Compositional and thermal equilibration of particles, drops and diapirs in geophysical flows

International audienceCore formation, crystal/melt separation, mingling of immiscible magmas, and diapirism are fundamental geological processes that involve differential motions driven by gravity. Diffusion modifies the compo- sition or/and temperature of the considered phases while they travel. Solid particles, liquid drops and viscous diapirs equilibrate while sinking/rising through their surroundings with a time scale that depends on the physics of the flow and the material properties. In particular, the internal circulation within a liquid drop or a diapir favors the diffusive exchange at the interface. To evaluate time scales of chemical/thermal equilibration between a material falling/rising through a deformable medium, we propose analytical laws that can be used at multiple scales. They depend mostly on the non-dimensional Péclet and Reynolds numbers, and are consistent with numerical simulations. We show that equilibration between a particle, drop or diapir and its host needs to be considered in light of the flow structure complexity. It is of fundamental importance to identify the dynamic regime of the flow and take into account the role of the inner circulation within drops and diapirs, as well as inertia that reduces the thickness of boundary layers and enhances exchange through the interface. The scaling laws are applied to predict nickel equilibration between metals and silicates that occurs within 130 m of fall in about 4 minutes during the metal rain stage of the Earth's core formation. For a mafic blob (10 cm diameter) sinking into a felsic melt, trace element equilibration would occur over 4500 m and in about 3 years

Studium rovnováhy mezi klesajícími kapkami železa a roztavenými silikáty v magmatických oceánech

During the Earth's accretion process deep magma oceans were episodically formed. Differentiation of iron took place within the melted zone and small droplets of iron were sinking to the base of the magma ocean due to the density contrast. In the present work we study the process of equilibration between dispersed metal droplets and surrounding silicates that proceeds by the advection transport and diffusion at the rim. We allow for steady state ow of a spherical liquid blob falling in a host liquid and establish the numerical code in axisymmetric spherical coordinates computing the chemical evolution of such heterogeneous system. We focus on determining the time scales of equilibration for which we propose an analytical model based on the boundary layer analysis. The obtained characteristic times are especially for low silicate viscosities very short that supports the idea that the drops attained equilibrium while sinking

Studium rovnováhy mezi klesajícími kapkami železa a roztavenými silikáty v magmatických oceánech

During the Earth's accretion process deep magma oceans were episodically formed. Differentiation of iron took place within the melted zone and small droplets of iron were sinking to the base of the magma ocean due to the density contrast. In the present work we study the process of equilibration between dispersed metal droplets and surrounding silicates that proceeds by the advection transport and diffusion at the rim. We allow for steady state ow of a spherical liquid blob falling in a host liquid and establish the numerical code in axisymmetric spherical coordinates computing the chemical evolution of such heterogeneous system. We focus on determining the time scales of equilibration for which we propose an analytical model based on the boundary layer analysis. The obtained characteristic times are especially for low silicate viscosities very short that supports the idea that the drops attained equilibrium while sinking

Nonlinear rheological models and dynamic processes in the Earth interior

Nu/ev prace: Nelinrarni n-olujMcke niodely: popis dynamickych procesu v xeni- skem nitru Autor: Martina Ulvrova. Katedra (ustav): Katedra geofyziky Vedouei bakalafskc prace: Mgr. Ha.na C'i/kova,. Ur. e-mail vedouciho: hk:(lkarel.1roja.niff.euni.c/ Abslrakt: V pfedlo/,ene praci studujeme uelineanii visko/ni reolojncky popis, ktery je tiYba uva/ovat \ni numi'i'iekem inodelova.ni j)rc)cesu litostericke subdukee. Na.s kompo/,itm' model xaliriiujf tfi tlelbrmacni ineehani'/mv: linearni ncwtonov- ske tcreiii. mocliimiy dislokaeni creep a neliiic'avii] Peieiisovo tectini. Pro nV/ne hlou!)ky a velikowti zrn ukazii)eme, Jake i'eolo^it:ke iiKx-liani/niy so nplatnnji xa. danyeh te])lotnich, tlakovych a uajjelovyeli pudiniiu'k od])ovida jieii-li ru/nym ob~ last.em ])lasle. Dale tento reoloj^icky popis a.plikujemc na model piedpokladanelio ro/lozeni teploty a nap(Hi v snbdukovane desce a diskuUijeme, ja.k se jedinitlive mechani/uiy podileji na defbrmaci desky. Klicova slova: snlxlukce liiosiery; rrolo^ie; dcformarni mapy Title: Nonlinear rheological models: Description of dynamic processes in the Earth 's interior Author: Martina Ulvrova Department: Dejjartment of geophysis Supervisor: M^r. liana Oi/kova, Dr. Supervisor's e-mail address: Abstract: In the present work we study nonlinear viscous rhrolov that should be..

Dynamique des fluides et des transports appliquée à la Terre primitive

We have studied the heat and mass transfer during the early Earth history at multiple scales and for multiple systems by means of numerical computing. Two different systems are approached. Firstly, we focus on the early stages of the Earth core formation when iron segregates from silicates and descends toward the interior of the planet. During the differentiation there are chemical and thermal interactions between dispersed iron blobs and surrounding molten silicates. We study the chemical transport of trace elements within and around the drops. We derive functional relations between critical parameters and show that the system tends to be in chemical equilibrium.During the accretion process of the Earth, extensive melting of its deep interior as well as formation of shallow magma oceans occurred.As heat radiation into space happens with high efficiency, surface molten silicates crystallize very rapidly, in about 10 My. The thermal history of the buried liquid layer, called the basal magma ocean (BMO), proceeds over a long time and it is proposed that its remnants are nowadays observable as partial melts in the core-mantle boundary region.We develop numerical models of the thermal history of the crystallizing basal magma ocean that enable to study coupling between the mantle and the core in the presence of the BMO. We derive parametrized relations for this convective system that undergoes solidification/melting. Obtained scaling equations applied to the BMO indicate that the temperature difference that can be maintained across the top and bottom boundaries of the BMO is minute. Hence, the temperature of the core follows the temperature of liquidus at the bottom of the mantle and thus the rate of the BMO cooling must be the same as that of the Earth's core.Nous avons étudié le transfert de chaleur et de matière au cours de l'histoire de la Terre primitive à de multiples échelles en utilisant des modèles numériques. Deux systèmes différents sont abordés. Tout d’abord, nous nous concentrons sur les premiers stades de la formation du noyau terrestre lorsque le fer se sépare des silicates et descend vers l'intérieur de la planète. Au cours de la différenciation, des interactions chimiques et thermiques se produisent entre les gouttes de fer dispersées dans des silicates fondus formant un océan de magma. Nous étudions le transport chimique des éléments traces à l'intérieur et autour des gouttes. Nous tirons quelques relations fonctionnelles dépendante du régime dynamique d'écoulement et montrons que le système tend à être en équilibre chimique extrêmement rapidement par rapport à l'échelle de temps de la descente de la goutte de fer. Peu de temps après la fin de l'accrétion de la Terre, la fusion extensive de son intérieur profond ainsi que la formation d'un océan de magma en surface a lieu. Comme le rayonnement de la chaleur dans l'espace est très efficace, les silicates fondus superficiels cristallisent très rapidement. L'histoire thermique de la couche liquide enterrée, appelée océan de magma basal (OMB), se déroule sur une longue période de temps et il est proposé que ses restes soient aujourd'hui observables sous forme de poches partiellement fondues au dessus de frontière noyau-manteau. Nous déterminons les paramètres régissant un système convectif dans lequel se produit une transition solide/liquide. Les lois d'échelle ainsi obtenues ont été appliquées à l'OMB et indiquent que la différence de température qui peut être maintenue dans les couches limites supérieure et inférieure de l'OMB est infime. Par conséquent, la température du noyau suit la température de liquidus à la base du manteau et ainsi la vitesse de refroidissement de l'OMB doit être la même que celle du noyau de la Terre

Dynamics of fluids and transport applied to the early Earth

Nous avons étudié le transfert de chaleur et de matière au cours de l'histoire de la Terre primitive à de multiples échelles en utilisant des modèles numériques. Deux systèmes différents sont abordés. Tout d’abord, nous nous concentrons sur les premiers stades de la formation du noyau terrestre lorsque le fer se sépare des silicates et descend vers l'intérieur de la planète. Au cours de la différenciation, des interactions chimiques et thermiques se produisent entre les gouttes de fer dispersées dans des silicates fondus formant un océan de magma. Nous étudions le transport chimique des éléments traces à l'intérieur et autour des gouttes. Nous tirons quelques relations fonctionnelles dépendante du régime dynamique d'écoulement et montrons que le système tend à être en équilibre chimique extrêmement rapidement par rapport à l'échelle de temps de la descente de la goutte de fer. Peu de temps après la fin de l'accrétion de la Terre, la fusion extensive de son intérieur profond ainsi que la formation d'un océan de magma en surface a lieu. Comme le rayonnement de la chaleur dans l'espace est très efficace, les silicates fondus superficiels cristallisent très rapidement. L'histoire thermique de la couche liquide enterrée, appelée océan de magma basal (OMB), se déroule sur une longue période de temps et il est proposé que ses restes soient aujourd'hui observables sous forme de poches partiellement fondues au dessus de frontière noyau-manteau. Nous déterminons les paramètres régissant un système convectif dans lequel se produit une transition solide/liquide. Les lois d'échelle ainsi obtenues ont été appliquées à l'OMB et indiquent que la différence de température qui peut être maintenue dans les couches limites supérieure et inférieure de l'OMB est infime. Par conséquent, la température du noyau suit la température de liquidus à la base du manteau et ainsi la vitesse de refroidissement de l'OMB doit être la même que celle du noyau de la Terre.We have studied the heat and mass transfer during the early Earth history at multiple scales and for multiple systems by means of numerical computing. Two different systems are approached. Firstly, we focus on the early stages of the Earth core formation when iron segregates from silicates and descends toward the interior of the planet. During the differentiation there are chemical and thermal interactions between dispersed iron blobs and surrounding molten silicates. We study the chemical transport of trace elements within and around the drops. We derive functional relations between critical parameters and show that the system tends to be in chemical equilibrium.During the accretion process of the Earth, extensive melting of its deep interior as well as formation of shallow magma oceans occurred.As heat radiation into space happens with high efficiency, surface molten silicates crystallize very rapidly, in about 10 My. The thermal history of the buried liquid layer, called the basal magma ocean (BMO), proceeds over a long time and it is proposed that its remnants are nowadays observable as partial melts in the core-mantle boundary region.We develop numerical models of the thermal history of the crystallizing basal magma ocean that enable to study coupling between the mantle and the core in the presence of the BMO. We derive parametrized relations for this convective system that undergoes solidification/melting. Obtained scaling equations applied to the BMO indicate that the temperature difference that can be maintained across the top and bottom boundaries of the BMO is minute. Hence, the temperature of the core follows the temperature of liquidus at the bottom of the mantle and thus the rate of the BMO cooling must be the same as that of the Earth's core

Tsunamis generated by subaqueous volcanic explosions in Taal Caldera Lake, Philippines

Co-auteur étrangerInternational audienceVolcanic subaqueous explosions can generate hazardous tsunamis, especially in lakes. In this paper, we simulate different scenarios of subaqueous explosions and related tsunamis in Taal Caldera Lake (Luzon, Philippines). Taal volcano is one of the most active volcanoes in Southeast Asia, and eruptive processes are mostly explosive. We test different energies of explosions at eight different explosion sites in the lake. The initial water surface displacement (ƞ0) generated by the explosion is estimated as a function of explosion energy at a given depth. We estimate the tsunami travel times, maximum wave heights, and wave periods at the shoreline. This type of hazard is typically neglected and our work has important implications for hazard assessment around Taal Lake. Due to fast propagation of tsunamis in the lake (waves typically crossing the lake in less than 10 min), there is only a short time available for issuing a warning. For ƞ0 ≤ 50 m, wave heights at the shoreline are less than 2 m with a non-dispersive numerical model, and less than 0.5 m with a dispersive model, whatever the explosion depth and location. Powerful explosions with ƞ0 > > 100 m generate wave heights greater than 2 m all around the lake and local peaks higher than 10 m

Tsunamis generated by subaqueous volcanic explosions in Taal Caldera Lake, Philippines

ISSN:0258-8900ISSN:1432-081

Breakup Without Borders: How Continents Speed Up and Slow Down During Rifting

ISSN:0094-8276ISSN:1944-800

Numerical simulations of tsunami generated by underwater volcanic explosions at Karymskoye Lake (Kamchatka, Russia) and Kolumbo volcano (Aegean Sea, Greece)

International audienceIncreasing human activities along the coasts of the world provoke the necessity to assess tsunami hazard from different sources (earthquakes, landslides, volcanic activity). In this paper, we simulate tsunamis generated by underwater volcanic explosions from (1) a submerged vent in a shallow water lake (Karymskoye Lake, Kamchatka), and (2) from Kolumbo submarine volcano (7 km NE of Santorini, Aegean Sea, Greece). The 1996 tsunami in Karymskoye lake is a well-documented example and thus serves as a case study for validating the calculations. The numerical model reproduces realistically the tsunami run-ups measured onshore. Systematic numerical study of tsunamis generated by explosions of the Kolumbo volcano is then conducted for a wide range of energies. Results show that in case of reawakening, the Kolumbo volcano might represent a significant tsunami hazard for the northern, eastern and southern coasts of Santorini, even for small-power explosions