Internal heating driven convection at infinite Prandtl number

We derive an improved rigorous bound on the space and time averaged temperature $$ of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries thermally driven by uniform internal heating. A novel approach is used wherein a singular stable stratification is introduced as a perturbation to a non-singular background profile, yielding the estimate $\geq 0.419[R\log(R)]^{-1/4}$ where $R$ is the heat Rayleigh number. The analysis relies on a generalized Hardy-Rellich inequality that is proved in the appendix

"Ultimate state" of two-dimensional Rayleigh-Benard convection between free-slip fixed temperature boundaries

Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Benard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number Nu is bounded in terms of the Rayleigh number Ra according to $Nu \leq 0.2295 Ra^{5/12}$ uniformly in the Prandtl number Pr. This Nusselt number scaling challenges some theoretical arguments regarding the asymptotic high Rayleigh number heat transport by turbulent convection.Comment: 4 page

Spectroscopic Identification of the Infrared Counterpart to GX5-1

Using CGS4 on UKIRT, we have obtained a 1.95-2.45 micron infrared spectrum of the primary candidate counterpart to the bright Z LMXB GX5-1. IR photometry by Naylor, Charles, & Longmore (1992) and the astrometry of Jonker et al. (2000) had previously identified this star as the most likely counterpart to GX5-1. The spectrum presented here clearly shows Brackett gamma and He lines in emission, for the first time confirming the identity of the counterpart. Similar to our previous spectroscopy of the Z source LMXBs Sco X-1 and Sco X-2 (Bandyopadhyay et al. 1999), the K-band spectrum of GX5-1 shows emission lines only. We briefly discuss the implications of this spectrum for the nature of the Z sources.Comment: accepted for publication as a Letter in MNRA

Canonical Sasakian Metrics

Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the squared $L^2$-norm of the scalar curvature. We prove that its critical points, or canonical representatives of the polarization, are Sasakian metrics that are transversally extremal. We define a Sasaki-Futaki invariant of the polarization, and show that it obstructs the existence of constant scalar curvature representatives. For a fixed CR structure of Sasaki type, we define the Sasaki cone of structures compatible with this underlying CR structure, and prove that the set of polarizations in it that admit a canonical representative is open.Comment: 36 pages, minor corrections made, example adde

The X-ray Transient XTE J2012+381

We present optical and infrared observations of the soft X-ray transient (SXT) XTE J2012+381 and identify the optical counterpart with a faint red star heavily blended with a brighter foreground star. The fainter star is coincident with the radio counterpart and appears to show weak H alpha emission and to have faded between observations. The RXTE/ASM lightcurve of XTE J2012+381 is unusual for an SXT in that after an extended linear decay, it settled into a plateau state for about 40 days before undergoing a weak mini-outburst. We discuss the nature of the object and suggest similarities to long orbital period SXTs.Comment: 5 pages, 7 postscript figures included, uses mn.sty. Accepted for publication in MNRA