The three-dimensional vortical nature of atmospheric and oceanic turbulent flows

Using a novel numerical method at unprecedented resolution, we demonstrate that structures of small to intermediate scale in rotating, stratified flows are intrinsically three-dimensional. Such flows are characterized by vortices (spinning volumes of fluid), regions of large vorticity gradients, and filamentary structures at all scales. It is found that such structures have predominantly three-dimensional dynamics below a horizontal scale LLR, where LR is the so-called Rossby radius of deformation, equal to the characteristic vertical scale of the fluid H divided by the ratio of the rotational and buoyancy frequencies f/N. The breakdown of two-dimensional dynamics at these scales is attributed to the so-called "tall-column instability" [D. G. Dritschel and M. de la Torre Juárez, J. Fluid. Mech. 328, 129 (1996)], which is active on columnar vortices that are tall after scaling by f/N, or, equivalently, that are narrow compared with LR. Moreover, this instability eventually leads to a simple relationship between typical vertical and horizontal scales: for each vertical wave number (apart from the vertically averaged, barotropic component of the flow) the average horizontal wave number is equal to f/N times the vertical wave number. The practical implication is that three-dimensional modeling is essential to capture the behavior of rotating, stratified fluids. Two-dimensional models are not valid for scales below LR. ©1999 American Institute of Physics.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime

We compare laboratory observations of equilibrated baroclinic waves in the rotating two-layer annulus, with numerical simulations from a quasi-geostrophic model. The laboratory experiments lie well outside the quasi-geostrophic regime: the Rossby number reaches unity; the depth-to-width aspect ratio is large; and the fluid contains ageostrophic inertia–gravity waves. Despite being formally inapplicable, the quasi-geostrophic model captures the laboratory flows reasonably well. The model displays several systematic biases, which are consequences of its treatment of boundary layers and neglect of interfacial surface tension and which may be explained without invoking the dynamical effects of the moderate Rossby number, large aspect ratio or inertia–gravity waves. We conclude that quasi-geostrophic theory appears to continue to apply well outside its formal bounds.

Purpose built teaching equipment for a laboratory based course in three phase machines and drives

The hazards associated with high voltage three phase inverters and the rotating shafts of large electrical machines have resulted in most of the engineering courses covering these topics to be predominantly theoretical. This paper describes a set of purpose built, low voltage and low cost teaching equipment which allows the "hands on" instruction of three phase inverters and rotating machines. By using low voltages, the student can experiment freely with the motors and inverter and can access all of the current and voltage waveforms, which until now could only be studied in text books or observed as part of laboratory demonstrations. Both the motor and the inverter designs are optimized for teaching purposes cost around $25 and can be made with minimal effort.

Three-phase machines and drives - equipment for a laboratory-based course

The hazards associated with high-voltage three-phase inverters and high-powered large electrical machines have resulted in most of the engineering courses covering three-phase machines and drives theoretically. This paper describes a set of purpose-built, low-voltage, and low-cost teaching equipment that allows the hands-on instruction of three-phase inverters and rotating machines. The motivation for moving towards a system running at low voltages is that the students can safely experiment freely with the motors and inverter. The students can also access all of the current and voltage waveforms, which until now could only be studied in textbooks or observed as part of laboratory demonstrations. Both the motor and the inverter designs are for teaching purposes and require minimal effort and cost

Wind turbine blade pitch control system

The present invention provides an improvement for a wind turbine (20) having at least one blade (21) mounted on a hub (22) for controlled rotation about a blade axis (yb-yb) to vary the pitch of the blade relative to an airstream. The hub is mounted on a nacelle (23) for rotation about a hub axis (xh-xh). The wind turbine includes a main pitch control system for selectively controlling the pitch of the blade, and/or a safety pitch control system for overriding the main blade pitch control system and for causing the blade to move toward a feathered position in the event of an overspeed or fault condition. The improvement includes: an energy storage device (26) mounted on the nacelle and associated with the blade; a pitch-axis controller (25) mounted on the nacelle and associated with the blade and with the energy storage device; an electro-mechanical actuator (28) mounted on the hub and associated with the blade; and at least one slip ring (29) operatively arranged to transmit power and/or data signals between the pitch-axis controller and the electro-mechanical actuator; whereby the mass on the rotating hub may be reduced.

An overview of Earth’s global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Vibrational perturbation theory

Expressions are derived for the Jacobian of the coriolis ζ interaction constants and the centrifugal stretching constants (DJ, DJK, etc.) with respect to the force constants in a vibrating-rotating molecule.

Analysis of the eyes formed in simulated tropical cyclones and polar lows

The structure and size of the eyes generated in numerically simulated tropical cyclones and polar lows have been studied. A primitive-equation numerical model simulated systems in which the structures of the eyes formed were consistent with available observations. Whilst the tropical cyclone eyes generated were usually rapidly rotating, it appeared impossible for an eye formed in a system with a polar environment to develop this type of structure. The polar low eyes were found to be unable to warm through the subsidence of air with high values of potential temperature, as the environment was approximately statically neutral. Factors affecting the size of the eye were investigated through a series of controlled experiments. In mature tropical cyclone systems the size of the eye was insensitive to small changes in initial conditions, surface friction and latent and sensible heating from the ocean. In contrast, the eye size was strongly dependent on these parameters in the mature polar lows. Consistent with the findings, a mechanism is proposed in which the size of the eye in simulated polar lows is controlled by the strength of subsidence within it.

Numerical simulation of the 12 May 1997 CME Event: The role of magnetic reconnection

We perform a numerical study of the evolution of a Coronal Mass Ejection (CME) and its interaction with the coronal magnetic field based on the 12 May 1997, CME event using a global MagnetoHydroDynamic (MHD) model for the solar corona. The ambient solar wind steady-state solution is driven by photospheric magnetic field data, while the solar eruption is obtained by superimposing an unstable flux rope onto the steady-state solution. During the initial stage of CME expansion, the core flux rope reconnects with the neighboring field, which facilitates lateral expansion of the CME footprint in the low corona. The flux rope field also reconnects with the oppositely orientated overlying magnetic field in the manner of the breakout model. During this stage of the eruption, the simulated CME rotates counter-clockwise to achieve an orientation that is in agreement with the interplanetary flux rope observed at 1 AU. A significant component of the CME that expands into interplanetary space comprises one of the side lobes created mainly as a result of reconnection with the overlying field. Within 3 hours, reconnection effectively modifies the CME connectivity from the initial condition where both footpoints are rooted in the active region to a situation where one footpoint is displaced into the quiet Sun, at a significant distance (≈1R ) from the original source region. The expansion and rotation due to interaction with the overlying magnetic field stops when the CME reaches the outer edge of the helmet streamer belt, where the field is organized on a global scale. The simulation thus offers a new view of the role reconnection plays in rotating a CME flux rope and transporting its footpoints while preserving its core structure.

Electrochemical and sonoelectrochemical monitoring of indigo reduction by glucose

The reduction of indigo (dispersed in water) to leuco-indigo (dissolved in water) is an important industrial process and investigated here for the case of glucose as an environmentally benign reducing agent. In order to quantitatively follow the formation of leuco-indigo two approaches based on (i) rotating disk voltammetry and (ii) sonovoltammetry are developed. Leuco-indigo, once formed in alkaline solution, is readily monitored at a glassy carbon electrode in the mass transport limit employing hydrodynamic voltammetry. The presence of power ultrasound further improves the leuco-indigo determination due to additional agitation and homogenization effects. While inactive at room temperature, glucose readily reduces indigo in alkaline media at 65 degrees C. In the presence of excess glucose, a surface dissolution kinetics limited process is proposed following the rate law d eta(leuco-indigo)/dt = k x c(OH-) x S-indigo where eta(leuco-indigo) is the amount of leuco-indigo formed, k = 4.1 x 10(-9) m s(-1) (at 65 degrees C, assuming spherical particles of I gm diameter) is the heterogeneous dissolution rate constant,c(OH-) is the concentration of hydroxide, and Sindigo is the reactive surface area. The activation energy for this process in aqueous 0.2 M NaOH is E-A = 64 U mol(-1) consistent with a considerable temperature effects. The redox mediator 1,8-dihydroxyanthraquinone is shown to significantly enhance the reaction rate by catalysing the electron transfer between glucose and solid indigo particles. (c) 2006 Elsevier Ltd. All fights reserved.

Wormlike micelle formation and flow alignment of a pluronic block copolymer in aqueous solution

The self-assembly into wormlike micelles of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer Pluronic P84 in aqueous salt solution (2 M NaCl) has been studied by rheology, small-angle X-ray and neutron scattering (SAXS/SANS), and light scattering. Measurements of the flow curves by controlled stress rheometry indicated phase separation under flow. SAXS on solutions subjected to capillary flow showed alignment of micelles at intermediate shear rates, although loss of alignment was observed for high shear rates. For dilute solutions, SAXS and static light scattering data on unaligned samples could be superposed over three decades in scattering vector, providing unique information on the wormlike micelle structure over several length scales. SANS data provided information on even shorter length scales, in particular, concerning "blob" scattering from the micelle corona. The data could be modeled based on a system of semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions. The micelle structure was compared at two temperatures close to the cloud point (47 degrees C). The micellar radius was found not to vary with temperature in this region, although the contour length increased with increasing temperature, whereas the Kuhn length decreased. These variations result in an increase of the low-concentration radius of gyration with increasing temperature. This was consistent with dynamic light scattering results, and, applying theoretical results from the literature, this is in agreement with an increase in endcap energy due to changes in hydration of the poly(ethylene oxide) blocks as the temperature is increased.

Fractionated crystallization and fractionated melting of confined PEO microdomains in PB-b-PEO and PE-b-PEO diblock copolymers

The confined crystallization of poly(ethylene oxide) (PEO) in predominantly spherical microdomains formed by several diblock copolymers was studied and compared. Two polybutadiene-b-poly(ethylene oxide) diblock copolymers were prepared by sequential anionic polymerization (with approximately 90 and 80 wt % polybutadiene (PB)). These were compared to equivalent samples after catalytic hydrogenation that produced double crystalline polyethylene-b-poly(ethylene oxide) diblock copolymers. Both systems are segregated into microdomains as indicated by small-angle X-ray scattering (SAXS) experiments performed in the melt and at lower temperatures. However, the PB-b-PEO systems exhibited a higher degree of order in the melt. A predominantly spherical morphology of PEO in a PB or a PE matrix was observed by both SAXS and transmission electron microscopy, although a possibly mixed morphology (spheres and cylinders) was formed when the PEO composition was close to the cylinder-sphere domain transitional composition as indicated by SAXS. Differential scanning calorimetry experiments showed that a fractionated crystallization process for the PEO occurred in all samples, indicating that the PE cannot nucleate PEO in these diblock copolymers. A novel result was the observation of a subsequent fractionated melting that reflected the crystallization process. Sequential isothermal crystallization experiments allowed us to thermally separate at least three different crystallization and melting peaks for the PEO microdomains. The lowest melting point fraction was the most important in terms of quantity and corresponded to the crystallization of isolated PEO spheres (or cylinders) that were either superficially or homogeneously nucleated. This was confirmed by Avrami index values of approximately 1. The isothermal crystallization results indicate that the PE matrix restricts the crystallization of the covalently bonded PEO to a higher degree compared to PB.

SAXS observation of RCM1 under cyclical shear

A cylinder forming poly(styrene-b-butadiene-b-styrene) triblock copolymer melt is cyclically processed through a capillary at a high shear rate in the Cambridge Multipass Rheometer (MPR). In situ X-ray diffraction experiments enable observation of the effect of the shear on the block copolymer (BCP) nanophase orientation, both during and after processing. Temporal resolution of the X-ray exposures is increased, whilst retaining intensity, by exploiting the cyclical nature of the shear and the material's response to it; short exposures from many cycles, individually having few counts, are added together to produce well resolved X-ray patterns. Orientation of the cylinders reduces during processing, then increases during pauses between processing. The loss of orientation is attributed to the high shear rate deforming the melt faster than the structure can respond, whilst it is believed that melt relaxation, linked to the compressibility of the material, produces much lower shear rates after mechanical processing has ceased, which induces strong orientation of the nanostructure.

Orientational ordering in the nematic phase of a polyethylene glycol-peptide conjugate in aqueous solution

The orientational ordering of the nematic phase of a polyethylene glycol (PEG)-peptide block copolymer in aqueous solution is probed by small-angle neutron scattering (SANS), with the sample subjected to steady shear in a Couette cell. The PEG-peptide conjugate forms fibrils that behave as semiflexible rodlike chains. The orientational order parameters (P) over bar (2) and (P) over bar (4) are obtained by modeling the data using a series expansion approach to the form factor of uniform cylinders. The method used is independent of assumptions on the form of the singlet orientational distribution function. Good agreement with the anisotropic two-dimensional SANS patterns is obtained. The results show shear alignment starting at very low shear rates, and the orientational order parameters reach a plateau at higher shear rates with a pseudologarithmic dependence on shear rate. The most probable distribution functions correspond to fibrils parallel to the flow direction under shear, but a sample at rest shows a bimodal distribution with some of the rodlike peptide fibrils oriented perpendicular to the flow direction.