Three-dimensional coating and rimming flow: a ring of fluid on a rotating horizontal cylinder

The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study “full-ring” solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load.\ud \ud We also describe the behaviour of the non-critical full-ring solution, and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the right-hand side of the cylinder

Thermoviscous Coating and Rimming Flow

A comprehensive description is obtained of steady thermoviscous (i.e. with temperature-dependent viscosity) coating and rimming flow on a uniformly rotating horizontal cylinder that is uniformly hotter or colder than the surrounding atmosphere. It is found that, as in the corresponding isothermal problem, there is a critical solution with a corresponding critical load (which depends, in general, on both the Biot number and the thermoviscosity number) above which no ``full-film'' solutions corresponding to a continuous film of fluid covering the entire outside or inside of the cylinder exist. The effect of thermoviscosity on both the critical solution and the full-film solution with a prescribed load is described. In particular, there are no full-film solutions with a prescribed load M for any value of the Biot number when M is greater than or equal to M_{c0} divided by the square root of f for positive thermoviscosity number and when M is greater than M_{c0} for negative thermoviscosity number, where f is a monotonically decreasing function of the thermoviscosity number and M_{c0} = 4.44272 is the critical load in the constant-viscosity case. It is also found that when the prescribed load M is less than 1.50315 there is a narrow region of the Biot number - thermoviscosity number parameter plane in which backflow occurs

Growth or decline in the Church of England during the decade of Evangelism: did the Churchmanship of the Bishop matter?

The Decade of Evangelism occupied the attention of the Church of England throughout the 1990s. The present study employs the statistics routinely published by the Church of England in order to assess two matters: the extent to which these statistics suggest that the 43 individual dioceses finished the decade in a stronger or weaker position than they had entered it and the extent to which, according to these statistics, the performance of dioceses led by bishops shaped in the Evangelical tradition differed from the performance of dioceses led by bishops shaped in the Catholic tradition. The data demonstrated that the majority of dioceses were performing less effectively at the end of the decade than at the beginning, in terms of a range of membership statistics, and that the rate of decline varied considerably from one diocese to another. The only exception to the trend was provided by the diocese of London, which experienced some growth. The data also demonstrated that little depended on the churchmanship of the diocesan bishop in shaping diocesan outcomes on the performance indicators employed in the study

The Spitzer View of Low-Metallicity Star Formation: II. Mrk 996, a Blue Compact Dwarf Galaxy with an Extremely Dense Nucleus

(abridged) We present new Spitzer, UKIRT and MMT observations of the blue compact dwarf galaxy (BCD) Mrk 996, with an oxygen abundance of 12+log(O/H)=8.0. This galaxy has the peculiarity of possessing an extraordinarily dense nuclear star-forming region, with a central density of ~10^6 cm^{-3}. The nuclear region of Mrk 996 is characterized by several unusual properties: a very red color J-K = 1.8, broad and narrow emission-line components, and ionizing radiation as hard as 54.9 eV, as implied by the presence of the OIV 25.89 micron line. The nucleus is located within an exponential disk with colors consistent with a single stellar population of age >1 Gyr. The infrared morphology of Mrk 996 changes with wavelength. The IRS spectrum shows strong narrow Polycyclic Aromatic Hydrocarbon (PAH) emission, with narrow line widths and equivalent widths that are high for the metallicity of Mrk 996. Gaseous nebular fine-structure lines are also seen. A CLOUDY model requires that they originate in two distinct HII regions: a very dense HII region of radius ~580 pc with densities declining from ~10^6 at the center to a few hundreds cm^{-3} at the outer radius, where most of the optical lines arise; and a HII region with a density of ~300 cm^{-3} that is hidden in the optical but seen in the MIR. We suggest that the infrared lines arise mainly in the optically obscured HII region while they are strongly suppressed by collisional deexcitation in the optically visible one. The hard ionizing radiation needed to account for the OIV 25.89 micron line is most likely due to fast radiative shocks propagating in an interstellar medium. A hidden population of Wolf-Rayet stars of type WNE-w or a hidden AGN as sources of hard ionizing radiation are less likely possibilities.Comment: 48 pages, 13 figures, accepted for publication in the Astrophysical Journa

Basic studies of baroclinic flows

Computations were completed of transition curves in the conventional annulus, including hysteresis effect. The model GEOSIM was used to compute the transition between axisymmetric flow and baroclinic wave flow in the conventional annulus experiments. Thorough testing and documentation of the GEOSIM code were also completed. The Spacelab 3 results from the Geophysical Fluid Flow Cell (GFFC) were reviewed and numerical modeling was performed of many of the cases with horizontal temperature gradients as well as heating from below, with different rates of rotation. A numerical study of the lower transition to axisymmetric flow in the baroclinic annulus was performed using GEOSIM