Dissolution of a sloping solid surface by turbulent compositional convection

2018 ◽  
Vol 846 ◽  
pp. 563-577 ◽  
Author(s):  
Craig D. McConnochie ◽  
Ross C. Kerr
Keyword(s):  
Solid Surface ◽  
Vertical Wall ◽  
Scaling Analysis ◽  
Laboratory Measurements ◽  
Ice Shelf ◽  
Interfacial Composition ◽  
Sloping Surface ◽  
Interfacial Temperature ◽  
Free Parameters ◽  
Compositional Convection

We examine the dissolution of a sloping solid surface driven by turbulent compositional convection. The scaling analysis presented by Kerr & McConnochie (J. Fluid Mech., vol. 765, 2015, pp. 211–228) for the dissolution of a vertical wall is extended to the case of a sloping wall. The model has no free parameters and no dependence on height. It predicts that while the interfacial temperature and interfacial composition are independent of the slope, the dissolution velocity is proportional to $\cos ^{2/3}\unicode[STIX]{x1D703}$, where $\unicode[STIX]{x1D703}$ is the angle of the sloping surface to the vertical. The analysis is tested by comparing it with laboratory measurements of the ablation of a sloping ice wall in contact with salty water. We apply the model to make predictions of the turbulent convective dissolution of a sloping ice shelf in the polar oceans.

Dissolution of a vertical solid surface by turbulent compositional convection

2015 ◽  
Vol 765 ◽  
pp. 211-228 ◽  
Author(s):  
Ross C. Kerr ◽  
Craig D. McConnochie
Keyword(s):  
Mass Transfer ◽  
Theoretical Model ◽  
Solid Surface ◽  
Vertical Wall ◽  
Scaling Analysis ◽  
Field Observations ◽  
Laboratory Measurements ◽  
Salty Water ◽  
Free Parameters ◽  
Compositional Convection

AbstractWe examine the dissolution of a vertical solid surface in the case where the heat and mass transfer is driven by turbulent compositional convection. A theoretical model of the turbulent dissolution of a vertical wall is developed, which builds on the scaling analysis presented by Kerr (J. Fluid Mech., vol. 280, 1994, pp. 287–302) for the turbulent dissolution of a horizontal floor or roof. The model has no free parameters and no dependence on height. The analysis is tested by comparing it with laboratory measurements of the ablation of a vertical ice wall in contact with salty water. The model is found to accurately predict the dissolution velocity for water temperatures up to approximately 5–$6\,^{\circ }\text{C}$, where there is a transition from turbulent dissolution to turbulent melting. We quantify the turbulent convective dissolution of vertical ice bodies in the polar oceans, and compare our results with some field observations.

Estimation and Scaling of the Near-Saturated Hydraulic Conductivity

1999 ◽  
Vol 30 (3) ◽  
pp. 177-190 ◽  
Author(s):  
Per Atle Olsen
Keyword(s):  
Hydraulic Conductivity ◽  
Saturated Hydraulic Conductivity ◽  
Scaling Analysis ◽  
Laboratory Measurements ◽  
Estimation Errors ◽  
Geometric Means ◽  
Top Soil ◽  
Structured Soils ◽  
Order Of Magnitude

The hydraulic conductivity in structured soils is known to increase drastically when approaching saturation. Tension infiltration allows in situ infiltration of water at predetermined matric potentials, thus allowing exploration of the hydraulic properties near saturation. In this study, the near saturated (ψ≥-0.15 m) hydraulic conductivity was estimated both in the top- and sub-soil of three Norwegian soils. A priory analysis of estimation errors due to measurement uncertainties was conducted. In order to facilitate the comparison between soils and depths, scaling analysis was applied. It was found that the increase in hydraulic conductivity with increasing matric potentials (increasing water content) was steeper in the sub-soil than in the top-soil. The estimated field saturated hydraulic conductivity was compared with laboratory measurements of the saturated hydraulic conductivity. The geometric means of the laboratory measurements was in the same order of magnitude as the field estimates. The variability of the field estimates of the hydraulic conductivity from one of the soils was also assessed. The variability of the field estimates was generally smaller than the laboratory measurements of the saturated hydraulic conductivity.

scholarly journals Assessment of ice flow dynamics in the zone close to the calving front of Antarctic ice shelves

2015 ◽  
Vol 61 (230) ◽  
pp. 1194-1206 ◽  
Author(s):  
Martin G. Wearing ◽  
Richard C.A. Hindmarsh ◽  
M. Grae Worster
Keyword(s):  
Flow Speed ◽  
Flow Dynamics ◽  
Rheological Parameters ◽  
Ice Thickness ◽  
Scaling Analysis ◽  
Ice Shelf ◽  
Ice Flow ◽  
Ice Shelves ◽  
The Relationship ◽  
Good Agreement

AbstractWe investigate the relationship between four ice-shelf characteristics in the area close to the calving front: ice flow speed, strain rate, ice thickness and shelf width. Data are compiled for these glaciological parameters at the calving fronts of 22 Antarctic ice shelves. Clarification concerning the viscous supply of ice to the calving front is sought following the empirical calving law of Alley and others (2008), derived from a similar but smaller dataset, and the scaling analysis of Hindmarsh (2012). The dataset is analysed and good agreement is observed between the expected theoretical scaling and geophysical data for the flow of ice near the calving front in the case of ice shelves that are laterally confined and have uniform rheology. The lateral confinement ensures flow is aligned in the along-shelf direction, and uniform rheological parameters mean resistance to flow is provided by near-stationary ice in the grounded margins. In other cases, the velocity is greater than predicted, which we attribute to marginal weakening or the presence of ice tongues.

Melting and dissolving of a vertical solid surface with laminar compositional convection

2011 ◽  
Vol 687 ◽  
pp. 118-140 ◽  
Author(s):  
Andrew J. Wells ◽  
M. Grae Worster
Keyword(s):  
Solid Surface ◽  
Thermal Transport ◽  
Convective Flow ◽  
Ablation Rate ◽  
Solute Concentration ◽  
Asymptotic Solutions ◽  
Two Component ◽  
Compositional Convection

AbstractWe consider laminar compositional convection of buoyant melt released by ablation of a vertical solid surface into a two-component fluid. Asymptotic solutions are used to describe separate cases: the ablation rate is either controlled by thermal transport, corresponding to melting, or by solutal transport, corresponding to dissolution. Melting is faster and generates a stronger flow than dissolving. We determine the temperature and solute concentration conditions leading to either melting or dissolving and find that these conditions do not vary with the strength of the buoyancy that drives convective flow.

Magnetically Damped Convection During Solidification of a Binary Metal Alloy

1993 ◽  
Vol 115 (2) ◽  
pp. 302-310 ◽  
Author(s):  
P. J. Prescott ◽  
F. P. Incropera
Keyword(s):  
Magnetic Field ◽  
Vertical Wall ◽  
Thermosolutal Convection ◽  
Scaling Analysis ◽  
Magnetic Damping ◽  
Transient Transport ◽  
Thermally Driven ◽  
Steady Magnetic Field ◽  
Convection Patterns ◽  
The Magnetic Field

The transient transport of momentum, energy, and species during solidification of a Pb-19 percent Sn alloy is numerically simulated with and without magnetic damping. The system is contained in an axisymmetric, annular mold, which is cooled along its outer vertical wall. Since thermosolutal convection accompanies solidification and is responsible for final macrosegregation patterns, application of a steady magnetic field, which is parallel to the axis of the mold, has the potential to reduce macrosegregation by damping buoyancy-driven flow during solidification. Results show that, during early stages of solidification, the magnetic field significantly affects thermally driven flow in the melt, as well as interactions between thermally and solutally driven flows. However, interdendritic flows and macrosegregation patterns are not significantly altered by moderate magnetic fields. Scaling analysis reveals that extremely strong fields would be required to effectively dampen convection patterns that contribute to macrosegregation.

LABORATORY MEASUREMENTS OF WAVE FORCES ON HEAVILY OVERTOPPED VERTICAL WALL

2007 ◽  
Author(s):  
Steven A. Hughes ◽  
David L. Kriebel ◽  
Harley S. Winer ◽  
Edward R. Blodgett ◽  
William C. Seabergh
Keyword(s):  
Vertical Wall ◽  
Wave Forces ◽  
Laboratory Measurements

Dissolving driven by vigorous compositional convection

1994 ◽  
Vol 280 ◽  
pp. 287-302 ◽  
Author(s):  
Ross C. Kerr
Keyword(s):  
Boundary Layer ◽  
Basaltic Magma ◽  
Critical Rayleigh Number ◽  
Scaling Analysis ◽  
Magma Chambers ◽  
Boundary Layer Instability ◽  
Fluid Concentration ◽  
The One ◽  
Rayleigh Benard ◽  
Compositional Convection

The one-dimensional dissolution that occurs when a binary melt is placed above or below a solid of a different composition is examined both theoretically and experimentally. In the case considered, the dissolution is driven by vigorous compositional convection that results from a Rayleigh-Bénard instability of the compositional boundary layer in the vicinity of the dissolving solid. A scaling analysis is used to derive theoretical expressions for both the dissolving velocity and the interfacial fluid concentration. Laboratory experiments are also described in which ice is dissolved when it is overlain or underlain by aqueous solutions. The measured dissolving velocities are consistent with the theoretical expressions, and yield estimates of the critical Rayleigh number for boundary-layer instability. The results of this study are then applied to predict the rate at which dissolution will occur when undersaturated mixed magmas are generated during the periodic replenishment of large basaltic magma chambers in the Earth's crust.

scholarly journals Scaling of instability time-scales of Antarctic outlet glaciers based on one-dimensional similitude analysis

2019 ◽  
Author(s):  
Anders Levermann ◽  
Johannes Feldmann
Keyword(s):  
Dimensional Analysis ◽  
Time Scales ◽  
Scaling Analysis ◽  
West Antarctica ◽  
Ice Shelf ◽  
Surface Mass ◽  
One Dimensional ◽  
Physical Conditions ◽  
Fast Ice ◽  
The One

Abstract. Recent observations and ice-dynamic modeling suggest that a marine ice sheet instability (MISI) might have been triggered in West Antarctica. The corresponding outlet glaciers, Pine Island Glacier (PIG) and Thwaites Glacier (TG), showed significant retreat during at least the last two decades. While other regions in Antarctica have the topographic predisposition for the same kind of instability it is so far unclear how fast these instabilities would unfold if they were initiated. Here we employ the concept of similitude to estimate the characteristic time scales of several potentially MISI-prone outlet glaciers around the Antarctic coast. The proposed one-dimensional scaling approach combines observational and model data with a scaling analysis of the governing equations for fast ice flow. Evaluating outlet-characteristic ice and bed geometry, surface mass balance and basal friction in the relevant region near the grounding line, we assume that the inferred time scales correspond to the outlet-specific initial responses time to potential destabilization. Our results suggest that TG and PIG have the fastest responses time of all investigated outlets, with TG responding about 1.25 to 2 times as fast as PIG, while other outlets around Antarctica would be up to ten times slower if destabilized. These results have to be viewed in light of the strong assumptions made in their derivation. These include the absence of ice-shelf buttressing, the one-dimensionality of the approach and the uncertainty of the available data, meaning strong caveats of the approach. We argue however that the current topographic situation and the physical conditions of the MISI-prone outlet glaciers carry the information of their respective time scale and that this information can be partially extracted through a similitude analysis. The one-dimensional analysis is only a first step. Whether a two-dimensional analysis is possible is beyond the scope of this study.

Melting driven by vigorous compositional convection

1994 ◽  
Vol 280 ◽  
pp. 255-285 ◽  
Author(s):  
Ross C. Kerr
Keyword(s):  
Aqueous Solutions ◽  
Continental Crust ◽  
Laboratory Experiments ◽  
Basaltic Magma ◽  
Melting Rate ◽  
Theoretical Expression ◽  
Scaling Analysis ◽  
Thermal Buoyancy ◽  
Geological Situation ◽  
Compositional Convection

The melting of a solid in contact with a hot fluid is quantified for the case in which a difference between the densities of the fluid and of the melted solid is able to drive vigorous compositional convection. A scaling analysis is first used to obtain a theoretical expression for the melting rate that is valid for a certain range of Stefan numbers. This expression is then compared with melting velocities measured in laboratory experiments in which ice and wax are melted when they are overlain or underlain by hot aqueous solutions. The melting velocities are consistent with the theoretical expression, and are found to depend on the heats of solution that are released when the melted solids mix with the solutions. The experiments also indicate that, for vigorous convection to occur during the melting of a floor, the unstable compositional buoyancy needs to be at least twice the stabilizing thermal buoyancy.An important geological situation in which melting occurs is when large volumes of basaltic magma are intruded into the Earth's continental crust. The theoretical and experimental results are used and extended to examine quantitatively the melting of the floor and walls of the magma chamber, and of crustal blocks that fall into the chamber.

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