Dissipation and enstrophy statistics in turbulence : are the simulations and mathematics converging?

Since the advent of cluster computing over 10 years ago there has been a steady output of new and better direct numerical simulation of homogeneous, isotropic turbulence with spectra and lower-order statistics converging to experiments and many phenomenological models. The next step is to directly compare these simulations to new models and new mathematics, employing the simulated data sets in novel ways, especially when experimental results do not exist or are poorly converged. For example, many of the higher-order moments predicted by the models converge slowly in experiments. The solution with a simulation is to do what an experiment cannot. The calculation and analysis of Yeung, Donzis & Sreenivasan (J. Fluid Mech., this issue, vol. 700, 2012, pp. 5–15) represents the vanguard of new simulations and new numerical analysis that will fill this gap. Where individual higher-order moments of the vorticity squared (the enstrophy) and kinetic energy dissipation might be converging slowly, they have focused upon ratios between different moments that have better convergence properties. This allows them to more fully explore the statistical distributions that eventually must be modelled. This approach is consistent with recent mathematics that focuses upon temporal intermittency rather than spatial intermittency. The principle is that when the flow is nearly singular, during ‘bad’ phases, when global properties can go up and down by many orders of magnitude, if appropriate ratios are taken, convergence rates should improve. Furthermore, in future analysis it might be possible to use these ratios to gain new insights into the intermittency and regularity properties of the underlying equations

Bounds for Euler from vorticity moments and line divergence

The inviscid growth of a range of vorticity moments is compared using Euler calculations of anti-parallel vortices with a new initial condition. The primary goal is to understand the role of nonlinearity in the generation of a new hierarchy of rescaled vorticity moments in Navier–Stokes calculations where the rescaled moments obey Dm ≥ Dm+1, the reverse of the usual Ωm+1 ≥ Ωm Hölder ordering of the original moments. Two temporal phases have been identified for the Euler calculations. In the first phase the 1 < m < ∞ vorticity moments are ordered in a manner consistent with the new Navier–Stokes hierarchy and grow in a manner that skirts the lower edge of possible singular growth with D2 m → � sup ӏωӏ ~ Am(Tc-t)-1 where the Am are nearly independent of m. In the second phase, the new Dm ordering breaks down as the Ωm converge towards the same super-exponential growth for all m. The transition is identified using new inequalities for the upper bounds for the -dD-2m/dt that are based solely upon the ratios Dm+1/Dm, and the convergent super-exponential growth is shown by plotting log(d log Ωm/dt). Three-dimensional graphics show significant divergence of the vortex lines during the second phase, which could be what inhibits the initial power-law growth

Current Knowledge and Attitudes Concerning Cost-Effectiveness in Glaucoma Pharmacotherapy: A Glaucoma Specialists Focus Group Study.

Background:Rising healthcare costs motivate continued cost-reduction efforts. To help lower costs associated with open-angle glaucoma (OAG), a prevalent, progressive disease with substantial direct and indirect costs, clinicians need to understand the cost-effectiveness of intraocular pressure (IOP)-lowering pharmacotherapies. There is little published information on clinicians' knowledge and attitudes about cost-effectiveness in glaucoma treatment. Purpose:This pilot focus group study aimed to explore clinician attitudes and perspectives around the costs and cost drivers of glaucoma therapy; the implementation of cost-effectiveness decisions; the clinical utility of cost-effectiveness studies; and the cost-effectiveness of available treatments. Methods:Six US glaucoma specialists participated in two separate teleconferencing sessions (three participants each), managed by an independent, skilled moderator (also a glaucoma specialist) using a discussion guide. Participants reviewed recent publications (n=25) on health economics outcomes research in glaucoma prior to the sessions. Results:Participants demonstrated a clear understanding of the economic burden of glaucoma therapy and identified medications, diagnostics, office visits, and treatment changes as key cost drivers. They considered cost-effectiveness an appropriate component of treatment decision-making but identified the need for additional data to inform these decisions. Participants indicated that there were only a few recent studies on health economics outcomes in glaucoma which evaluate parameters important to patient care, such as quality of life and medication adherence, and that longitudinal data were scant. In addition to efficacy, participants felt patient adherence and side-effect profile should be included in economic evaluations of glaucoma pharmacotherapy. Recently approved medications were evaluated in this context. Conclusion:Clinicians deem treatment decisions based on cost-effectiveness data as clinically appropriate. Newer IOP-lowering therapies with potentially greater efficacy and favorable side-effect and adherence profiles may help optimize cost-effectiveness. Future studies should include: clinicians' perspectives; lack of commercial bias; analysis of long-term outcomes/costs; more comprehensive parameters; real-world (including quality-of-life) data; and a robust Markov model