Broad Cones Research Articles

Flows Over Rotating Disks and Cones

Rotating-disk flows were first considered by von Kármán in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary cross-flow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Kármán's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.

Rotating disks and cones a centennial of von Kármán’s 1921 paper

It is now more than 100 years since the work of von Kármán (1921) on the boundary-layer flow over a rotating disk was published in the first volume of Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM, Vol. 1(4), pp 233-252). Recently, there has been a large amount of work undertaken addressing the instability and transition of the boundary-layer flows over rotating disks and cones using theoretical, numerical and experimental techniques. Here we will discuss some different methods to analyze experimental data that can give insight into the instability and transition to turbulence of boundary-layer flows over rotating slender and broad cones (including the disk). At first, we discuss the pdf-method (probability density function) that allows a simple way to determine regions of instability growth, transition and fully developed turbulence. Secondly, we look at various ways to use spectral information to investigate the boundary layers giving a deeper understanding of the transition process. Finally, a method to determine the most probable flow structure leading up to fully developed turbulence is discussed. We envisage that some of these methods can be useful in analyzing instability and transition also in other flow cases.

Partitioning of gene expression among zebrafish photoreceptor subtypes

Vertebrate photoreceptors are categorized into two broad classes, rods and cones, responsible for dim- and bright-light vision, respectively. While many molecular features that distinguish rods and cones are known, gene expression differences among cone subtypes remain poorly understood. Teleost fishes are renowned for the diversity of their photoreceptor systems. Here, we used single-cell RNA-seq to profile adult photoreceptors in zebrafish, a teleost. We found that in addition to the four canonical zebrafish cone types, there exist subpopulations of green and red cones (previously shown to be located in the ventral retina) that express red-shifted opsin paralogs (opn1mw4 or opn1lw1) as well as a unique combination of cone phototransduction genes. Furthermore, the expression of many paralogous phototransduction genes is partitioned among cone subtypes, analogous to the partitioning of the phototransduction paralogs between rods and cones seen across vertebrates. The partitioned cone-gene pairs arose via the teleost-specific whole-genome duplication or later clade-specific gene duplications. We also discovered that cone subtypes express distinct transcriptional regulators, including many factors not previously implicated in photoreceptor development or differentiation. Overall, our work suggests that partitioning of paralogous gene expression via the action of differentially expressed transcriptional regulators enables diversification of cone subtypes in teleosts.

On the stability of boundary-layer flow over a rotating cone in an enforced axial free stream

Studies into the boundary-layer stability of rotating cones in an axial free stream have considered both cases of broad-angled cones and slender-angled ones. This distinction is made due to the findings that the dominant instability in the quiescent-fluid case results from different physical mechanisms for broad and slender cones. These investigations made use of an Orr-Sommerfeld-type analysis derived from the assumption of a small perturbation to a similarity-type solution for the mean fluid flow around the cone. In this work, we investigate the efficacy of a combination of sophisticated numerical techniques to find the basic flow, using ideas both from automatic differentiation and spectral collocation methods, to maximise the accuracy of the obtained solution. We inspect the solutions obtained for the Orr-Sommerfeld system in this setting and compare them to the results from previous studies.

Instability and transition in the boundary layer driven by a rotating slender cone

Abstract

The convective instability of the boundary-layer flow over a rotating cone in and out of a uniform magnetic field

We present convective instability analyses of the boundary-layer flows originated over cones (with half-angle ψ≤90∘) rotating in an otherwise still conducting fluid. A uniform magnetic field (with magnetic strength parameter, m≥0) is acting normally on the surface of each cone. In the non-magnetic case of cones, comparison of present results with existing experimental and theoretical studies lead *to propose that onset of instabilities may be attributed to crossflow (type I) modes and streamline curvature (type II) modes for broad cones (with ψ≥40∘) and more slender cones (with ψ≤15∘), respectively. For slender cones with half-angle ψ in the vicinity of 25° the presented results validate the hypothesis of centrifugal (type III) modes ( discovered by Garrett et al. (2014)). In the magnetic case, increasing magnetic strength m∈(0,11] considerably delays the onset of instabilities (due to both type I and type II modes) over each rotating cone with fixed ψ. The stabilising influence of magnetism is in agreement with the meagrely available theoretical studies for magnetic rotating disk case ψ=90∘. In addition, our results lead to suggest that streamline curvature mode over each cone with fixed half-angle ψ become sensitive with increasing m. A minimum m0∈[0,11] exists for each fixed half-angle ψ0≤90∘ such that whenever m≥m0 the onset of instabilities (in the sense of minimum critical Reynolds numbers) over every cone with half-angle (ψ≤ψ0) are commenced by type II mode instead of type I mode whilst the aforementioned conjecture of stabilising effect of magnetism is not violated in the considered range of parameters. Under non-stationary vortices assumption with magnetism, we show that crossflow modes travelling at around 75% of the cone surface are likely to be selected in applications where smooth and frictionless surfaces are used. This finding is in complete agreement with the non-magnetic case of rotating cone in existing studies.

The centrifugal instability of the boundary-layer flow over slender rotating cones

AbstractExisting experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.

Boundary-Layer Transition on Broad Cones rotating in an Imposed Axial Flow

We present stability analyses for the boundary-layer flow over broad cones (half-angle > 40 ◦ ) rotating in imposed axial flows. Preliminary convective instability analyses are presented that are based on the Orr–Sommerfeld equation for a variety of axial-flow speeds. The results are discussed in terms of the limited existing experimental data and previous stability analyses on related bodies. The results of an absolute instability analysis are also presented which are intended to further those by Garrett & Peake 21 through the use of a more rigorous steady-flow formulation. Axial flow is seen to delay the onset of both convective and absolute instabilities.

Linear growth rates of types I and II convective modes within the rotating-cone boundary layer

Experimental observations have shown that the transition characteristics of the boundary-layer flow over rotating cones depends on the cone half-angle. In particular, pairs of counter-rotating Görtler-type vortices are observed over cones with slender half-angles and co-rotating vortices are observed over broad cones. Garrett et al (2009 J. Fluid Mech. 622 209–32) have hypothesized the existence of a centrifugal instability mode over slender cones that is more dangerous than the types I (crossflow) and II (streamline curvature) modes which dominate over rotating disks and broad cones. Work is currently underway to clarify this alternative mode; however, a clear understanding of the growth rates of types I and II modes is crucial to the ultimate understanding of how the dominant mode changes with half-angle. In this paper, we demonstrate that the maximum growth rate for types I and II modes decreases with reduced half-angle, which clears the way for the dominance of the alternative instability mode. Furthermore, it is suggested that vortices travelling at 75% of the cone surface speed will be selected over smooth, clean rotating cones with half-angle such that the type I mode is dominant. Interestingly, this vortex speed has been experimentally observed by Kobayashi and Arai within the rotating-sphere boundary layer.

Variations of the H2O maser emission of W51M in 1981–1998

The results of spectral monitoring of the maser source W51M carried out in the water-vapor line at 1.35 cm (22GHz) on the 22-m telescope of the Pushchino Radio Astronomy Observatory in 1981–1998 are reported and interpreted. Long-term variations of the maser flux with a period of 12–13 years are found. W51M may be a rotating and simultaneously expanding toroidal cloud of gas and dust around a young star with a mass of the order of ∼15M⊙, with numerous high-velocity jets of maser condensations flowing out in two broad cones along the polar axis of the torus. A stellar wind with a velocity of about 2000–3000 km/s is responsible for the maser pumping.

Time-extended acceleration of energetic particles in the corona during the 19 October 1989 GLE

The broad injection cones and long durations of large solar energetic particle events (SEPs) have been recently considered as evidence for particle acceleration in the shock wave generated by a coronal mass ejection. Radio observations of an energetic flare on 19 Oct 1989 show that energetic electrons radiate both near the flare site and several tens of heliocentric degrees away. This is evidence for rapid particle propagation from the flare site or else for the simultaneous activation of widely separated sites of acceleration. At some places energetic electron signatures persist over at least several hours after the flare. We argue that even if the CME-associated shock wave may contribute to the acceleration, it competes with processes in the low and middle corona which may supply energetic particles to interplanetary space over several hours and with injection cones comparable with the width of CMEs.

Optical recording of calcium and voltage transients following impulses in cell bodies and processes of identified leech neurons in culture

Optical methods were used to examine the spread of electrical potentials and the distribution and time course of calcium transients in individual identified nerve cells isolated from the leech. A photodiode array detected voltage transients by measuring absorbance changes of cells stained with the voltage-sensitive dye RH155 added to the bath. Calcium transients were recorded by measuring absorbance changes of the dye arsenazo III, which had been injected into the cells. In addition, Lucifer yellow was injected to outline the some and processes. Calcium changes resulting from individual action potentials were recorded from N, P, and Retzius cells without averaging. Signals from T cells and anterior pagoda (AP) cells were weaker but could be detected with averaging. These results are in accord with previous studies on calcium contributions to action potentials in these cells. For all cells, larger or wider action potentials gave bigger signals. Calcium changes from each of a train of action potentials were of equal amplitude, showing no sign of facilitation. Calcium transients from Retzius cells that had formed chemical synapses with P cells had properties similar to those of isolated cells. We were also able to detect responses from prolonged subthreshold depolarizations to -40 mV from a hyperpolarized membrane potential (-65 mV). These signals rose throughout the duration of the pulse (1-2 sec). With the photodiode array we mapped the distribution of the calcium signals. The amplitudes from each pixel are proportional to the amount of calcium entering that element in response to the stimulating pulse, if the simplifying assumption is made that the calcium buffering of the cytoplasm is uniform throughout the cell. The largest signals were detected over the axon stump left from the cell isolation procedure. Large signals were also detected from the soma. Weak signals were detected from the processes of some cells. From many Retzius cells, no signals at all were detected from the newly formed processes. Using the photodiode array, we also recorded voltage transients from the cells. Signals were recorded from all over the arborization of the neuron, with no obvious variation in time course, showing that the entire cell, including fine slender processes and broad growth cones, was essentially isopotential. Combining these observations with the measured distribution of calcium transients in the same cell suggests that the density of calcium channels in most cells is less in the outgrowing processes than in the soma or axon stump.

A scanning electron microscope study of the in vitro development of dissociated hippocampal cells

Cultures of dissociated hippocampal neurons from 18-day-old rat fetuses were examined by scanning electron microscopy after periods between one hour and 20 days following plating on a poly-L-lysine coated substrate. Cell attachment was virtually complete within one hour after plating, and at that stage many cells could be seen which had started to extend processes with broad growth cones. By four hours in culture, process formation was well advanced and some cells had already assumed a pyramidal configuration. After 16 hours in culture, numerous contacts were seen between neighboring growth cones, and this frequently led to fasciculation of the interacting fibers. During the next three weeks the cell bodies enlarged considerably and rounded-up, and two distinct types of processes became evident: large, rapidly tapering dendrite-like processes and finer, essentially uniform-diametered processes that resemble axons. In most of the older cultures a dense plexus of processes was formed, and many of the finer processes appeared to have "bouton-like" swellings as they traversed the upper surfaces of the neuronal perikarya. Non-neuronal elements, which comprised only about 5% of the cells initially plated, rapidly proliferated in our cultures and within three to six days formed a confluent monolayer beneath the neurons.

A Biological Survey of Oil Platforms in the Santa Barbara Channel

During 1975 biologist-divers surveyed the marine life found on and near two offshore structures in the Santa Barbara Channel. The detailed biological and chemical inventory performed showed a great abundance of many specks, large sizes of some organisms, and a lack of contamination. Introduction The objectives of the studies reported in this paper were to obtain facts about the present status of the sea life on and near two offshore structures and to compare the quantity and quality of life there now with that which lived at the towers several years ago and with that at nearby control sites. The undisturbed muddy and rocky bottoms that were used for controls offer conditions similar to those that would exist if the platforms had not been built. Studies of the biology of both platforms by California Dept. of Fish and Game biologists in 1960 and 1970 provided historical data for comparison. Having made repeated direct observations, measurements of oceanographic parameters, precise chemical analyses of many samples, and extensive biological studies, we found that life on and around the two platforms is healthy and shows no indication of the uptake of any toxicant. Species diversity and abundance are greater than at the control sites. The number of fish now living under each platform is 20 to 50 times the number that lived in the area before construction. Platforms Hilda and Hazel were installed by the Standard Oil Co. of California in 1958 and 1960, respectively. These structures are about 100 ft (34 m) square and stand in water depths of about 100 ft (31 m) about 2 nautical miles south of Loon Point in the Santa Barbara Channel (Fig. 1). Of the 25 wells drilled from Hazel, eight are now producing 290 B/D of 28- to 40-degrees API-gravity oil. Of the 24 wells drilled from Hilda, seven are now producing 318 B/D of similar crude. No special precautions were taken to prevent pollution during the uneventful development of this field. The cuttings were dumped in a heap on the sea floor under the platforms, where they make broad cones about 5 m high (to which 1 meter of mussel shells has been added). Shortly after the platforms were installed, marine biologists began to study the effects of these new manmade reefs by diving to make direct examinations. Fish counts and collections of organisms were made over a 29-month period. The scientists found (1) 47 species of fish, 40 species of invertebrates, and 14 species of algae around the platforms; (2) little life on the cuttings pile; and (3) the fish population under Hazel stabilized at 6,000 fish (after a temporary peak at 62,000 fish caused by schools of transient fish). In Aug. 1970 another group of California Fish and Game biologists resurveyed the site and found the resident fish population had increased to 12,500 under Hilda and 18,000 under Hazel. Numerous other biological studies of the area made after the Santa Barbara oil spill of Jan. 1969 (from Platform A, only about 4 miles away) did not address the question of the resident platform fauna. In early 1975 the Southern California Coastal Water Research Project received a grant from the Institute of Marine Resources of the U. of California to update the past work and investigate more thoroughly the effects of these platforms on marine ecology. The Institute of Marine Resources was in turn supported by API. JPT P. 1280^

Protection Requirements of One-Million-Volt (1-Mv.) and Two-Million-Volt (2-Mv.) Roentgen-Ray Installations

The protection against radiation produced at one million volts and higher has been determined in the past mainly from attenuation data obtained under conditions differing considerably from those found in practice. Most absorption curves have been based on measurements made with narrow beams, while protective barriers generally are exposed to broad cones of radiation. It has been shown previously (1) that the attenuation is less with broad beams because part of the scattered radiation is retained within the confines of the primary beam. It is important, therefore, that the protection requirements be based upon measurements made under conditions actually met in practice. In many instances the lack of dependable data has resulted in inadequate protection against the primary beam and in an excessively high factor of safety for the barriers exposed to scattered rays only. The purpose of this paper is to report the results of our radiation surveys of nine one-million-volt (1-Mv.) and one two-million-volt (2-Mv....

Sanitation of Recreational Areas

areas in California are as full of interest for the historian, geologist, or lover of the outdoors as the mountain range which extends across the central portion of Los Angeles County. Recently formed by the vertical uplift of a huge block of once gently sloping plain, it is still undergoing the rapid change of appearance that we associate with the period of infancy. Its steep boulder-strewn canyons terminating in broad alluvial cones, and its barren rocky slopes all bespeak a mountain range not only of striking beauty but one of sudden terrible floods and tremendous erosion possibilities. This area was too large and inaccessible to be carried along with the wave of development which swept over the valley area to the south where early mission life has long since given way to the bustle of cities. In the mountain area may be found the unchanged homes of settlers of the time before the Gold Rush, occupied by people who still practice and preserve the charm of life of an earlier day. When an area such as this is situated immediately adjacent to a huge metropolitan district made up largely of pleasure-loving outdoor people, it is only natural that it should be widely used for recreational purposes, especially when good roads make all parts of it easily reachable in a short time. The picture presented by the mountain area today, therefore, is one of contrast. The early bona fide settlers of the mountain region are still there but have been so far out numbered as to be almost obscured by the thousands of people who weekly use the mountains as a playground. Some of these people occupy the 6,000 private cabins in this area, others patronize the many commercial resorts and children's summer camps, but the largest proportion of this huge crowd of pleasure seekers, numbering several