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

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

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)

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

Can feedback from the jumbo CD market improve bank surveillance?

Banks and banking

Can feedback from the jumbo-CD market improve bank surveillance?

We examine the value of jumbo certificate-of-deposit (CD) signals in bank surveillance. To do so, we first construct proxies for default premiums and deposit runoffs and then rank banks based on these risk proxies. Next, we rank banks based on the output of a logit model typical of the econometric models used in off-site surveillance. Finally, we compare jumbo-CD rankings and surveillance-model rankings as tools for predicting financial distress. Our comparisons include eight out-of-sample test windows during the 1990s. We find that rankings obtained from jumbo-CD data would not have improved on rankings obtained from conventional surveillance tools. More importantly, we find that jumbo-CD rankings would not have improved materially over random rankings of the sample banks. These findings validate current surveillance practices and, when viewed with other recent empirical tests, raise questions about the value of market signals in bank surveillance.Finance ; Banks and banking ; Bank supervision

The role of a CAMEL downgrade model in bank surveillance

This article examines the potential contribution to bank supervision of a model designed to predict which banks will have their supervisory ratings downgraded in future periods. Bank supervisors rely on various tools of off-site surveillance to track the condition of banks under their jurisdiction between on-site examinations, including econometric models. One of the models that the Federal Reserve System uses for surveillance was estimated to predict bank failures. Because bank failures have been so rare during the last decade, the coefficients on this model have been "frozen" since 1991. Each quarter the surveillance staff at the Board of Governors provide the supervision staff in the Reserve Banks the probabilities of failure by the banks subject to Fed supervision, based on the coefficients of this bank failure model and the latest call report data for each bank. The number of banks downgraded to problem status in recent years has been substantially larger than the number of bank failures. During a period of few bank failures, the relevance of this bank failure model for surveillance depends to some extent on the accuracy of the model in predicting which banks will have their supervisory ratings downgraded to problem status in future periods. This paper compares the ability of two models to predict downgrades of supervisory ratings to problem status: the Board staff model, which was estimated to predict bank failures, and a model estimated to predict downgrades of supervisory ratings. We find that both models do about as well in predicting downgrades of supervisory ratings for the early 1990s. Over time, however, the ability of the downgrade model to predict downgrades improves relative to that of the model estimated to predict failures. This pattern reflects the value of using a model for surveillance that can be re-estimated frequently. We conclude that the downgrade model may prove to be a useful supplement to the Board's model for estimating failures during periods when most banks are healthy, but that the downgrade model should not be considered a replacement for the current surveillance framework.Bank supervision

Can feedback from the jumbo-CD market improve off-site surveillance of community banks?

We examine the value of feedback from the jumbo-certificate-of-deposit (CD) market in the off-site surveillance of community banks. Using accounting data, we construct proxies for default premiums on jumbo CDs. Then, we produce rank orderings of community banks -- defined as institutions holding less than $500 million in assets (constant 1999 dollars) -- based on these proxies. Next, we use an econometric surveillance model to generate rank orderings based on the probability of encountering financial distress. Finally, we compare these rank orderings as tools for flagging emerging problems. Our comparisons include eight out-of-sample test windows during the 1990s. We find that feedback from the jumbo-CD market would have added little value in community-bank surveillance during our sample period. Specifically, rank orderings based on output from the econometric model significantly outperformed rank orderings based on jumbo-CD default premiums. More important, the jumbo-CD orderings improved little over a random ordering. Other attempts to extract risk signals from the jumbo-CD data yielded similar results. Taken together, our findings validate current surveillance practices. We conclude by arguing that the robust economic environment of the 1990s probably plays a large role in our results.Community banks ; Bank supervision

Critical layer and radiative instabilities in shallow-water shear flows

In this study a linear stability analysis of shallow-water flows is undertaken for a representative Froude number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}F=3.5$F=3.5 . The focus is on monotonic base flow profiles $U$U without an inflection point, in order to study critical layer instability (CLI) and its interaction with radiative instability (RI). First the dispersion relation is presented for the piecewise linear profile studied numerically by Satomura (J. Meterol. Soc. Japan, vol. 59, 1981, pp. 148–167) and using WKBJ analysis an interpretation given of mode branches, resonances and radiative instability. In particular surface gravity (SG) waves can resonate with a limit mode (LM) (or Rayleigh wave), localised near the discontinuity in shear in the flow; in this piecewise profile there is no critical layer. The piecewise linear profile is then continuously modified in a family of nonlinear profiles, to show the effect of the vorticity gradient $Q^{\prime } = - U^{\prime \prime }$Q ′ =−U ′′ on the nature of the modes. Some modes remain as modes and others turn into quasi-modes (QM), linked to Landau damping of disturbances to the flow, depending on the sign of the vorticity gradient at the critical point. Thus an interpretation of critical layer instability for continuous profiles is given, as the remnant of the resonance with the LM. Numerical results and WKBJ analysis of critical layer instability and radiative instability for more general smooth profiles are provided. A link is made between growth rate formulae obtained by considering wave momentum and those found via the WKBJ approximation. Finally the competition between the stabilising effect of vorticity gradients in a critical layer and the destabilising effect of radiation (radiative instability) is studied