Crest Shape Research Articles

Design of Labyrinth Spillways

The capacity of a labyrinth spillway is a function of the total head, the effective crest length, and the crest coefficient. The crest coefficient depends on the total head, weir height, thickness, crest shape, apex configuration, and the angle of the side legs. Data and a procedure are presented for designing labyrinth weirs for angles between 6° and 35°, and for a range of heads. The design procedure allows the angle of the side legs and the number of cycles to be varied until the desired layout and capacity are achieved. The solution is presented in a spreadsheet format that automatically calculates the dimensions for the labyrinth. Even though the design procedure is quite accurate, it is recommended that the capacity and performance be verified with a model study. The model can evaluate factors not included in the design procedure, like aeration effects at low heads, unusual flow conditions in the approach channel, and flow conditions in the discharge channel.

First dinosaur bones from Western Australia

A proximal end of a reptilian right humerus from the Late Maastrichtian Miria Formation, Carnarvon Basin, is identified as possibly belonging to a theropod dinosaur, based on the shape of the deltopectoral crest and the slender shaft. A small caudal vertebra from the Middle Jurassic Colalura Sandstone, near Geraldton, may belong to the Dinosauria on the basis of its overall similarity with caudal vertebrae of sauropod dinosaurs. These are the first recorded bones of dinosaurs from Western Australia.

Penetrative convective flows induced by internal heating and mantle compressibility

The effects of internal heating on anelastic, compressible convection have been investigated in a spherical shell, with the ratio of inner to outer radii appropriate to lower mantle convection. The internal heating and the compressibility are characterized by two dimensionless numbers: R, the ratio of two Rayleigh numbers, and D, the dissipation number. Isothermal, stress‐free boundary conditions are applied at the top and at the bottom of the shell. The equations have been solved, with a time‐dependent finite difference code, in a temperature, vorticity, stream function formulation (axisymmetrical configuration) for Rayleigh numbers Rab ranging from the critical Rc up to 2000 Rc. The neutral surface computed over the (D,R) space leads to an unexpected crest shape which is correlated with a shift toward higher‐degree harmonics of the most unstable modes. The phenomenon of penetrative convection is generated, for the weakly nonlinear cases, by the combination of large internal heating rates R and large dissipation numbers D. Small cells appear at the top of the shell, counterrotating with respect to the surrounding global circulation. The onset of time dependence (at Rab = Rtd) and the evolution of bottom topography have been monitored over the (D,R) space by increasing the Rayleigh numbers gradually from the critical. With no internal heating the stabilizing effect of compressibility delays the transition to time dependence. However, the combined effects of internal heating and compressibility drastically reduce the threshold of time dependence to Rtd = 3 Rc, for R = 16, D = 0.6. The study of the topographic deflection of the bottom interface conducted with the same set of (D, R, Rab) values shows that this deflection always decreases with the increase of the Rayleigh number. To reach situations as close as possible to mantle conditions we have focused on D = 0.3 and R = 16 for Rayleigh numbers up to 2000 Rc. In these highly nonlinear regimes, penetrative convection cells are still generated at the top or at the bottom of the shell and evolve by breaking the surrounding chaotic circulations or by pairing with the closest corotating cells. The destruction of these transient cells by viscous dissipation leaves a persisting hot thermal anomaly. The internal heating combined with compressibility reinforces the chaotic character of convection. As a consequence, the bottom topographic deflections display highly time‐dependent behavior, and the thermal anomaly spectra contain energy up to degree 100. Serious assumptions are imposed on the modeling of the Earth's mantle by the mathematical and numerical difficulties of the problem, in particular by the introduction of an isothermal stress‐free upper boundary. In spite of these limitations we propose that penetrative convection, due to the combination of internal heating and compressibility, could be a mechanism able to generate spontaneously layered convection and local melting in the mantle.

Descriptions of anatomical differences between skulls and mandibles ofEquus zebraandE. burchellifrom Southern Africa

The external anatomical differences between the skulls and mandibles of 10 mountain zebras Equus zebra and 10 plains zebras E. burchelli of both sexes were studied. The nomenclature used conforms to Nomina Anatomica Veterinaria (1983). Eleven structural differences are described for the first time and illustrated, viz., outline of the foramen magnum; length of the alar canal; comparative presence of the For. alare parvum; proportions of the mastoid process of the temporal bone; shape and development of the pterygoid crest; notch at the rostral end of the facial crest in E. burchelli; different inclination of the caudal end of the zygomatic arch; shape and length of the retroarticular process; relative size of the supraorbital foramina; presence of incisive canals in E. zebra; difference in the junction of the interalveolar border of the mandible with the alveolar border of the first cheek tooth. If three or more differences are used for identification, it should be possible to train any worker to distinguish between the skulls of these two species.

Continuous Crest Profile for Standard Spillway

As a modification of the currently recommended U.S. Army Corps of Engineers Waterways Experiment Station (W.E.S.) standard spillway crest profile, a crest geometry of which the curvature is continuous is proposed. Such a crest shape is particularly useful to predict the bottom pressure distribution. Moreover, negative pressure peaks might be reduced significantly from those as encountered in the present design.

A sand wave field in the entrance to Bahia Blanca Estuary, Argentina

Sand waves in the mouth of the Bahía Bllanca Estuary show differences in wavelength, crestlength and crest shape characteristics between two sectors of the field. These differences may be explained by assuming that the residual ebboriented currents are stronger in the southern sector. Crest bifurcations on the centerline are suggestive of intermediate energy conditions and the development of secondary flows oblique to the main current direction. The large lee slopes and the presence of megaripple fans are indicative of flow separation, a condition seldom mentioned for subtidal sand waves. Boundaries of the sand wave field may be controlled by the thickness of the surficial sand layer, rapid reduction of the water depth as produced by a large marginal shoal, and variations in grain size. An average migration rate of 33 m yr −1 was calculated from repeated bathymetric surveys. Assuming that sand waves preserve shape and size, the established net sediment flux over the crests is 0.025 cm 3 cm −1 s −1. Current measurements made during four individual tidal cycles yielded a net bedload sediment transport of 0.048 cm 3 cm −1 s −1.

Transverse bedforms on the Amazon shelf

Echo-sounder profiles and side-scan sonograms reveal the presence of asymmetric bedforms on the middle Amazon shelf in water depths of 30–35 m and symmetric bedforms on the outer Amazon shelf at depths of 75–85 m. The asymmetric bedforms have crests parallel to isobaths, wavelengths of 1–40 m, and heights consistently <2 m. The presence of bedforms with a high degree of variability in shape, spacing, and sharpness of crests over distances of only a few kilometers suggests that sediment texture and flow processes are spatially variable. Offshore-facing lee slopes and grain size in the fine sand range (0.08−0.12 mm) suggest bed-material transport of sediment by ebbing tidal currents. Middle-shelf sands and associated bedforms apparently are a reflection of extant shelf dynamical processes. Symmetric bedforms on the outer shelf, characterized by crests perpendicular to isobaths, wavelengths of 100 and 1000 m, and wave heights of 1–5 m, are easily identifiable from distinctive sonogram tonal contrasts that result from changing bottom slope and variable textural character of the sediment mantle. Textural variability may be due to the superimposition of muds on a coarse carbonate substrate. The symmetry, characteristic of both sand waves and sand ridges, is indicative of formation by oscillatory tidal currents in which there is no preferred directionality of motion. Large, coherent outer-shelf features have been interpreted tentatively as ancient reef deposits. Composition of the outer-shelf deposits and character of bedforms present indicate that both are relict, products of a time when sea level was 25–45 m lower than it is today.

A Lagrangian solution for internal waves

A perturbation procedure is used to obtain first- and second-order solutions for small-amplitude internal waves in a Lagrangian coordinate system. The first-order Lagrangian equations are formally accurate to the same order as the first-order Eulerian equations; however, they are different and the Lagrangian solution gives a more realistic wave shape. First-order Lagrangian solutions for internal waves in uniformly stratified fluid have a shape similar to that found in the second-order Eulerian solution. Wave profiles in uniformly stratified fluid exhibit broad crests and narrow troughs near the surface, a sinusoidal shape at mid-depth, and narrow crests and broad troughs near the bottom. The difference between the shape of crests and troughs grows as the wave amplitude is increased. Solutions obtained in a uniformly stratified fluid with a small bottom slope yield plausible shapes for breaking waves.

Distribution of Snow Drifts on Ridge Slopes: Measurements and Theoretical Approximations

During several winters the positions and magnitudes of excess snow deposits or denudation zones caused by wind have been evaluated on the flanks of regular, elongated mountain ridges. The surveys were carried out by conventional measurements of mass balance. According to angle of slope (10 to 35°), shape of crest (hump- or wedge-shaped) and orientation to the wind, various patterns of snow deposition may be found. It is shown that, on ridges oriented perpendicularly to the main wind direction (north-west) during snow storms, near-periodic snow deposits may be expected on the lee slope. On the windward side, there is a denudation zone near the crest. The measurements indicate that lee slopes, of mean slope angle, are buried in mid-winter under twice as much snow as the adjacent windward slopes. However, the ridge system as a whole accumulates the same amounts of snow as do areas of flat terrain. Theoretical approximations based on theories of potential flow and semi-empi rical plume models are used to simulate the presumed dispersion of snow. The model calculations, intended as diagnostic tools, suggest that snow may be diffused and deposited on lee slopes in a plume-like manner similar to other particulate matter. Snowfall, together with low-level blowing snow as an additional source of suspended particles, appears to increase the snow deposits, mainly on the foot of steeper ridges.

Distribution of Snow Drifts on Ridge Slopes: Measurements and Theoretical Approximations

During several winters the positions and magnitudes of excess snow deposits or denudation zones caused by wind have been evaluated on the flanks of regular, elongated mountain ridges. The surveys were carried out by conventional measurements of mass balance. According to angle of slope (10 to 35°), shape of crest (hump- or wedge-shaped) and orientation to the wind, various patterns of snow deposition may be found. It is shown that, on ridges oriented perpendicularly to the main wind direction (north-west) during snow storms, near-periodic snow deposits may be expected on the lee slope. On the windward side, there is a denudation zone near the crest. The measurements indicate that lee slopes, of mean slope angle, are buried in mid-winter under twice as much snow as the adjacent windward slopes. However, the ridge system as a whole accumulates the same amounts of snow as do areas of flat terrain. Theoretical approximations based on theories of potential flow and semi-empi rical plume models are used to simulate the presumed dispersion of snow. The model calculations, intended as diagnostic tools, suggest that snow may be diffused and deposited on lee slopes in a plume-like manner similar to other particulate matter. Snowfall, together with low-level blowing snow as an additional source of suspended particles, appears to increase the snow deposits, mainly on the foot of steeper ridges.

X-ray K-edge absorption spectra of Fe minerals and model compounds: Near-edge structure

Synchrotron radiation has been used to collect high-resolution Fe K absorption near-edge spectra of a suite of Fe minerals and compounds having a range of Fe environments. These spectra, along with those of previous workers, indicate that the number, position, and intensity of near-edge features are characteristic of Fe valence and general site geometry. For example, the crest of the K-edge for Fe2+ in a six-coordinated site in the oxides studied is about 3 eV lower in energy than that for Fe3+ in a similar site. The K-edge crest for Fe3+ in a four-coordinated site is 1 to 2 eV lower than for Fe3+ in a regular site. The shape of the edge crest is sensitive to the details of first-neighbor bonding distances, tending to be broader in species with irregular Fe sites and varying in energy according to the average bond length. Comparison with Ca2+ and Zn2+ spectra from the literature is made and the applicability and utility of edge measurements discussed.

Jaw movement, dental function, and diet in the Paleocene multituberculate Ptilodus

The shape and arrangement of cusps and crests and the orientation of wear striations on the cheek teeth of fossil mammals can be used to reconstruct occlusal patterns. Occlusal patterns have been documented previously in a variety of therian mammals and also in triconodonts and docodonts among nontherians. This is the first detailed analysis of patterns of jaw movement and dental function in a member of the highly specialized nontherian order Multituberculata (Allotheria). Ptilodus, a Paleocene multituberculate, appears to have had two cycles of mastication that followed different paths of movement and utilized different sets of teeth. The first cycle, the slicing-crushing cycle, occurred as the large, laterally-compressed fourth lower premolar (P4) sliced orthally into food items held primarily against the fourth upper premolar (P4). Food items sliced in this manner passed down both the labial and lingual sides of P4, forming subparallel striations in valleys between the nearly vertical enamel ridges. The second cycle is the grinding cycle in which the mandible was retracted while the molars were in tight occlusion, thus producing longitudinal striations on the molars. Unlike the pattern in therians, triconodonts, and docodonts, there is no transversely triangular masticatory orbit in the grinding cycle of multituberculates. The generally accepted idea that the labial aspect of P4 in ptilodontoid multituberculates sheared orthally against the lingual aspect of P4 is not supported. Instead, predominantly horizontal striations developed on the posterolabial wear facet of P4, and on a conjoined facet posterolingually on P4 and anterolingually on the first upper molar (M1), indicate that relative movement between these surfaces was largely palinal (i.e., the jaw moved from front to back), rather than orthal and occurred during the grinding cycle of mastication.In considering the dietary preferences of ptilodontoid multituberculates, it appears that most members were not folivorous. The small size of many species of Ptilodontoidea suggests that they could not have subsisted on a folivorous diet, which is rich in structural carbohydrates. The length of striations on the sides of P4 of Ptilodus, one of the largest of the Ptilodontoidea, indicates that large, hard food items were ingested. The presence of both smooth and highly-striated enamel on homologous dental wear facets in different individuals of Ptilodus mediaevus from a single quarry sample suggests a varied diet. The recent suggestion that ptilodontoids were omnivorous is supported.

The Cytology and Taxonomy of the Genus Pleione D. Don (Orchidaceae)

(P. F. H.) commenced a taxonomic study of the genus Pleione D. Don with especial reference to those species found in cultivation. The preliminary results of this work, including a key for the identification of the species with horticultural notes, has already been published (Roy. Hort. Soc., Dict. Gard., Suppl., 1969) but the purpose of the following contribution is to reduce formally to synonymy many of the concepts hitherto considered distinct. An originally independent survey into the cytology of the cultivated species was begun in 1965 by one of us (C. G. V.) but as the results of the two approaches, cytological and taxonomic, were so inter-related it was agreed to collaborate and publish them in this joint paper. About forty specific epithets have been published in the genus Pledone and considerable confusion exists among the names given to plants in cultivation. Understandable and acceptable differences of taxonomic opinion were confounded with outright mis-identifications. Minor colour variations with, occasionally, very small differences in labellum shape, size and number of crests have been used in the past as differential characters. To complicate the problem further, the species in cultivation were usually represented by a very few clones which often represented only the extremes of variation in colour, etc. Few intermediate plants have been seen by horticultural authors, who, naturally, base their opinions on the living material with which they are familiar.

Storm Wave Characteristics

Abstract Accurate prediction of storm wave characteristics are needed for design of offshore structures. Statistical methods of random noise analysis provide techniques for predicting required wave properties. These techniques have been used to analyze and characterize storm wave profiles from Gulf of Mexico recording installations in 34, 65 and 98 ft of water. Correlations based on the results can be used to predict wave crest probabilities and wave shapes for a range of Gull water depths and storm conditions. Example predictions of wave crest probability as a function of water depth for a particular set of storm conditions are given. Introduction Accurate predictions of wave crests and wave shapes are needed for design of offshore structures. With predictions of wave crests, platform deck elevations giving adequate protection from exposure to storm waves can be selected. Use of hydrodynamic wave theories with the wave crest and wave shape predictions permits an estimate of the wave forces an offshore structure must withstand. Observation of ocean waves suggests use of statistical analysis for studying wave characteristics for water depths beyond the breaking wave zone; recent wave generation theories lend support to this approach. One of the most powerful methods of statistically analyzing wave profiles was introduced by Cartwright and Longuet-Higgins; most of the basic relations used were developed by Rice in studies of random noise theory. This method predicts wave crest elevation probabilities from two parameters characterizing a wave profile. The statistical approach also provides a means for predicting wave shapes. In the random noise model of a wave profile, surface elevation is represented as an infinite sum of sine waves with closely spaced frequencies and random phase angles. Power density is proportional to the sum of the squares of the amplitudes of sine waves having frequencies within a narrow band, and the distribution of power density as a function of frequency is called the power density spectrum, or power spectrum. The power spectrum characterizes an irregular sea, and hence finds use in motion studies of ships, barges and semisubmersible drilling platforms. From the power spectrum, a wave profile of any duration of time can, in principle, be calculated; this long wave profile depicts the many wave shapes to which a structure may be exposed. Thus, the statistical methods of wave analysis provide an approach to selecting wave shapes as well as wave crest elevations needed for design of offshore structures. For practical application of these techniques, power spectra and related quantities must be predicted from storm properties. Barber and Tucker have reviewed correlations of wave properties and storm conditions. Their review summarizes work of Darbyshire, among others, in which a correlation of power spectra with wind intensity of the North Atlantic was developed. These results, plus more recent work by Pierson and Moskowitz and Kitaigorodskii, establish feasibility of correlation, but there is no theoretical basis for modifications extending the relations to other area's as remote as the Gulf of Mexico. Hence, to predict characteristics of Gulf of Mexico waves, a study of local observations is needed. This paper presents - a practical approach to computing wave profiles that depict shapes of waves for use in force calculations, - a summary of relations for predicting probabilities of wave crest elevations, - correlations of parameters needed to apply these methods in the Gulf of Mexico and - examples of application of the techniques. THEORETICAL BACKGROUND The following sections summarize relations needed to calculate wave profiles and to estimate wave crest probabilities.

Ship waves in a stratified ocean

The velocity potential for a simple source moving in a straight line at constant depth in a two-layer ocean is obtained by the Fourier transform method. It is used to develop a formula for the wave-making resistance of a ‘thin’ ship for both surface and internal waves. An asymptotic expansion is used to delineate quantitatively the internal wave system. It is shown that at speeds less than the critical speed transverse and divergent wave systems are excited, while at speeds greater than the critical internal wave speed only the divergent wave system is excited. Examples of the shape of wave crests and of wave heights are given.