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Tim R Orr - One of the best experts on this subject based on the ideXlab platform.
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a sinuous tumulus over an active Lava Tube at klauea volcano evolution analogs and hazard forecasts
Journal of Volcanology and Geothermal Research, 2015Co-Authors: Tim R Orr, Jacob E Bleacher, Matthew R Patrick, Kelly M WootenAbstract:Abstract Inflation of narrow Tube-fed basaltic Lava flows (tens of meters across), such as those confined by topography, can be focused predominantly along the roof of a Lava Tube. This can lead to the development of an unusually long tumulus, its shape matching the sinuosity of the underlying Lava Tube. Such a situation occurred during Kīlauea Volcano's (Hawai'i, USA) ongoing East Rift Zone eruption on a Lava Tube active from July through November 2010. Short-lived breakouts from the Tube buried the flanks of the sinuous, ridge-like tumulus, while the tumulus crest, its surface composed of Lava formed very early in the flow's emplacement history, remained poised above the surrounding younger flows. At least several of these breakouts resulted in irrecoverable uplift of the Tube roof. Confined sections of the prehistoric Carrizozo and McCartys flows (New Mexico, USA) display similar sinuous, ridge-like features with comparable surface age relationships. We contend that these distinct features formed in a fashion equivalent to that of the sinuous tumulus that formed at Kīlauea in 2010. Moreover, these sinuous tumuli may be analogs for some sinuous ridges evident in orbital images of the Tharsis volcanic province on Mars. The short-lived breakouts from the sinuous tumulus at Kīlauea were caused by surges in discharge through the Lava Tube, in response to cycles of deflation and inflation (DI events) at Kīlauea's summit. The correlation between DI events and subsequent breakouts aided in Lava flow forecasting. Breakouts from the sinuous tumulus advanced repeatedly toward the sparsely populated Kalapana Gardens subdivision, destroying two homes and threatening others. Hazard assessments, including flow occurrence and advance forecasts, were relayed regularly to the Hawai'i County Civil Defense to aid their Lava flow hazard mitigation efforts while this Lava Tube was active.
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Lava Tube shatter rings and their correlation with Lava flux increases at kīlauea volcano hawai i
Bulletin of Volcanology, 2011Co-Authors: Tim R OrrAbstract:Shatter rings are circular to elliptical volcanic features, typically tens of meters in diameter, which form over active Lava Tubes. They are typified by an upraised rim of blocky rubble and a central depression. Prior to this study, shatter rings had not been observed forming, and, thus, were interpreted in many ways. This paper describes the process of formation for shatter rings observed at Kīlauea Volcano during November 2005–July 2006. During this period, tilt data, time-lapse images, and field observations showed that episodic tilt changes at the nearby Pu‘u ‘Ō‘ō cone, the shallow magmatic source reservoir, were directly related to fluctuations in the level of Lava in the active Lava Tube, with periods of deflation at Pu‘u ‘Ō‘ō correlating with increases in the level of the Lava stream surface. Increases in Lava level are interpreted as increases in Lava flux, and were coincident with Lava breakouts from shatter rings constructed over the Lava Tube. The repetitive behavior of the Lava flux changes, inferred from the nearly continuous tilt oscillations, suggests that shatter rings form from the repeated rise and fall of a portion of a Lava Tube roof. The locations of shatter rings along the active Lava Tube suggest that they form where there is an abrupt decrease in flow velocity through the Tube, e.g., large increase in Tube width, abrupt decrease in Tube slope, and (or) sudden change in Tube direction. To conserve volume, this necessitates an abrupt increase in Lava stream depth and causes over-pressurization of the Tube. More than a hundred shatter rings have been identified on volcanoes on Hawai‘i and Maui, and dozens have been reported from basaltic Lava fields in Iceland, Australia, Italy, Samoa, and the mainland United States. A quick study of other basaltic Lava fields worldwide, using freely available satellite imagery, suggests that they might be even more common than previously thought. If so, this confirms that episodic fluctuation in Lava effusion rate is a relatively common process at basaltic volcanoes, and that the presence of shatter rings in prehistoric Lava flow fields can be used as evidence that such fluctuations have occurred.
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Lava Tube shatter rings and their correlation with Lava flux increases at Kīlauea Volcano, Hawai‘i
Bulletin of Volcanology, 2010Co-Authors: Tim R OrrAbstract:Shatter rings are circular to elliptical volcanic features, typically tens of meters in diameter, which form over active Lava Tubes. They are typified by an upraised rim of blocky rubble and a central depression. Prior to this study, shatter rings had not been observed forming, and, thus, were interpreted in many ways. This paper describes the process of formation for shatter rings observed at Kīlauea Volcano during November 2005–July 2006. During this period, tilt data, time-lapse images, and field observations showed that episodic tilt changes at the nearby Pu‘u ‘Ō‘ō cone, the shallow magmatic source reservoir, were directly related to fluctuations in the level of Lava in the active Lava Tube, with periods of deflation at Pu‘u ‘Ō‘ō correlating with increases in the level of the Lava stream surface. Increases in Lava level are interpreted as increases in Lava flux, and were coincident with Lava breakouts from shatter rings constructed over the Lava Tube. The repetitive behavior of the Lava flux changes, inferred from the nearly continuous tilt oscillations, suggests that shatter rings form from the repeated rise and fall of a portion of a Lava Tube roof. The locations of shatter rings along the active Lava Tube suggest that they form where there is an abrupt decrease in flow velocity through the Tube, e.g., large increase in Tube width, abrupt decrease in Tube slope, and (or) sudden change in Tube direction. To conserve volume, this necessitates an abrupt increase in Lava stream depth and causes over-pressurization of the Tube. More than a hundred shatter rings have been identified on volcanoes on Hawai‘i and Maui, and dozens have been reported from basaltic Lava fields in Iceland, Australia, Italy, Samoa, and the mainland United States. A quick study of other basaltic Lava fields worldwide, using freely available satellite imagery, suggests that they might be even more common than previously thought. If so, this confirms that episodic fluctuation in Lava effusion rate is a relatively common process at basaltic volcanoes, and that the presence of shatter rings in prehistoric Lava flow fields can be used as evidence that such fluctuations have occurred.
Michele Dragoni - One of the best experts on this subject based on the ideXlab platform.
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Thermal anomaly at the Earth's surface associated with a Lava Tube
Journal of Volcanology and Geothermal Research, 2016Co-Authors: Antonello Piombo, Andrea Tallarico, Marco Di Bari, Michele DragoniAbstract:Lava Tubes are frequently encountered in volcanic areas. The formation of Lava Tubes has strong implications on the volcanic hazard during effusive eruptions. The thermal dissipation of Lava flowing in a Tube is reduced in respect to the Lava flowing in an open channel so the Lava may threaten areas that would not be reached by flows in open channels: for this reason it is important to detect the presence of Lava Tubes.\ud In this work we propose a model to detect the presence and the characteristics of Lava Tubes by their thermal footprint at the surface. We model numerically the temperature distribution and the heat flow, both in the steady and the transient state, and we take into account the principal thermal effects due to the presence of an active Lava Tube, i.e. the conduction to the ground and the atmosphere, the convection and the radiation in the atmosphere. We assume that Lava fluid is at high temperature, in motion inside a sloping Tube under the gravity force.\ud The thermal profile across the Tube direction, in particular the width of the temperature curve, allows to evaluate the depth of the Tube. The values of maximum temperature and of Tube depth allow to estimate the area of the Tube section. The shape of the temperature curve and its asymmetry can give information about the geometry of the Tube.\ud If we observe volcanic areas at different times by thermal cameras, we can detect anomalies and evaluate their causes during an eruption; in particular, we can evaluate whether they are due to active Lava flows or not and what is their state. For Lava Tubes, we can connect thermal anomalies with Lava Tube position, characteristics and state
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Effects of the curvature of a Lava channel on flow dynamics and crust formation
Geophysical Journal International, 2011Co-Authors: Antonella Valerio, Andrea Tallarico, Michele DragoniAbstract:SUMMARY Bends in Lava channels are often observed in volcanic fields. The curvature of a channel affects flow dynamics and surface morphology and may be a trigger for the formation of Lava Tube. We propose a model to describe the effects of curvature on velocity, shear stress and the formation of crust at the flow surface. Lava is described as a Newtonian, homogeneous, isotropic and incompressible fluid. The steady-state solution of the Navier-Stokes equation is found for a unidirectional flow, in cylindrical coordinates. The flow levees are described as arcs of concentric circumferences, with their centres in the origin of the coordinate system. Under the assumption that the gravity force has no radial component, in the bend the fluid moves parallel to the levees. The velocity is assumed to depend on the radial coordinate only. As an effect of curvature, velocity and shear stress are asymmetric with respect to the centre of the channel. The maximum of surface velocity is shifted toward the internal levee, and the shear stress has larger values close to the internal levee. This effect is greater for wider channels.Heatradiationandconvectionintotheatmosphereareconsideredasthemaincooling mechanisms and the temperature distribution along the channel is calculated. Crust formation at the flow surface is considered under the assumption that solid Lava is a plastic body. The amount of crust coverage is mainly controlled by the channel width: narrow channels have a greater coverage than wide channels for a given radius of curvature. The effect of a bend is to favour the crust growth toward the internal levee, while the crust coverage toward the external levee decreases. The presence of a bend in a Lava channel may favour the formation of a Lava Tube. The analytical solution will serve as a benchmark for numerical models. Understanding the mechanism of formation of Lava Tubes is crucial to the simulation of actual Lava flows and to evaluation of the associated hazard.
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channelled flow of Lava with temperature dependent pseudoplastic rheology condition for Tube formation
EGU General Assembly Conference Abstracts, 2010Co-Authors: Marilena Filippucci, Andrea Tallarico, Michele DragoniAbstract:The surface crust formation seems to depend on several factors as the flow rate, the ground slope, the surface cooling rate, and the rheology of the flowing fluid; the transition to a Lava Tube also depends on thermal, dynamical and rheological properties of the flow and on topography (Dragoni et al., 1995; Cashman et al., 2005). Valerio et al. (2008) investigated the condition of crust and Tube formation assuming Lava with newtonian rheology. We are interested now in understanding which variations can arise from changing the assumption on rheology and considering a pseudoplastic rheology with temperature dependence.
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thermoelastic deformation associated with a Lava Tube
Bulletin of Volcanology, 2009Co-Authors: Michele Dragoni, Antonello PiomboAbstract:Active Lava Tubes have much higher temperatures than the surrounding rocks. Any change in the Tube temperature produces a change in the temperature distribution in the rocks and induces a thermoelastic deformation in them. We calculate such a deformation by solving the equilibrium equation of linear thermoelasticity. We assume that the initial temperature distribution in the medium is the steady-state solution of the heat equation for a very long cylindrical Tube at constant temperature, embedded in a medium with uniform thermal conductivity. We calculate the displacement and stress fields in the medium following to a temperature change of the Tube. A temperature increase produces a dilatation of the medium and a contraction of the Tube, while a temperature decrease produces the opposite effect. For a temperature change equal to 100 K, thermal stresses in the order of 10 MPa are produced, which are large enough to fracture the rocks surrounding the Tube.
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temperature field and heat flow around an elliptical Lava Tube
Journal of Volcanology and Geothermal Research, 2008Co-Authors: Michele Dragoni, Andrea TallaricoAbstract:We study the temperature distribution around a cylindrical Lava Tube with an elliptical cross section. The steady-state heat equation is solved by assuming an unbounded medium and a uniform temperature of the Tube wall. An analytical solution for the temperature field is obtained by the conformal mapping technique. It is found that the isothermal lines on the planes perpendicular to the Tube are confocal ellipses. The heat flow in the medium surrounding the Tube has hyperbolic field lines, while the curves on which the magnitude of heat flow is constant are Cassini ovals. At the Tube wall, the heat flow density is proportional to the cubic root of the curvature of the wall. A solution is also obtained for a Tube embedded in a half-space, when the size of the Tube is small with respect to its depth. Formulae are given relating the heat flow at the surface of the half-space to the eccentricity and to the orientation of the major axis of the Tube cross section, as well as to the temperature and the depth of the Tube. For eccentricity equal to zero, all the formulae are reduced to those for a circular Tube.
K. S. Woo - One of the best experts on this subject based on the ideXlab platform.
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Geological Heritage Values of the Yongcheon Cave (Lava Tube Cave), Jeju Island, Korea
Geoheritage, 2019Co-Authors: K. S. Woo, L. Kim, Yongmun Jeon, Chun Gil Ryu, Hyoseon Ji, C. WoodAbstract:Yongcheon Cave is a typical Lava Tube cave, which formed by multiple flows of Lava during the Late Quaternary. However, it is also a lime-decorated cave with numerous splendid carbonate speleothems along two parts of the passage. This paper deals with these special unique features of the cave together with their formation processes and the geoheritage significance based on detailed investigation of overlying carbonate sand dunes and speleothems. The cave is about 3360 m long, composed of 2590-m-long main passage and about 370-m-long branch passages. Because the cave contains unexplored passages at the downstream end, it is estimated that the total length can be at least about 400 m longer. The cave contains various microtopographic characteristics such as multiple and various forms of Lava coatings on the surface as well as dented features by thermal erosion. They include pahoehoe and aa Lavas, rockfalls, Lava falls, Lava benches, gutters with overflowed Lava levees, Tube-in-Tubes, and Lava benches on the floor. Lava flowlines are prominent on the wall, and also, anastomosing branches, Lava bridges, and multiple leveled floors are other distinctive morphological features. Carbonate sand dunes were formed by transportation of beach sands nearby and partially overlie two parts of the cave passage. Carbonate sediments are medium sand-sized and are mostly composed of mollusk and coralline red algae fragments up to 60~70% with a minor contribution of benthic foraminifers, echinoderms, bryozoans, and volcanic rock fragments, which may well represent typical temperate carbonate constituents elsewhere. Beach sediments, the source of carbonate dune sands, also show the similar texture and composition. This suggests that the dune sands were transported onto the area by wind along the valleys. Previous age dating results of four carbonate sand dunes including several paleosol layers imply the formation ages of the dunes at each site since the deposition of carbonate sands in shallow seas between 4700 and 6000 years BP due to full deglaciation after Last Glacial Maximum. Carbonate speleothems began to grow in the cave after the deposition of dunes. Detailed mapping of the cave and dune fields strongly suggest that the dune distributions are directly related to the formation of carbonate speleothems. A variety of carbonate speleothems are found in Yongcheon Cave such as soda straws, stalactites, stalagmites, columns, rimstones, flowstones, cave corals, draperies (curtains and bacon sheets), cave pearls, shelfstones, and moonmilks. However, many carbonate speleothems show erratic morphologies that cannot be seen in any limestone caves elsewhere. It is because the formation of erratic speleothems is directly influenced by distribution of plant roots which helped to transport rainwater into the cave and to precipitate calcite mineral. Their unique abundance of carbonate speleothems providing splendid scenic values as well as Jeju’s special geological conditions for their formation is considered to be the outstanding universal value for the World Heritage site.
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reconstruction of the northeast asian monsoon climate history for the past 400 years based on textural carbon and oxygen isotope record of a stalagmite from yongcheon Lava Tube cave jeju island korea
Quaternary International, 2015Co-Authors: K. S. Woo, Hai Cheng, Lawrence R Edwards, Gi Hoon HongAbstract:Abstract Paleoclimatic changes over the past 400 years were investigated based on textural and geochemical characteristics of the YC-2 stalagmite which grew in Yongcheon Cave (Lava Tube cave) on Jeju Island, Korea. The stalagmite is about 68 mm long and annual growth laminae are distinctively identified. The age of the stalagmite was mainly determined by counting annual growth laminae supplemented by other radiometric dating methods, and it is estimated that the stalagmite grew at least for ca . 242 years including the hiatus. This hiatus is located at about 15 mm from the base and is present in the form of one thick brown growth lamina which was formed when the stalagmite stopped to grow. Texturally, the stalagmite can be divided into two phases: Fluid inclusion-poor, compact columnar calcite (Phase A) and fluid inclusion-rich, sparse columnar calcite (Phase B). This textural division is intimately related to the spacing of growth laminae, that is, Phase A is characterized by narrower spacing of growth laminae. Phase A with narrow-spaced growth laminae indicates the slower growth rate due to lower amount of rainfall when Northeast Asian summer monsoon intensity was relatively lower. Based on high resolution carbon isotope trend, the stalagmite can be divided into three stages (Stages I, II and III). The relatively more positive carbon isotopic compositions of the Stage I (δ 13 C = −3.3–0.4‰, PDB) in the lower part indicate that it grew during the Little Ice Age (LIA) under cold and dry climate with less vegetation. The Stage II is a transitional period from cold and dry to warm and wet climate with a continuous decrease in carbon isotope values (from 0.6 to −9.6‰ in δ 13 C). This stage shows the gradual weakening of the LIA climate. Carbon isotope trend also suggests that the LIA interval was terminated near middle 1870's around Korean peninsula. Relatively low carbon isotopic compositions during Stage III (δ 13 C = −11.0 ∼ −8.0‰) in the upper part should indicate that climate was changed to the warm and wet Current Warm Period. Warming since 1960 can also be recognized. Complete coincidence between textural data (internal calcite texture and growth laminae spacing) and high resolution carbon isotope compositions strongly suggests that past climate changes such as monsoonal variations in Northeast Asia have been clearly recorded in the stalagmite in Yongcheon Cave.
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the origin of erratic calcite speleothems in the dangcheomul cave Lava Tube cave jeju island korea
Quaternary International, 2008Co-Authors: K. S. Woo, Jeong Chan Kim, Don Won Choi, Jin Kyung Kim, Ryeon Kim, Odette NehzaAbstract:Abstract Dangcheomul Cave in Jeju Island, Korea, is a Lava Tube about 110 m long. The cave is located only a few meters below the surface under alkali basalt, and contains numerous and various calcite speleothems such as soda straws, stalactites, stalagmites, columns, cave corals, curtains, flowstones, rimstones, carbonate powders, and shelfstones. Carbonate sand dunes overlying the Lava Tube are responsible for the formation of calcite speleothems. The sand dunes were formed from the carbonate sediments transported from adjacent shallow seas and beaches, and are composed of mollusks, echinoderms, coralline algae, benthic foraminifers, bryozoans, etc. Oxygen isotopic compositions of some speleothems and cave water indicate that the spelothems have grown mostly by evaporation of cave water. Also, carbon isotopic compositions suggest that the majority of carbon was derived from overlying carbonates with a minor contribution of organic carbon from the overlying soil. Most speleothems in Dangcheomul Cave do not show typical morphology as can be commonly seen in limestone caves. These erratic forms imply a different mode of speleothem formation. High density of soda straws, stalactites, and columns as well as erratic morphology may also provide the evidence that the plant roots are responsible for their growth.
Odette Nehza - One of the best experts on this subject based on the ideXlab platform.
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the origin of erratic calcite speleothems in the dangcheomul cave Lava Tube cave jeju island korea
Quaternary International, 2008Co-Authors: K. S. Woo, Jeong Chan Kim, Don Won Choi, Jin Kyung Kim, Ryeon Kim, Odette NehzaAbstract:Abstract Dangcheomul Cave in Jeju Island, Korea, is a Lava Tube about 110 m long. The cave is located only a few meters below the surface under alkali basalt, and contains numerous and various calcite speleothems such as soda straws, stalactites, stalagmites, columns, cave corals, curtains, flowstones, rimstones, carbonate powders, and shelfstones. Carbonate sand dunes overlying the Lava Tube are responsible for the formation of calcite speleothems. The sand dunes were formed from the carbonate sediments transported from adjacent shallow seas and beaches, and are composed of mollusks, echinoderms, coralline algae, benthic foraminifers, bryozoans, etc. Oxygen isotopic compositions of some speleothems and cave water indicate that the spelothems have grown mostly by evaporation of cave water. Also, carbon isotopic compositions suggest that the majority of carbon was derived from overlying carbonates with a minor contribution of organic carbon from the overlying soil. Most speleothems in Dangcheomul Cave do not show typical morphology as can be commonly seen in limestone caves. These erratic forms imply a different mode of speleothem formation. High density of soda straws, stalactites, and columns as well as erratic morphology may also provide the evidence that the plant roots are responsible for their growth.
Andrea Tallarico - One of the best experts on this subject based on the ideXlab platform.
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Thermal anomaly at the Earth's surface associated with a Lava Tube
Journal of Volcanology and Geothermal Research, 2016Co-Authors: Antonello Piombo, Andrea Tallarico, Marco Di Bari, Michele DragoniAbstract:Lava Tubes are frequently encountered in volcanic areas. The formation of Lava Tubes has strong implications on the volcanic hazard during effusive eruptions. The thermal dissipation of Lava flowing in a Tube is reduced in respect to the Lava flowing in an open channel so the Lava may threaten areas that would not be reached by flows in open channels: for this reason it is important to detect the presence of Lava Tubes.\ud In this work we propose a model to detect the presence and the characteristics of Lava Tubes by their thermal footprint at the surface. We model numerically the temperature distribution and the heat flow, both in the steady and the transient state, and we take into account the principal thermal effects due to the presence of an active Lava Tube, i.e. the conduction to the ground and the atmosphere, the convection and the radiation in the atmosphere. We assume that Lava fluid is at high temperature, in motion inside a sloping Tube under the gravity force.\ud The thermal profile across the Tube direction, in particular the width of the temperature curve, allows to evaluate the depth of the Tube. The values of maximum temperature and of Tube depth allow to estimate the area of the Tube section. The shape of the temperature curve and its asymmetry can give information about the geometry of the Tube.\ud If we observe volcanic areas at different times by thermal cameras, we can detect anomalies and evaluate their causes during an eruption; in particular, we can evaluate whether they are due to active Lava flows or not and what is their state. For Lava Tubes, we can connect thermal anomalies with Lava Tube position, characteristics and state
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Effects of the curvature of a Lava channel on flow dynamics and crust formation
Geophysical Journal International, 2011Co-Authors: Antonella Valerio, Andrea Tallarico, Michele DragoniAbstract:SUMMARY Bends in Lava channels are often observed in volcanic fields. The curvature of a channel affects flow dynamics and surface morphology and may be a trigger for the formation of Lava Tube. We propose a model to describe the effects of curvature on velocity, shear stress and the formation of crust at the flow surface. Lava is described as a Newtonian, homogeneous, isotropic and incompressible fluid. The steady-state solution of the Navier-Stokes equation is found for a unidirectional flow, in cylindrical coordinates. The flow levees are described as arcs of concentric circumferences, with their centres in the origin of the coordinate system. Under the assumption that the gravity force has no radial component, in the bend the fluid moves parallel to the levees. The velocity is assumed to depend on the radial coordinate only. As an effect of curvature, velocity and shear stress are asymmetric with respect to the centre of the channel. The maximum of surface velocity is shifted toward the internal levee, and the shear stress has larger values close to the internal levee. This effect is greater for wider channels.Heatradiationandconvectionintotheatmosphereareconsideredasthemaincooling mechanisms and the temperature distribution along the channel is calculated. Crust formation at the flow surface is considered under the assumption that solid Lava is a plastic body. The amount of crust coverage is mainly controlled by the channel width: narrow channels have a greater coverage than wide channels for a given radius of curvature. The effect of a bend is to favour the crust growth toward the internal levee, while the crust coverage toward the external levee decreases. The presence of a bend in a Lava channel may favour the formation of a Lava Tube. The analytical solution will serve as a benchmark for numerical models. Understanding the mechanism of formation of Lava Tubes is crucial to the simulation of actual Lava flows and to evaluation of the associated hazard.
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channelled flow of Lava with temperature dependent pseudoplastic rheology condition for Tube formation
EGU General Assembly Conference Abstracts, 2010Co-Authors: Marilena Filippucci, Andrea Tallarico, Michele DragoniAbstract:The surface crust formation seems to depend on several factors as the flow rate, the ground slope, the surface cooling rate, and the rheology of the flowing fluid; the transition to a Lava Tube also depends on thermal, dynamical and rheological properties of the flow and on topography (Dragoni et al., 1995; Cashman et al., 2005). Valerio et al. (2008) investigated the condition of crust and Tube formation assuming Lava with newtonian rheology. We are interested now in understanding which variations can arise from changing the assumption on rheology and considering a pseudoplastic rheology with temperature dependence.
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temperature field and heat flow around an elliptical Lava Tube
Journal of Volcanology and Geothermal Research, 2008Co-Authors: Michele Dragoni, Andrea TallaricoAbstract:We study the temperature distribution around a cylindrical Lava Tube with an elliptical cross section. The steady-state heat equation is solved by assuming an unbounded medium and a uniform temperature of the Tube wall. An analytical solution for the temperature field is obtained by the conformal mapping technique. It is found that the isothermal lines on the planes perpendicular to the Tube are confocal ellipses. The heat flow in the medium surrounding the Tube has hyperbolic field lines, while the curves on which the magnitude of heat flow is constant are Cassini ovals. At the Tube wall, the heat flow density is proportional to the cubic root of the curvature of the wall. A solution is also obtained for a Tube embedded in a half-space, when the size of the Tube is small with respect to its depth. Formulae are given relating the heat flow at the surface of the half-space to the eccentricity and to the orientation of the major axis of the Tube cross section, as well as to the temperature and the depth of the Tube. For eccentricity equal to zero, all the formulae are reduced to those for a circular Tube.
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Temperature field and heat flow around an elliptical Lava Tube
Journal of Volcanology and Geothermal Research, 2008Co-Authors: Michele Dragoni, Andrea TallaricoAbstract:We study the temperature distribution around a cylindrical Lava Tube with an elliptical cross section. The steady-state heat equation is solved by assuming an unbounded medium and a uniform temperature of the Tube wall. An analytical solution for the temperature field is obtained by the conformal mapping technique. It is found that the isothermal lines on the planes perpendicular to the Tube are confocal ellipses. The heat flow in the medium surrounding the Tube has hyperbolic field lines, while the curves on which the magnitude of heat flow is constant are Cassini ovals. At the Tube wall, the heat flow density is proportional to the cubic root of the curvature of the wall. A solution is also obtained for a Tube embedded in a half-space, when the size of the Tube is small with respect to its depth. Formulae are given relating the heat flow at the surface of the half-space to the eccentricity and to the orientation of the major axis of the Tube cross section, as well as to the temperature and the depth of the Tube. For eccentricity equal to zero, all the formulae are reduced to those for a circular Tube. (C) 2007 Elsevier B.V. All rights reserved