Transient Convective Spin-up Dynamics

We study the formation, longevity and breakdown of convective rings during impulsive spin-up in square and cylindrical containers using direct numerical simulations. The rings, which are axisymmetric alternating regions of up- and down-welling flow that can last for O (100) rotation times, were first demonstrated experimentally and arise due to a balance between Coriolis and viscous effects. We study the formation of these rings in the context of the Greenspan-Howard spin-up process, the disruption of which modifies ring formation and evolution. We show that, unless imprinted by boundary geometry, convective rings can only form when the surface providing buoyancy forcing is a free-slip surface, thereby explaining an apparent disagreement between experimental results in the literature. For Prandtl numbers from 1--5 we find that the longest-lived rings occur for intermediate Prandtl numbers, with a Rossby number dependence. Finally, we find that the constant evaporative heat-flux conditions imposed in the experiments are essential in sustaining the rings and in maintaining the vortices that form in consequence of the ring breakdown.Comment: 12 pages, 23 figure

Isolation and characterisation of 2-Tert-butyl-8-hydroxyquinoline as a crystalline solid and its blue fluorescent Li complex

Copyright © 2014 Poopathy Kathirgamanathan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.2-Tert-butyl-8-hydroxyquinoline (2-TB-8-hq) has been isolated as a crystalline solid and its X-ray structure elucidated, resolving three decades of controversy, since it was previously wrongly reported as yellow oil by some other workers. An improved synthetic method has been developed which increases the yield from 20% to 60%. The lithium complex of 2-TB-8-hq is blue emitting and the HOMO and LUMO levels are lowered by 0.86 eV and 0.74 eV, respectively, compared with the parent lithium 8-hydroxyquinolinolate (Li 8-hq)

Delayed Mode Quality control of Indian Argo floats

An observational network array of about 3000 autonomous profiling floats, known as Argo, has been evolving since the year 2000. India is a participant of the International Argo program, and Indian National Centre for Ocean Information Services(INCOIS) has the overall responsibility for implementation of the Indian Argo project, including the Argo regional centre (ARC) for the Indian ocean. One of the prime responsibility of regional data centre is delayed mode duality control (DMQC). The Argo array is delivering large number vertical profiles of temperature,salinity and other parameters from the surface to depths up to 2000 m. While floats are expected to give good measurements of temperature and pressure, salinity measurements sometimes show significant sensor drift with time or offsetsThe calibration procedure is called WJO method in short and OW method, after the recent modification by Owens and Wong [2009]. This report presents the major components of the work carried out at INCOIS using the WJO/OW software to provide best quality data to the end user. This report also presents all floats calibrated at INCOIS and their WJO/OW recommended corrections and the final decision taken about each floats considering the regional oceanography and various other factors (in attached CD-ROM)

Dynamics of circular arrangements of vorticity in two dimensions

The merger of two like-signed vortices is a well-studied problem, but in a turbulent flow, we may often have more than two like-signed vortices interacting. We study the merger of three or more identical co-rotating vortices initially arranged on the vertices of a regular polygon. At low to moderate Reynolds numbers, we find an additional stage in the merger process, absent in the merger of two vortices, where an annular vortical structure is formed and is long-lived. Vortex merger is slowed down significantly due to this. Such annular vortices are known at far higher Reynolds numbers in studies of tropical cyclones, which have been noticed to a break down into individual vortices. In the pre-annular stage, vortical structures in a viscous flow are found here to tilt and realign in a manner similar to the inviscid case, but the pronounced filaments visible in the latter are practically absent in the former. Interestingly at higher Reynolds numbers, the merger of an odd number of vortices is found to proceed very differently from that of an even number. The former process is rapid and chaotic whereas the latter proceeds more slowly via pairing events. The annular vortex takes the form of a generalised Lamb-Oseen vortex (GLO), and diffuses inwards until it forms a standard Lamb-Oseen vortex. For lower Reynolds number, the numerical (fully nonlinear) evolution of the GLO vortex follows exactly the analytical evolution until merger. At higher Reynolds numbers, the annulus goes through instabilities whose nonlinear stages show a pronounced difference between even and odd mode disturbances. It is hoped that the present findings, that multiple vortex merger is qualitatively different from the merger of two vortices, will motivate studies on how multiple vortex interactions affect the inverse cascade in two-dimensional turbulence.Comment: Abstract truncated. Paper to appear in Physical Review

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Sufficient Conditions for Starlike Functions Associated with the Lemniscate of Bernoulli

Let -1\leq B<A\leq 1. Condition on \beta, is determined so that 1+\beta zp'(z)/p^k(z)\prec(1+Az)/(1+Bz)\;(-1<k\leq3) implies p(z)\prec \sqrt{1+z}. Similarly, condition on \beta is determined so that 1+\beta zp'(z)/p^n(z) or p(z)+\beta zp'(z)/p^n(z)\prec\sqrt{1+z}\;(n=0, 1, 2) implies p(z)\prec(1+Az)/(1+Bz) or \sqrt{1+z}. In addition to that condition on \beta is derived so that p(z)\prec(1+Az)/(1+Bz) when p(z)+\beta zp'(z)/p(z)\prec\sqrt{1+z}. Few more problems of the similar flavor are also considered