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.

Compositional convection caused by olivine crystallization in a synthetic basalt melt

1996 ◽  
Vol 60 (398) ◽  
pp. 115-130 ◽  
Author(s):  
Jon K. Seedhouse ◽  
Colin H. Donaldson
Keyword(s):  
Boundary Layer ◽  
Density Difference ◽  
Crystal Glass ◽  
Compositional Variation ◽  
Magma Chambers ◽  
Alumina Crucible ◽  
Contour Maps ◽  
Glass Interface ◽  
Compositional Variations ◽  
Compositional Convection

AbstractCompositional convection in magma chambers is thought to be an important process in the fractionation of liquid from crystals during the differentiation of magmas. It has been tested for in this study by undertaking isothermal crystal growth experiments in a silicate melt at atmospheric pressure in air. The melt used is a synthetic basalt in which iron is replaced by cobalt to minimise redox problems. Co-Mg olivine rims were overgrown on forsteritic olivine seeds cemented to the floor of a 2.4 cm deep alumina crucible. Following quenching and sectioning, glasses were examined optically for colour variations and by EPMA for compositional variations. It had been expected that the colour intensity of the blue glass would diminish in the Co-depleted zone that develops around crystal overgrowths, whereas in fact little difference is normally found, except for a slight fading of colour in glass above the apex of a seed in a few experiments. By contrast EPMA revealed zones up to 50 μm wide around seeds that are depleted in Co and Mg by up to 25 % at the crystal-glass interface and in patches above some crystals. Contour maps of X-ray count-rate data obtained in grids of analytical points show Co- and Mg-depleted glass around the overgrowths and in patches above the highest point of each seed, demonstrating that convection in the melt does occur during growth of individual crystals. As the experiments were carried out in a stable temperature gradient and the crystal seeds had no contact with the melt meniscus, thermal and surface-tensional convection are both eliminated, and the convection is inferred to be caused by a density difference resulting from compositional variation across the chemical boundary layer around a growing crystal. The density difference between the inside and outside of a boundary layer is calculated to be approximately −1%.

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.

scholarly journals Boundary layer instability over a rotating slender cone under non-axial inflow

2021 ◽  
Vol 910 ◽  
Author(s):  
Sumit Tambe ◽  
Ferry Schrijer ◽  
Arvind Gangoli Rao ◽  
Leo Veldhuis
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Instability

Abstract

scholarly journals Energy dissipation caused by boundary layer instability at vanishing viscosity – ERRATUM

2018 ◽  
Vol 857 ◽  
pp. 952-952
Author(s):  
Natacha Nguyen van yen ◽  
Matthias Waidmann ◽  
Rupert Klein ◽  
Marie Farge ◽  
Kai Schneider
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Vanishing Viscosity ◽  
Boundary Layer Instability

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

scholarly journals Heat transfer in rotating Rayleigh–Bénard convection with rough plates

2017 ◽  
Vol 830 ◽  
Author(s):  
Pranav Joshi ◽  
Hadi Rajaei ◽  
Rudie P. J. Kunnen ◽  
Herman J. H. Clercx
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Ekman Layer ◽  
Ekman Pumping ◽  
Ekman Boundary Layer ◽  
Bénard Convection ◽  
Roughness Elements ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This experimental study focuses on the effect of horizontal boundaries with pyramid-shaped roughness elements on the heat transfer in rotating Rayleigh–Bénard convection. It is shown that the Ekman pumping mechanism, which is responsible for the heat transfer enhancement under rotation in the case of smooth top and bottom surfaces, is unaffected by the roughness as long as the Ekman layer thickness $\unicode[STIX]{x1D6FF}_{E}$ is significantly larger than the roughness height $k$. As the rotation rate increases, and thus $\unicode[STIX]{x1D6FF}_{E}$ decreases, the roughness elements penetrate the radially inward flow in the interior of the Ekman boundary layer that feeds the columnar Ekman vortices. This perturbation generates additional thermal disturbances which are found to increase the heat transfer efficiency even further. However, when $\unicode[STIX]{x1D6FF}_{E}\approx k$, the Ekman boundary layer is strongly perturbed by the roughness elements and the Ekman pumping mechanism is suppressed. The results suggest that the Ekman pumping is re-established for $\unicode[STIX]{x1D6FF}_{E}\ll k$ as the faces of the pyramidal roughness elements then act locally as a sloping boundary on which an Ekman layer can be formed.

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