On the third order structure function for rotating 3D homogeneous turbulent flow

A form for the two-point third order structure function has been calculated for three dimensional homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalisation of the 3D incompressible turbulence owing to rotation.Comment: This revised version corrects some serious flaws in the discussions after the equation (2) and the equation (13) of the earlier version. Some typos are also correcte

Investigation of whisker growth from alkaline non-cyanide zinc electrodeposits

Electroplated zinc finishes have been widely used in the packaging of electronic products for many years as a result of their excellent corrosion resistance and relatively low cost. However, the spontaneous formation of whiskers on zinc electroplated components, which are capable of resulting in electrical shorting or other damaging effects, can be highly problematic for the reliability of long-life electrical and electronic equipment. This work investigated the mechanism for whisker growth from zinc electrodeposited mild steel substrates. The incubation time for whisker growth from the surface of nodules on the surface of the electrodeposit was considerably reduced compared with that from the planar deposit surface. Recrystallisation of the as-deposited columnar structure was observed at the whisker root. This result is consistent with some recent whisker growth models based on recrystallisation. There was no evidence of iron-zinc (Fe-Zn) intermetallic formation at the iron/zinc (Fe/Zn) interface or within the zinc coating beneath the whiskers

Statistical geometry in scalar turbulence

A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized by strong clustering. The quantitative counterpart is the existence of special functions of particle configurations which are statistically invariant under the flow. These are the statistical integrals of motion controlling the scalar statistics at small scales and responsible for the breaking of scale invariance associated to intermittency.Comment: 4 pages, 5 figure

Opportunities for use of exact statistical equations

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc

Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum

Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasi-geostrophic turbulence.Comment: Invited review; accepted by J. Low Temp. Phys.; Proceedings for Warwick Turbulence Symposium Workshop on Universal features in turbulence: from quantum to cosmological scales, 200

Zinc whisker growth from electroplated finishes – a review

Electroplated zinc finishes have been associated with the electronics industry for many years as a result of their excellent corrosion resistance and relatively low cost. They are normally applied onto ferrous products to provide corrosion protection in a range of different environments. However, the formation of spontaneously grown whiskers on zinc-electroplated components, which are capable of resulting in electrical shorting or other damaging effects, can be highly problematic for the reliability of long life electrical and electronic equipment. The growth of zinc whiskers has been identified as the cause of some electrical and electronic failures in telecommunications and aerospace-based applications, with consequences ranging from mild inconvenience to complete system failures. Investigators have been striving to address the problems induced by whisker growth since 1940s. However, most research effort has been focused on tin whiskers, especially following European Union environmental legislation that restricted the use of lead (Pb), which when alloyed with tin (3–10% by weight) provided effective tin whisker mitigation. Compared with tin whisker research, much less attention has been paid to zinc whiskers. A number of mechanisms to explain zinc whisker growth have been proposed, but none of them are widely accepted and some are in conflict with each other. The aim of this paper is to review the available literature in regard to zinc whiskers, to discuss the reported growth mechanisms, to evaluate the effect of deposition parameters and to explore potential mitigation methods. This paper presents a chronologically ordered review of zinc whisker-related studies from 1946 to 2013. Some important early research, which investigated whisker growth in tin and cadmium, as well as zinc, has also been included