAMELS rating for each supervised bank. Banks identified as risky by either model receive closer supervisory scrutiny than other state-member banks.> Because many of the banks flagged by the SEER models have already tumbled into poor condition and, hence, would already be receiving considerable supervisory attention, we developed an alternative model to identify safe-and-sound banks that potentially are headed for financial distress. Such a model could help supervisors allocate scarce on- and off-site resources by pointing out banks not currently under scrutiny that need watching.> It is possible, however, that our alternative model improves little over the current SEER framework. All three models—the SEER risk rank model, the SEER rating model, and our downgrade model—produce ordinal rankings based on overall risk. If the financial factors that explain CAMELS downgrades differ little from the financial factors that explain failures or CAMELS ratings, then all three models will produce similar risk ratings and, hence, similar watch lists of one- and two-rated banks.> We find only slight differences in the ability of the three models to spot emerging financial distress among safe-and-sound banks. In out-of-sample tests for 1992 through 1998, the watch lists produced by the downgrade model outperform the watch lists produced by the SEER models by only a small margin. We conclude that, in relatively tranquil banking environments like the 1990s, a downgrade model adds little value in off-site surveillance. We caution, however, that a downgrade model might prove useful in more turbulent banking times.Bank supervision

Vortex motion in a weak background shear flow

Copyright © 2004 Cambridge University Press. Published version reproduced with the permission of the publisher.A point vortex is introduced into a weak background vorticity gradient at finite Reynolds number. As the vortex spreads viscously so the background vorticity becomes wrapped around it, leading to enhanced diffusion of vorticity, but also giving a feedback on the vortex and causing it to move. This is investigated in the linear approximation, using a similarity solution for the advection of weak vorticity around the vortex, at finite and infinite Reynolds number. A logarithmic divergence in the far field requires the introduction of an outer length scale $L$ and asymptotic matching. In this way results are obtained for the motion of a vortex in a weak vorticity field modulated on the large scale $L$ and these are confirmed by means of numerical simulations

Diffusion and the formation of vorticity staircases in randomly strained two-dimensional vortices

Copyright © 2009 Cambridge University PressThe spreading and diffusion of two-dimensional vortices subject to weak external random strain fields is examined. The response to such a field of given angular frequency depends on the profile of the vortex and can be calculated numerically. An effective diffusivity can be determined as a function of radius and may be used to evolve the profile over a long time scale, using a diffusion equation that is both nonlinear and non-local. This equation, containing an additional smoothing parameter, is simulated starting with a Gaussian vortex. Fine scale steps in the vorticity profile develop at the periphery of the vortex and these form a vorticity staircase. The effective diffusivity is high in the steps where the vorticity gradient is low: between the steps are barriers characterized by low effective diffusivity and high vorticity gradient. The steps then merge before the vorticity is finally swept out and this leaves a vortex with a compact core and a sharp edge. There is also an increase in the effective diffusion within an encircling surf zone. In order to understand the properties of the evolution of the Gaussian vortex, an asymptotic model first proposed by Balmforth, Llewellyn Smith & Young (J. Fluid Mech., vol. 426, 2001, p. 95) is employed. The model is based on a vorticity distribution that consists of a compact vortex core surrounded by a skirt of relatively weak vorticity. Again simulations show the formation of fine scale vorticity steps within the skirt, followed by merger. The diffusion equation we develop has a tendency to generate vorticity steps on arbitrarily fine scales; these are limited in our numerical simulations by smoothing the effective diffusivity over small spatial scales