Local Depression Research Articles

VORTEX MACHINING: LOCALIZED SURFACE MODIFICATION USING AN OSCILLATING FIBER PROBE

This paper demonstrates for the first time a method for surface modification of a substrate material based on the generation of localized vortices of abrasive slurry using slender oscillating fibers. In experiments presented in this paper, the abrasive slurry is a water based suspension of 1 µm alumina particles. This is pumped onto, and flows across, the specimen surface. A fiber (typically 7 µm in diameter and between 3.5 to 5 mm long) is immersed into this flowing slurry and oscillated at frequencies around 30–40 kHz to produce a small rotational flow (vortex) that results in the locally accelerated particles. Using such a system, it has been possible, over machining times of 6–24 hours, to produced localized depressions in the surface of a silicon substrate with typical depths of around 60–700 nm and widths of around 10–300 µm. Based on these initial studies the material removal rate is estimated to be approximately 40 nm per hour. Using white light interferometry and stylus profilometry the surface deviations (roughness) of these features have a root mean square variation in the region 1–2 nm, which is comparable to that of the surface remote from the machined feature.

Gravity-Capillary Lumps Generated by a Moving Pressure Source

The nonlinear wave pattern generated by a localized pressure source moving over a liquid free surface at speeds below the minimum phase speed (c{min}) of linear gravity-capillary waves is investigated experimentally and theoretically. At these speeds, freely propagating fully localized solitary waves, or "lumps," are known theoretically to be possible. For pressure-source speeds far below c{min}, the surface response is a local depression similar to the case with no forward speed. As the speed is increased, a critical value is reached c{c} approximately 0.9c{min} where there is an abrupt transition to a wavelike state that features a steady disturbance similar to a steep lump behind the pressure forcing. As the speed approaches c{min}, a second transition is found; the new state is unsteady and is characterized by continuous shedding of lumps from the tips of a V-shaped pattern.

Explaining prehistoric variation in the abundance of large prey: A zooarchaeological analysis of deer and rabbit hunting along the Pecho Coast of Central California

Three main hypotheses are commonly employed to explain diachronic variation in the relative abundance of remains of large terrestrial herbivores: (1) large prey populations decline as a function of anthropogenic overexploitation; (2) large prey tends to increase as a result of increasing social payoffs; and (3) proportions of large terrestrial prey are dependent on stochastic fluctuations in climate. This paper tests predictions derived from these three hypotheses through a zooarchaeological analysis of eleven temporal components from three sites on central California’s Pecho Coast. Specifically, we examine the trade-offs between hunting rabbits ( Sylvilagus spp.) and deer ( Odocoileus hemionus) using models derived from human behavioral ecology. The results show that foragers exploited a robust population of deer throughout most of the Holocene, only doing otherwise during periods associated with climatic trends unfavorable to larger herbivores. The most recent component (Late Prehistoric/Contact era) shows modest evidence of localized resource depression and perhaps greater social benefits from hunting larger prey; we suggest that these final changes resulted from the introduction of bow and arrow technology. Overall, results suggest that along central California’s Pecho Coast, density independent factors described as climatically-mediated prey choice best predict changes in the relative abundance of large terrestrial herbivores through the Holocene.

Nucleation Enhancement Effect in Poly(l-lactide) (PLLA)/Poly(ϵ-caprolactone) (PCL) Blend Induced by Locally Activated Chain Mobility Resulting from Limited Miscibility

The enhancement effect of nucleation in immiscible blend systems has recently attracted interest. Although several authors have reported that the effect occurs at the phase interface, little is known about the mechanism involved. We focused on poly(l-lactide) (PLLA)/poly(ϵ-caprolactone) (PCL) immiscible blend systems in which the presence of PCL enhanced the nucleation of PLLA at low temperature. We investigated the nucleation behavior of PLLA during aging at temperatures below Tg. Generally, neat polymers, including PLLA, seldom generate nuclei below Tg due to restrictions in chain mobility. However, through DSC analysis of the crystallization behavior following an aging process, we revealed that the nucleation of PLLA occurs during aging even at temperatures below Tg in the PLLA/PCL blend. Since the nuclei density became saturated with increasing aging time, the nucleation behavior was regarded as heterogeneous nucleation. The asymptotic density of nuclei depended on the PCL content, indicating that dispersed PCL acted as active sites for nucleation. The nucleation rate R was almost independent of the aging temperature, suggesting that the marked decrease in chain mobility due to the glass transition is locally evaded at the active sites. Nucleation was observed even at temperatures as much as 40 °C lower than Tg following the addition of only 1 wt % PCL, while the Tg obtained by a DSC heating scan showed a subtle decrease. This suggests that the limited miscibility of PLLA/PCL leads to the aggregation of PCL and induces local and deep depression of Tg at the interface of the PCL domains, resulting in marked enhancement of PLLA nucleation.

Tectonic evolution of the Anadyr Basin, northeastern Eurasia, and its petroleum resource potential

The published data on the sedimentation conditions, structure, and tectonic evolution of the Anadyr Basin in the Mesozoic and Cenozoic are reviewed. These data are re-examined in the context of modern tectonic concepts concerning the evolution of the northwestern Circum-Pacific Belt. The re-examination allows us not only to specify the regional geology and tectonic history, but also to forecast of the petroleum resource potential of the sedimentary cover based on a new concept. The sedimentary cover formation in the Anadyr Basin is inseparably linked with the regional tectonic evolution. The considered portion of the Chukchi Peninsula developed in the Late Mesozoic at the junction of the ocean-type South Anyui Basin, the Asian continental margin, and convergent zones of various ages extending along the Asia-Pacific interface. Strike-slip faulting and pulses of extension dominated in the Cenozoic largely in connection with oroclinal bending of structural elements pertaining to northeastern Eurasia and northwestern North America against the background of accretion of terranes along the zone of convergence with the Pacific oceanic plates. Three main stages are recognized in the formation of the sedimentary cover in the Anadyr Basin. (1) The lower portion of the cover was formed in the Late Cretaceous-Early Eocene under conditions of alternating settings of passive and active continental margins. The Cenomanian-lower Eocene transitional sedimentary complex is located largely in the southern Anadyr Basin (Main River and Lagoonal troughs). (2) In the middle Eocene and Oligocene, sedimentation proceeded against the background of extension and rifting in the northern part of the paleobasin and compression in its southern part. The compression was caused by northward migration of the foredeep in front of the accretionary Koryak Orogen. The maximum thickness of the Eocene-Oligocene sedimentary complex is noted mainly in the southern part of the basin and in the Central and East Anadyr troughs. (3) The middle Miocene resumption of sedimentation was largely related to strike-slip faulting and rifting. In the Miocene to Quaternary, sedimentation was the most intense in the central and northern parts of the Anadyr Basin, as well as in local strike-slip fault-line depressions of the Central Trough. Geological and geophysical data corroborate thrusting in the southern Anadyr Basin. The amplitude of thrusting over the Main River Trough reaches a few tens of kilometers. The vertical thickness of the tectonically screened Paleogene and Neogene rocks in the southern Main River Trough exceeds 10 km. The quantitative forecast of hydrocarbon emigration from Cretaceous and Paleogene source rocks testifies to the disbalance between hydrocarbons emigrated and accumulated in traps of petroleum fields discovered in the Anadyr Basin. The southern portion of the Anadyr Basin is the most promising for the discovery of new petroleum fields in the Upper Cretaceous, Eocene, and Upper Oligocene-Miocene porous and fracture-porous reservoir rocks in subthrust structural and lithological traps.

Early stage cavitation erosion within ceramics—An experimental investigation

Six ceramic material types were considered within an experimental investigation to identify the erosion damage mechanisms resulting from cavitation exposure. These materials were a Y-TZP-type zirconia, different commercially available silicon nitrides, a high-purity alumina and a hardened high-nitrogen stainless steel as reference. An ultrasonic transducer was utilised to produce cavitation conditions and the configuration was “static specimen method” using a 5-mm diameter probe, 20-kHz and 50-μm amplitude. The exposure times were periods from 15 s to 3 h. Experimental methods employed to characterise wear mechanisms were light microscopy, scanning light interferometry and scanning electron microscopy. It was found that the zirconia and silicon nitrides demonstrated evidence of local pseudo-plastic deformation or depression prior to more pronounced erosion damage by fracture. Zirconia showed evidence of delayed surface changes when the sample is at rest stored in air, possibly by spontaneous phase transformation after the completion of the erosion tests. Alumina showed evidence of brittle surface fracture and negligible or no pseudo-plastic deformation. All wear mechanisms are discussed, and the materials are ranked in terms of cavitation resistance performance.

Cyber-knife radiosurgery for spine and spinal cord tumors treatment

Radiosurgery is a new direction in treatment of different diseases, mainly oncology. After Gamma-knife clinical introduction the search of possibilities for radiosurgical interventions, performing in extracranial areas, including spine and spinal cord, has began. Basic principles of Cyber-knife-radiosurgery in treatment of spine and spinal cord tumors are described. Also an analysis of literature data was made, where results of 971 patients with spinal tumors using Cyber-knife were described.Taking into consideration novelty of this method (FDA permitted to use Cyber-knife in clinic only in 2001) sufficient follow-up information is absent, but first results are hopeful. Decrease of pain intensity was marked at 84–96% of patients with spinal tumors, local depression of tumor growth — at 75–100% (depending on tumor histological type).Complications and failures of Cyber-knife radiosurgery are conditioned by continuing tumor growth, neurological and common postradiation disorders.This review shows that Cyber-knife-radiosurgery is a perspective method for spinal and spinal cord tumors treatment.

Reflection of the Voronezh crystalline massif in the seismic noises of neotectonic structures

In this paper, we describe the results of investigation of the correlation between the seismic noise parameters and the geological structure combined with geodynamic conditions of neotectonic structure formation. This investigation is based on data on the characteristics of seismic noise at 102 points located in the central and eastern parts of the VCM over an area exceeding 75 000 km 2 . The massif, which is part of the East European Platform, is a differentiated block-dome elevation of the Precambrian basement covered with a sedimentary layer from 50 to 600 m thick. The study region is located in the conjunction zone between the two largest neotectonic elements: the Middle Russia Rise and Oka‐Don Depression [3]. Elements of the second and higher orders were distinguished within these structures (Fig. 1). In the genetic relation they can be related to the structures of the stamp type, which are formed in the sedimentary cover owing to free-bulk motions of the basement [4]. The boundaries of stamp structures related to the fracture zones in the crystalline basement are presented in the sedimentary cover by the regions of dynamic influence of these fractures. In the NeogeneQuaternary structural material complex within the investigated territory, these regions are presented by flat flexures, linear troughs that are frequently complicated by local depressions and elevations. Superfracture structural parageneses of the study region formed at the boundaries between modern stamp structures are related to large and wide fracture zones in the Precambrian basement, which appeared in different stages of the basement formation and were subjected to multiple activations. The zones important in neotectonics are related to the Saltykovskii and Krivoborskii linear flexures, which are oriented in the submeridional direction, and separate the Middle Russia Rise from the Oka‐Don Depression. While characterizing the modern structure of the territory, it is worth noting the following peculiarities:

TEST BENCH AND METHODOLOGY FOR STERNAL CLOSURE SYSTEM TESTING

A custom test bench was developed for comparative testing of sternal closure devices over a single setup, which allows the installation of the closure device and subsequent testing under lateral in-plane distraction forces. The bench is capable of generating a range of testing modes, which comprise static (characterization of the closure device) and dynamic (simulation of deep breathing and coughing fits) testing without additional manipulations of the closed sternum. This method permits the acquisition of the compression force applied to the sternum midline and the measurement of its evolution throughout the different testing stages. In the framework of the present study, an artificial sternum model made of polyurethane is used. If in-depth comparative testing has to be completed, the testing bench can easily be adapted to the testing of biological models. For each testing mode, experimental data with the commonly used seven-wire sternum closure system configuration are provided and statistically treated (see Table 2). The gradual decrease in sternum midline compressive forces is explained by the observed local depression at the wire—sternum interface.

Application of the remnant in repairing the reconstructed ear in microtia

To explore the application of the remnant in repairing the reconstructed ear in microtia. From October 2000 to July 2006, 1,823 patients with reconstructed ear underwent the second operation for repairing. The remnants were used to reconstruct tragus, antitragus, crus of helix, concha cavum, or relax the adhesion between the reconstructed auricle and cranio wall, or insert into the reconstructed lobule or under the basement of the costal cartilage frame to restore the cranio-auricular angle or to the preauricular subcutaneous to correct the facial local depression. In 1,823 cases, the tragus, antitragus and concha cavum was reconstructeded by remnant auricle in 1,180 cases; helix crus was repaired by remnant auricle in 743 cases; the wound was repaired by remnant auricle flap resulted from relaxing the adhesion between the reconstructed auricle and cranial wall in 68 cases; Subcutaneous and cartilage flap was formed and transferred in 95 cases, and among them the flap was transferred under the basement of the frame to restore the cranio-auricular angle in 77 cases and was transferred to the preauricular subcutaneous to correct the facial local depression in 18 cases; the skin flap was formed by remnant auricle to repair the lobule in 37 cases. All flaps survived completely. The appearance of reconstructed ear was satisfied. The remnant is very useful in repairing the reconstructed ear in microtia. It should be preserved propriately in auricular reconstruction.

Quantitative estimation of vegetation changes by comparing two vegetation maps

The main goal of our work was to estimate how large the errors are associated with repeated vegetation mapping. We compared two vegetation maps (both 1:10 000) of the Pieniny National Park—ca 2300 ha (southern Poland), the first made in 1966 and the second in 2001. We superimposed—using the ARC-INFO software—a dense grid of points (50 × 50 m) upon each map, and we determined the identity of vegetation unit in each point for the year 1966 and for the year 2001. That procedure was repeated 100 times, each time changing the position of the grid by a random vector. To estimate the size of mapping errors, we compared the patches of communities which should not change their location during 35 years: vegetation of rocky outcrops and local wet depressions, and fertile beech forest, considered a climax community for the Pieniny Mountains. Overlapping small vegetation patches (average patch size below 0.5 ha) yielded highly erroneous results, while the reliability of overlapping the communities with large patches is much higher, exceeding 80% for average patch size of 5 ha. Taking into consideration the communities of average patch size of 1 ha, we can estimate that the vegetation has undergone profound changes: some communities expanded, while others shrunk. The area of meadows remained about the same, but majority of meadows in 2001 was located in former arable fields and previous meadow areas become forested. Among beech forests, we recorded an increase of area covered by floristically rich variants at the expense of floristically poor variants. We conclude that some information about vegetation changes may be obtained only by comparing sequential vegetation maps, but the reliability of the results strongly depends on the size of vegetation patches.

The flora of the former Łęczyca iron ore dumps

The flora of the former Łęczyca iron ore dumps Iron ore mines of the Łęczyca region started operating in the sixties and seventies of the 20th century and brought about considerable changes in the agricultural landscape of the town of Łęczyca and its vicinity. As a result of the ore exploitation, rock dumps as well as local depressions were created there. The subject of the present research was flora occurring in areas transformed by iron ore mining in the Łęczyca region. The flora is of spontaneous and anthropogenic (as a result of planting - reclamation) character. The results of the conducted research indicate that areas transformed by mining significantly increase their biological diversity.

A comparison of existing surficial hydrological data layers in a low-relief forested Ontario landscape with those derived from a LiDAR DEM

The current provincial-extent digital elevation model (DEM) and corresponding hydrological maps for Ontario have been produced using traditional photogrammetry and aerial photograph interpretation. This process is labour-intensive and requires visual interpretation of stereo image pairs. The ground surface and small hydrological features may be inaccurately delineated in areas where vegetation is dense or the ground is otherwise shielded from aerial view. In an effort to improve and automate delineation of hydrological features, we examined the behaviour and final products of the D8 flowrouting algorithm in 2 software environments (TAS and TauDEM for ArcGIS) operating on a high spatial resolution DEM derived using canopy-penetrating light detection and ranging (LiDAR) technology in a pilot study in the Romeo Malette Forest (41.25°N, 81.50°W). Filtered LiDAR data points (5-m spacing) were interpolated using IDW, TIN, and splines, each resulting in a 2.5-m spatial resolution DEM. Results demonstrate improved realism in the characterization of surficial hydrology by LIDAR derived products as compared to applying identical algorithms on existing coarser provincial data. Benefits include the ability to represent streams of lower Strahler order to define crisp watershed boundaries, and the more accurate identification of local depressions that form potentially wet sites. This approach identifies wet sites that should be avoided during forest operations (e.g., skidder traffic) and can provide additional information for trail layout, road planning, and water crossings. By increasing the number of uses of LiDAR, the capital investment in these data becomes increasingly palatable for forest companies interested in obtaining detailed plans of their forest holdings. Key words: LiDAR, DEM, OBM, spatial resolution, interpolation, Strahler stream order, flow routing, topographic wetness

Fossil Association from the Lower Cambrian Yanjiahe Formation in the Yangtze Gorges Area, Hubei, South China

Abstract: Apart from previously reported Small Shelly Fossils (SSFs), a macroscopic fossil assemblage, comprising abundant algae, cone‐shaped tubular fossil forms, and probable impressions of a megascopic metazoan, comes from the Lower Cambrian Yanjiahe Formation in the Yangtze Gorges area of western Hubei Province, south China. The visible fossils are preserved in thinlaminated siltstone or muddy siltstone intercalated between 8–15 mm‐thick carbonate deposits, probably representing sedimentary settings of a constrained local depression in the shallow water carbonate platform during the Early Cambrian Meishucunian Stage. The macroscopic fossil association provides significant fossil evidence about the evolution of life from the late Precambrian to the ‘Cambrian explosion’ interval.

Automated algorithm for mapping regions of cold‐air pooling in complex terrain

In complex terrain, air in contact with the ground becomes cooled from radiative energy loss on a calm clear night and, being denser than the free atmosphere at the same elevation, sinks to valley bottoms. Cold‐air pooling (CAP) occurs where this cooled air collects on the landscape. This article focuses on identifying locations on a landscape subject to considerably lower minimum temperatures than the regional average during conditions of clear skies and weak synoptic‐scale winds, providing a simple automated method to map locations where cold air is likely to pool. Digital elevation models of regions of complex terrain were used to derive surfaces of local slope, curvature, and percentile elevation relative to surrounding terrain. Each pixel was classified as prone to CAP, not prone to CAP, or exhibiting no signal, based on the criterion that CAP occurs in regions with flat slopes in local depressions or valleys (negative curvature and low percentile). Along‐valley changes in the topographic amplification factor (TAF) were then calculated to determine whether the cold air in the valley was likely to drain or pool. Results were checked against distributed temperature measurements in Loch Vale, Rocky Mountain National Park, Colorado; in the Eastern Pyrenees, France; and in Yosemite National Park, Sierra Nevada, California. Using CAP classification to interpolate temperatures across complex terrain resulted in improvements in root‐mean‐square errors compared to more basic interpolation techniques at most sites within the three areas examined, with average error reductions of up to 3°C at individual sites and about 1°C averaged over all sites in the study areas.

Post‐partum depression in Kinshasa, Democratic Republic of Congo: Validation of a concept using a mixed‐methods cross‐cultural approach

To determine if a post-partum depression syndrome exists among mothers in Kinshasa, Democratic Republic of Congo, by adapting and validating standard screening instruments. Using qualitative interviewing techniques, we interviewed a convenience sample of 80 women living in a large peri-urban community to better understand local conceptions of mental illness. We used this information to adapt two standard depression screeners, the Edinburgh Post-partum Depression Scale and the Hopkins Symptom Checklist. In a subsequent quantitative study, we identified another 133 women with and without the local depression syndrome and used this information to validate the adapted screening instruments. Based on the qualitative data, we found a local syndrome that closely approximates the Western model of major depressive disorder. The women we interviewed, representative of the local populace, considered this an important syndrome among new mothers because it negatively affects women and their young children. Women (n = 41) identified as suffering from this syndrome had statistically significantly higher depression severity scores on both adapted screeners than women identified as not having this syndrome (n = 20; P < 0.0001). When it is unclear or unknown if Western models of psychopathology are appropriate for use in the local context, these models must be validated to ensure cross-cultural applicability. Using a mixed-methods approach we found a local syndrome similar to depression and validated instruments to screen for this disorder. As the importance of compromised mental health in developing world populations becomes recognized, the methods described in this report will be useful more widely.

Opioid Receptors on Bulbospinal Respiratory Neurons Are Not Activated During Neuronal Depression by Clinically Relevant Opioid Concentrations

Opioids depress the activity of brain stem respiratory-related neurons, but it is not resolved whether the mechanism at clinical concentrations consists of direct neuronal effects or network effects. We performed extracellular recordings of discharge activity of single respiratory neurons in the caudal ventral respiratory group of decerebrate dogs, which were premotor neurons with a likelihood of 90%. We used multibarrel glass microelectrodes, which allowed concomitant highly localized picoejection of opioid receptor agonists or antagonists onto the neuron. Picoejection of the mu receptor agonist [d-Ala(2), N-Me-phe(4), gly-ol(5)]-enkephalin (DAMGO, 1 mM) decreased the peak discharge frequency (mean +/- SD) of expiratory neurons to 68 +/- 22% (n = 12), the delta(1) agonist d-Pen(2,5)-enkephalin (DPDPE, 1 mM) to 95 +/- 11% (n = 15), and delta(2) receptor agonist [d-Ala(2)] deltorphin-II to 86 +/- 17% (1 mM, n = 15). The corresponding values for inspiratory neurons were: 64 +/- 12% (n = 11), 48 +/- 30% (n = 12), and 75 +/- 15% (n = 11), respectively. Naloxone fully reversed these effects. Picoejection of morphine (0.01-1 mM) depressed most neurons in a concentration dependent fashion to maximally 63% (n = 27). Picoejection of remifentanil (240-480 nM) did not cause any significant depression of inspiratory (n = 11) or expiratory neurons (n = 9). 4. Intravenous remifentanil (0.2-0.6 microg.kg(-1).min(-1)) decreased neuronal peak discharge frequency to 60 +/- 12% (inspiratory, n = 7) and 58 +/- 11% (expiratory, n = 11). However, local picoejection of naloxone did not reverse the neuronal depression. Our data suggest that mu, delta(1), and delta(2) receptors are present on canine respiratory premotor neurons. Clinical concentrations of morphine and remifentanil caused no local depression. This lack of effect and the inability of local naloxone to reverse the neuronal depression by intravenous remifentanil suggest that clinical concentrations of opioids produce their depressive effects on mechanisms upstream from respiratory bulbospinal premotor neurons.

Historical water management in the river basin of the Baaksche Beek and the adaptations to the water system as a result of change in land use

In the 19th and the first part of the 20th century large parts of the sandy area of The Netherlands were transformed from heath and woodland into agricultural areas. These areas were made suitable for agricultural use by significantly adapting the existing water systems (improving existing brooks, digging new watercourses, etc.). Adaptations will once again be needed, as climate change will increase both precipitation and the peak flow flood waves in the Dutch large rivers. New, pre-emptive adaptations of the current waters system are needed to maintain good agricultural and living conditions, and to prevent catastrophes. Study of the reaction of the water system as a result of previous adaptations is directly relevant to current planning, since such study should reveal the likely long-term outcomes of future adaptations necessitated by climate change. To select an area for this study, preliminary information was gathered about hydrological properties and hydrological data, such as surface water levels and discharges in various parts of the country; data sources included historical maps, reports on hydrological measurements and historical descriptions. From these data, a drainage basin in the relatively high and sandy part of The Netherlands – the Baaksche Beek basin in the eastern part of The Netherlands – was selected. The period chosen for investigation was 1850–2000. In 1850 the basin was in a fairly natural state, with large areas of woods and moorland. Sufficient data were available in the following period till 2000. It was found that great changes took place in the water system following reclamation. Before reclamation, the water management used the capacity of the river basin to store great amounts of water temporarily in local depressions and along the river basin, reducing peak flows in the river. Since reclamation of the heath and woodland, many of these natural depressions in the landscape have been connected with a water course, decreasing their ability to store water. This reduced the basin’s ability to act as a hydrological sponge by storing flood water temporarily on the soil surface in depressions and releasing it slowly later on. Thus, while in the past, smaller water courses inundated the adjacent areas annually, such inundations are very rare nowadays, occurring about once every 100 years. Instead, peak flow flood waves on the river have increased. Recovering the hydrological sponge property can be used as a strategy against increased peak flow flood waves brought by climate change. Thus a partial convalescence of the historical situation, restoring the hydrological sponge function, would aid in counteracting the negative effects of climate change on the water system. However some adaptations, like flattening of the soil surface, are irreversible and so additional means to reach the same end need to be considered. These could include re-meandering and re-dimensioning rivers, which would also increase the possibility to store water in or along a river, or removing watercourses to increase the possibility to store water in the soil and on the soil surface.

Core‐mantle boundary topography estimated from numerical simulations of instantaneous mantle flow

Core‐mantle boundary (CMB) topography is estimated from numerical simulations of instantaneous mantle flow in a three‐dimensional spherical shell geometry. Density anomaly models of the Earth's mantle are derived from geodynamic models constrained principally by seismic tomography results. To account for the small (±∼1.5 km) CMB topographic relief inferred from recent seismological results, lateral viscosity variations in the mantle, compositionally dense piles in the deep mantle, and a low‐viscosity D″ layer are all required for the numerical models. Low‐viscosity subducting slabs in the lower mantle serve to reduce the topographic amplitude below high‐velocity regions (i.e., the circum‐Pacific belt). The existence of dense piles may cause the local topographic depressions even below low‐velocity regions (i.e., the South Pacific and Atlantic Africa regions).

Influence of Upstream Conditions and Gravity on Highly Inertial Thin-Film Flow

Steady two-dimensional thin-film flow of a Newtonian fluid is examined in this theoretical study. The influence of exit conditions and gravity is examined in detail. The considered flow is of moderately high inertia. The flow is dictated by the thin-film equations of boundary layer type, which are solved by expanding the flow field in orthonormal modes in the transverse direction and using Galerkin projection method, combined with integration along the flow direction. Three types of exit conditions are investigated, namely, parabolic, semiparabolic, and uniform flow. It is found that the type of exit conditions has a significant effect on the development of the free surface and flow field near the exit. While for the parabolic velocity profile at the exit, the free surface exhibits a local depression, for semiparabolic and uniform velocity profiles, the height of the film increases monotonically with streamwise position. In order to examine the influence of gravity, the flow is studied down a vertical wall as well as over a horizontal wall. The role of gravity is different for the two types of wall orientation. It is found that for the horizontal wall, a hydraulic-jump-like structure is formed and the flow further downstream exhibits a shock. The influence of exit conditions on shock formation is examined in detail.