Reassessment of the classical closures for scalar turbulence

In deducing the consequences of the Direct Interaction Approximation, Kraichnan was sometimes led to consider the properties of special classes of nonlinear interactions in degenerate triads in which one wavevector is very small. Such interactions can be described by simplified models closely related to elementary closures for homogeneous isotropic turbulence such as the Heisenberg and Leith models. These connections can be exploited to derive considerably improved versions of the Heisenberg and Leith models that are only slightly more complicated analytically. This paper applies this approach to derive some new simplified closure models for passive scalar advection and investigates the consistency of these models with fundamental properties of scalar turbulence. Whereas some properties, such as the existence of the Kolmogorov–Obukhov range and the existence of thermal equilibrium ensembles, follow the velocity case closely, phenomena special to the scalar case arise when the diffusive and viscous effects become important at different scales of motion. These include the Batchelor and Batchelor–Howells–Townsend ranges pertaining, respectively, to high and low molecular Schmidt number. We also consider the spectrum in the diffusive range that follows the Batchelor range. We conclude that improved elementary models can be made consistent with many nontrivial properties of scalar turbulence, but that such models have unavoidable limitations.     

Simulation of homogeneous turbulent shear flows at higher Reynolds numbers: numerical challenges and a remedy

In a recent study, Isaza and Collins [J. Fluid Mech., 637 (2009), pp. 213–239] found the asymptotic state of homogeneous turbulent shear flows (HTSFs) to be sensitively dependent on the initial shear parameter (), and yet be almost independent of the initial Reynolds number (R _λ≡qλ/ν). The stringent resolution criteria they employed, however, restricted their studies to relatively low Reynolds numbers. In this paper, we present higher resolution direct numerical simulations of HTSFs over a wider range of Reynolds numbers, aided in part by an improved parallelisation scheme that utilises two-dimensional domain decomposition. We maximise the time-window for our simulations by determining appropriate settings for the initial energy spectrum, viscosity and domain configuration, thereby ensuring that we attain the highest possible asymptotic Reynolds number at the chosen grid resolution. In the course of our study, we find that the pseudo-spectral method suffers from Gibbs oscillations while resolving the thin vortical structures that tend to form in HTSFs. The nonlinear growth of these oscillations leads to spurious energy buildup in the high-wavenumber region of the spectrum, and contaminates the flow field. Consequently, the growth of the integral length scale is found to be numerically stunted, well before the intended final Reynolds number is attained. The issue is rectified by the application of exponential-type spectral filters, which stabilise the simulations and extend the runtime window, permitting attainment of larger asymptotic Reynolds numbers. Various large-scale flow statistics are then studied, and their dependence on the initial value of the shear parameter and Reynolds number corroborates the findings of Isaza and Collins.     

1‐Bromo‐2‐(cyclopropylidenemethyl)benzene: A Useful Building Block in the Palladium‐Catalyzed Reaction of 2‐Alkynylbenzenamine

A novel palladium‐catalyzed domino reaction of 1‐bromo‐2‐(cyclopropylidenemethyl)benzene and 2‐alkynylbenzenamine is reported, which generates 2‐(naphthalen‐2‐yl)benzenamines and 5H‐indeno[1,2‐c]quinolines via 6‐endo and 5‐exo cyclization, respectively. The regioselectivity for the final outcome can be affected by phosphine and N‐heterocyclic carbene ligands.     

Recent Developments on the Trifluoromethylation of (Hetero)Arenes

Aryl‐CF₃ as an extremely important family of fluorinated organic compounds holds wide applications in pharmaceuticals, agrochemicals, and advanced materials. Traditionally, such trifluoromethylated compounds have been synthesized from the corresponding aryl trichlorides via Cl exchange reactions (Scheme 1 ). This Focus review gives an overview over the recent development of trifluoromethylation of (hetero)arenes.     

Precipitation Under Homogeneous or Heterogeneous Conditions by Photochemical Action

Abstract

Precipitation reagents may be formed in situ by photochemistry but the formation cannot be completely homogeneous due to the exponential nature of light absorption (Beer's Law). By proper adjustment of concentrations, one may vary the conditions from near homogeneous to heterogeneous formation of photoprecipitate.     

Deoxygenative reduction of carbon dioxide to methane, toluene, and diphenylmethane with [Et2Al]+ as catalyst

The strong Lewis acid [Et(2)Al](+) catalyzes the reduction of carbon dioxide with hydrosilanes under mild conditions to methane. In benzene solution, the side products toluene and diphenylmethane are also obtained through Lewis acid catalyzed benzene alkylation by reaction intermediates.