Scaling laws for stagnant-lid convection with a buoyant crust

2021 ◽  
Vol 228 (1) ◽  
pp. 631-663
Author(s):  
Kyle Batra ◽  
Bradford Foley
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Thermal Evolution ◽  
Crustal Thickness ◽  
Plate Motion ◽  
Crustal Layer ◽  
Lithospheric Thickness ◽  
Thin Crust ◽  
Mantle Temperature ◽  
Thick Crust

SUMMARY Stagnant-lid convection, where subduction and surface plate motion is absent, is common among the rocky planets and moons in our solar system, and likely among rocky exoplanets as well. How stagnant-lid planets thermally evolve is an important issue, dictating not just their interior evolution but also the evolution of their atmospheres via volcanic degassing. On stagnant-lid planets, the crust is not recycled by subduction and can potentially grow thick enough to significantly impact convection beneath the stagnant lid. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a buoyant crustal layer. We systematically vary the crustal layer thickness, crustal layer density, Rayleigh number and Frank–Kamenetskii parameter for viscosity to map out system behaviour and determine the new scaling laws. We find two end-member regimes of behaviour: a ‘thin crust limit’, where convection is largely unaffected by the presence of the crust, and the thickness of the lithosphere is approximately the same as it would be if the crust were absent; and a ‘thick crust limit’, where the crustal thickness itself determines the lithospheric thickness and heat flux. Scaling laws for both limits are developed and fit the numerical model results well. Applying these scaling laws to rocky stagnant-lid planets, we find that the crustal thickness needed for convection to enter the thick crust limit decreases with increasing mantle temperature and decreasing mantle reference viscosity. Moreover, if crustal thickness is limited by the formation of dense eclogite, and foundering of this dense lower crust, then smaller planets are more likely to enter the thick crust limit because their crusts can grow thicker before reaching the pressure where eclogite forms. When convection is in the thick crust limit, mantle heat flux is suppressed. As a result, mantle temperatures can be elevated by 100 s of degrees K for up to a few Gyr in comparison to a planet with a thin crust. Whether convection enters the thick crust limit during a planet’s thermal evolution also depends on the initial mantle temperature, so a thick, buoyant crust additionally acts to preserve the influence of initial conditions on stagnant-lid planets for far longer than previous thermal evolution models, which ignore the effects of a thick crust, have found.

Towards constraining Mars' thermal evolution using machine learning

2021 ◽  
Author(s):  
Siddhant Agarwal ◽  
Nicola Tosi ◽  
Pan Kessel ◽  
Sebastiano Padovan ◽  
Doris Breuer ◽  
...  
Keyword(s):  
Activation Energy ◽  
Enrichment Factor ◽  
Activation Volume ◽  
Initial Conditions ◽  
Thermal Evolution ◽  
Diffusion Creep ◽  
Dynamic Simulations ◽  
Mixture Density ◽  
Lithospheric Thickness ◽  
Mantle Temperature

<p>The thermal evolution of terrestrial planets depends strongly on several parameters and initial conditions that are poorly constrained. Often, direct or indirect observables from planetary missions such as elastic lithospheric thickness, crustal thickness and duration of volcanism are inverted to infer the unknown parameter values and initial conditions. The non-uniqueness and non-linearity of this inversion necessitates a probabilistic inversion framework. However, due to the expensive nature of forward dynamic simulations of thermal convection , Markov Chain Monte Carlo methods are rarely used. To address this shortcoming, some studies have recently shown the effectiveness of Mixture Density Networks (MDN) (Bishop 1995) in being able to approximate the posterior probability using only the dataset of simulations run prior to the inversion (Meier et al. 2007, de Wit et al. 2013, Käufl et al. 2016, Atkins et al. 2016).</p><p>Using MDNs, we systematically isolate the degree to which a parameter can be constrained using different “present-day” synthetic observables from 6130 simulations for a Mars-like planet. The dataset – generated using the mantle convection code GAIA (Hüttig et al. 2013)- is the same as that used by Agarwal et al. (2020) for a surrogate modelling study.</p><p>The loss function used to optimize the MDN (log-likelihood) provides a single robust quantity that can be used to measure how well a parameter can be constrained. We test different numbers and combinations of observables (heat flux at the surface and core-mantle boundary, radial contraction, melt produced, elastic lithospheric thickness, and duration of volcanism) to constrain the following parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. If all observables are available, reference viscosity can be constrained to within 32% of its entire range (10<sup>19</sup>−10<sup>22</sup> Pa s), crustal enrichment factor (1−50) to within 15%, activation energy (10<sup>5</sup>−5×10<sup>5</sup> J mol-1 ) to within 80%, and initial mantle temperature (1600−1800K) to within 39%. The additional availability of the full present-day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4×10<sup>-6</sup> −10×10<sup>-6</sup>  m<sup>3</sup> mol<sup>-1</sup>) cannot be constrained and requires research into new observables in space and time, as well as fields other than just temperature. Testing different levels of uncertainty (simulated using Gaussian noise) in the observables, we found that constraints on different parameters loosen at different rates, with initial temperature being the most sensitive. Finally, we present how the marginal MDN proposed by Bishop (1995) can be modified to model the joint probability for all parameters, so that  the inter-parameter correlations and the associated degeneracy can be capture, thereby providing a more comprehensive picture of all the evolution scenarios that fit given observational constraints.</p>

scholarly journals Regional crustal and lithospheric thickness model for Alaska, the Chukchi shelf, and the inner and outer bering shelves

2019 ◽  
Vol 220 (1) ◽  
pp. 522-540
Author(s):  
Montserrat Torne ◽  
Ivone Jiménez–Munt ◽  
Jaume Vergés ◽  
Manel Fernàndez ◽  
Alberto Carballo ◽  
...  
Keyword(s):  
Sedimentary Basins ◽  
Crustal Thickness ◽  
Pacific Plate ◽  
Plate Motion ◽  
The South ◽  
Brooks Range ◽  
Potential Field Data ◽  
Denali Fault ◽  
Lithospheric Thickness ◽  
Chukchi Shelf

SUMMARY This study presents for the first time an integrated image of the crust and lithospheric mantle of Alaska and its adjacent western shelves of the Chukchi and Bering seas based on joint modelling of potential field data constrained by thermal analysis and seismic data. We also perform 3-D forward modelling and inversion of Bouguer anomalies to analyse density heterogeneities at the crustal level. The obtained crustal model shows northwest-directed long wavelength thickening (32–36 km), with additional localized trends of thicker crust in the Brooks Range (40 km) and in the Alaska and St Elias ranges (50 km). Offshore, 28–30-km-thick crust is predicted near the Bearing slope break and 36–38 km in the northern Chukchi Shelf. In interior Alaska, the crustal thickness changes abruptly across the Denali fault, from 34–36 to the north to above 30 km to the south. This sharp crustal thickness gradient agrees with the presence of a crustal tectonic buttress guiding block motion west and south towards the subduction zone. The average crustal density is 2810 kg m−3. The denser crust, up to 2910 kg m−3, is found south of the Denali Fault likely related to the oceanic nature of the Wrangellia Composite Terrane rocks. Offshore, less dense crust (<2800 kg m−3) is found along the sedimentary basins of the Chukchi and Beaufort shelves. At LAB levels, there is a regional SE–NW trend that coincides with the current Pacific Plate motion, with a lithospheric root underneath the Brooks Range, Northern Slope, and Chuckchi Sea, that may correspond to a relic of the Chukotka-Artic Alaska microplate. The obtained lithospheric root (above 180 km) agrees with the presence of a boundary of cold, strong lithosphere that deflects the strain towards the South. South of the Denali Fault the LAB topography is quite complex. East of 150°W, below Wrangellia and the eastern side of Chugach terranes, the LAB is much shallower than it is west of this meridian. The NW trending limit separating thinner lithosphere in the east and thicker in the west agrees with the two-tiered slab shape of the subducting Pacific Plate.

Siphon Flows in Stratified Coronal Loops

1994 ◽  
Vol 144 ◽  
pp. 185-187
Author(s):  
S. Orlando ◽  
G. Peres ◽  
S. Serio
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Flow Model ◽  
Supersonic Flows ◽  
Coronal Loops ◽  
Characteristic Parameters

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

scholarly journals Planetary Magnetic Fields and Habitability in Super Earths

2018 ◽  
Vol 27 (1) ◽  
pp. 183-231 ◽  
Author(s):  
Pablo Cuartas-Restrepo
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Scaling Laws ◽  
Thermal Evolution ◽  
Solid Core ◽  
Direct Influence ◽  
Physical Processes ◽  
Planetary Magnetic Fields ◽  
Planetary Magnetic Field ◽  
Planetary Dynamos

Abstract This work seeks to summarize some special aspects of a type of exoplanets known as super-Earths (SE), and the direct influence of these aspects in their habitability. Physical processes like the internal thermal evolution and the generation of a protective Planetary Magnetic Field (PMF) are directly related with habitability. Other aspects such as rotation and the formation of a solid core are fundamental when analyzing the possibilities that a SE would have to be habitable. This work analyzes the fundamental theoretical aspects on which the models of thermal evolution and the scaling laws of the planetary dynamos are based. These theoretical aspects allow to develop models of the magnetic evolution of the planets and the role played by the PMF in the protection of the atmosphere and the habitability of the planet.

An earthquake-explosion reversed refraction line in the Peninsular Ranges of southern California and Baja California Norte

1982 ◽  
Vol 72 (4) ◽  
pp. 1195-1206
Author(s):  
F. Alejandro Nava ◽  
James N. Brune
Keyword(s):  
Sierra Nevada ◽  
High Velocity ◽  
Southern California ◽  
Baja California ◽  
Crustal Thickness ◽  
Arrival Times ◽  
Narrow Zone ◽  
Peninsular Ranges ◽  
Thick Crust

abstract An approximate reversed refraction profile has been obtained for the center of the Peninsular Ranges of southern California and Baja California Norte using arrival times from Corona blasts to obtain the NW-SE profile, and arrival times from the well-located Pino Solo earthquake of 17 July 1975 to obtain the reversing SE-NW profile. The results indicate a relatively high-velocity crust, with P velocities of 6.57 to 6.95 km/sec, similar to the high velocities found by Hadley and Kanamori (1979). A crustal thickness of about 40 km was found for the axis of the Peninsular Ranges, significantly greater than was found by Hadley and Kanamori (1979) for the average crustal thickness of the northern part of the province. This suggests that the thick crust may be confined to a relatively narrow zone along the axis of the province. The crustal thickness found here is approximately 10 km less than found for the deeper crust of the Sierra Nevada (Bateman and Eaton, 1967; Pakiser and Brune, 1980).

scholarly journals Parameterisations of interior properties of rocky planets

2020 ◽  
Vol 638 ◽  
pp. A129 ◽  
Author(s):  
Lena Noack ◽  
Marine Lasbleis
Keyword(s):  
Thermodynamic Properties ◽  
Scaling Laws ◽  
Thermal State ◽  
Thermal Evolution ◽  
Pure Water ◽  
Mass Composition ◽  
Temperature Profiles ◽  
Interior Structure ◽  
Water Ice ◽  
Simple Mass

Context. Observations of Earth-sized exoplanets are mostly limited to information on their masses and radii. Simple mass-radius relationships have been developed for scaled-up versions of Earth or other planetary bodies such as Mercury and Ganymede, as well as for one-material spheres made of pure water(-ice), silicates, or iron. However, they do not allow a thorough investigation of composition influences and thermal state on a planet’s interior structure and properties. Aims. In this work, we investigate the structure of a rocky planet shortly after formation and at later stages of thermal evolution assuming the planet is differentiated into a metal core and a rocky mantle (consisting of Earth-like minerals, but with a variable iron content). Methods. We derived possible initial temperature profiles after the accretion and magma ocean solidification. We then developed parameterisations for the thermodynamic properties inside the core depending on planet mass, composition, and thermal state. Results. We provide the community with robust scaling laws for the interior structure, temperature profiles, and core- and mantle-averaged thermodynamic properties for planets composed of Earth’s main minerals but with variable compositions of iron and silicates. Conclusions. The scaling laws make it possible to investigate variations in thermodynamic properties for different interior thermal states in a multitude of applications such as deriving mass-radius scaling laws or estimating magnetic field evolution and core crystallisation for rocky exoplanets.

Mixed Convection in Air in an Open Ended Cavity With a Moving Plate Parallel to the Cavity Open Surface

2005 ◽  
Author(s):  
Assunta Andreozzi ◽  
Nicola Bianco ◽  
Vincenzo Naso ◽  
Oronzio Manca
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Mixed Convection ◽  
Plate Motion ◽  
Uniform Heat Flux ◽  
Geometrical Parameters ◽  
Heated Plate ◽  
Open Surface ◽  
Moving Plate ◽  
Plate Temperature

In this study, a numerical investigation of mixed convection in air in an open ended cavity, with a moving plate parallel to the cavity open surface, is carried out. The moving plate has a constant velocity, whereas a vertical plate of the open cavity is heated at uniform heat flux. All the other walls are adiabatic. The numerical analysis is obtained by means of the commercial code FLUENT. Two configurations, assisting and opposing, are analyzed. In the assisting configuration, natural convection is supported by the plate motion, whereas, in the opposing configuration, natural convection and plate motion have opposing effects. The effect of different geometrical parameters, heat flux and moving plate velocity are analyzed. Results in terms of heated plate and moving plate temperature profiles are presented and simple monomial correlation equations for both the configurations are proposed between the terms Nu/Re0.6 and Ri.

scholarly journals Scaling laws and flow structures of double diffusive convection in the finger regime

2016 ◽  
Vol 802 ◽  
pp. 667-689 ◽  
Author(s):  
Yantao Yang ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Density Ratio ◽  
Copper Ion ◽  
Double Diffusive Convection ◽  
Parallel Plates ◽  
Diffusive Convection ◽  
Prandtl Numbers ◽  
Salinity Difference ◽  
Double Diffusive

Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates. The Prandtl numbers, i.e. the ratios between the viscosity and the molecular diffusivities of scalars, are similar to the values of seawater. The DDC flow is driven by an unstable salinity difference (here across the two plates) and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: the non-dimensional salinity flux $\mathit{Nu}_{S}$ mainly depends on the salinity Rayleigh number $\mathit{Ra}_{S}$, which measures the strength of the salinity difference and exhibits a very weak dependence on the density ratio $\unicode[STIX]{x1D6EC}$, which is the ratio of the buoyancy forces induced by two scalar differences. The non-dimensional flow velocity $Re$ and the non-dimensional heat flux $\mathit{Nu}_{T}$ are dependent on both $\mathit{Ra}_{S}$ and $\unicode[STIX]{x1D6EC}$. However, the rescaled Reynolds number $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ and the rescaled convective heat flux $(\mathit{Nu}_{T}-1)\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{T}^{eff}}$ depend only on $\mathit{Ra}_{S}$. The two exponents are dependent on the fluid properties and are determined from the numerical results as $\unicode[STIX]{x1D6FC}_{u}^{eff}=0.25\pm 0.02$ and $\unicode[STIX]{x1D6FC}_{T}^{eff}=0.75\pm 0.03$. Moreover, the behaviours of $\mathit{Nu}_{S}$ and $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ agree with the predictions of the Grossmann–Lohse theory which was originally developed for the Rayleigh–Bénard flow. The non-dimensional salt-finger width and the thickness of the velocity boundary layers, after being rescaled by $\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}/2}$, collapse and obey a similar power-law scaling relation with $\mathit{Ra}_{S}$. When $\mathit{Ra}_{S}$ is large enough, salt fingers do not extend from one plate to the other and horizontal zonal flows emerge in the bulk region. We then show that the current scaling strategy can be successfully applied to the experimental results of a heat–copper–ion system (Hage & Tilgner, Phys. Fluids, vol. 22, 2010, 076603). The fluid has different properties and the exponent $\unicode[STIX]{x1D6FC}_{u}^{eff}$ takes a different value $0.54\pm 0.10$.

scholarly journals THERMAL EVOLUTION OF A RADIATING ANISOTROPIC STAR WITH SHEAR

2006 ◽  
Vol 15 (07) ◽  
pp. 1053-1065 ◽  
Author(s):  
N. F. NAIDU ◽  
M. GOVENDER ◽  
K. S. GOVINDER
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Dissipation ◽  
Thermal Evolution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Pressure Anisotropy ◽  
Radiating Star ◽  
Anisotropic Star

We study the effects of pressure anisotropy and heat dissipation in a spherically symmetric radiating star undergoing gravitational collapse. An exact solution of the Einstein field equations is presented in which the model has a Friedmann-like limit when the heat flux vanishes. The behavior of the temperature profile of the evolving star is investigated within the framework of causal thermodynamics. In particular, we show that there are significant differences between the relaxation time for the heat flux and the relaxation time for the shear stress.

scholarly journals Quasi-static thermal evolution of compact objects

2015 ◽  
Vol 93 (8) ◽  
pp. 920-934
Author(s):  
L. Becerra ◽  
H. Hernández ◽  
L.A. Núñez
Keyword(s):  
Heat Flux ◽  
Thermal Evolution ◽  
Compact Objects ◽  
Temperature Profiles ◽  
Gravitational System ◽  
Static Approximation ◽  
Quasi Static Approximation ◽  
Radiated Energy ◽  
Causal Thermodynamics

We study under what conditions the thermal peeling is present for dissipative local and quasi-local anisotropic spherical matter configurations. Thermal peeling occurs when different signs in the velocity of fluid elements appear, giving rise to the splitting of the matter configuration. The evolution is considered in the quasi-static approximation and the matter contents are radiant, anisotropic (unequal stresses) spherical local, and quasi-local fluids. The heat flux and the associated temperature profiles are described by causal thermodynamics consistent with this approximation. It is found that both types of configurations can exhibit thermal peeling when most of the radiated energy emerges from the first half of the distribution, and thermal peeling appears to be associated with extreme astrophysical scenarios (highly relativistic and very energetic gravitational system).

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