Overturn Time Research Articles

Archean cratons and mantle dynamics

The apparent stability of Archean cratons and cratonic keels for billions of years is a difficult observation for geodynamic modeling to explain. While it may be straight-forward to assert that chemical buoyancy and high viscosity are needed to stabilize cratons, there are many questions regarding craton formation, variability (both in space and time), and evolution that remain unanswered. In numerical studies, strong and buoyant cratonic keels survive relatively undeformed for several mantle overturn times (the equivalent of several hundred million years); extending this to several billion years remains a challenge. The strength required to stabilize keels in some of these numerical experiments exceeds reasonable estimates of the laboratory measurements of strength of mantle materials (including both the effects of temperature and melt-depletion). In addition, the most common explanation of keel formation, vertical stacking of subducted plate, requires the keel material to be deformable at the time of formation and soon afterward the keel material becomes strong enough to resist shearing. The extent to which cratonic keels interact with and influence the pattern of mantle convection, by nucleating small-scale edge-driven convection or by coupling plate motions to deeper mantle flow, remains an open question.

Longevity and stability of cratonic lithosphere: Insights from numerical simulations of coupled mantle convection and continental tectonics

The physical conditions required to provide for the tectonic stability of cratonic crust and for the relative longevity of deep cratonic lithosphere within a dynamic, convecting mantle are explored through a suite of numerical simulations. The simulations allow chemically distinct continents to reside within the upper thermal boundary layer of a thermally convecting mantle layer. A rheologic formulation, which models both brittle and ductile behavior, is incorporated to allow for plate‐like behavior and the associated subduction of oceanic lithosphere. Several mechanisms that may stabilize cratons are considered. The two most often invoked mechanisms, chemical buoyancy and/or high viscosity of cratonic root material, are found to be relatively ineffective if cratons come into contact with subduction zones. High root viscosity can provide for stability and longevity but only within a thick root limit in which the thickness of chemically distinct, high‐viscosity cratonic lithosphere exceeds the thickness of old oceanic lithosphere by at least a factor of 2. This end‐member implies a very thick mechanical lithosphere for cratons. A high brittle yield stress for cratonic lithosphere as a whole, relative to oceanic lithosphere, is found to be an effective and robust means for providing stability and lithospheric longevity. This mode does not require exceedingly deep strength within cratons. A high yield stress for only the crustal or mantle component of the cratonic lithosphere is found to be less effective as detachment zones can then form at the crust‐mantle interface which decreases the longevity potential of cratonic roots. The degree of yield stress variations between cratonic and oceanic lithosphere required for stability and longevity can be decreased if cratons are bordered by continental lithosphere that has a relatively low yield stress, i.e., mobile belts. Simulations that combine all the mechanisms can lead to crustal stability and deep root longevity for model cratons over several mantle overturn times, but the dominant stabilizing factor remains a relatively high brittle yield stress for cratonic lithosphere.

Stretching and mixing of viscous blobs in Earth's mantle

The stretching and mixing of blobs more viscous than the surrounding mantle is an important issue: The subducted lithospheric material at depth might be more viscous than the surrounding mantle, and its ability to mix affects its properties as a geochemical reservoir. In order to study the effect of the viscosity ratio λ (viscosity of the blob to the viscosity of the surrounding mantle) on the deformation we perform three types of two‐dimensional numerical simulations: a pure shear simulation, a simulation of steady state convection, and a simulation of time‐dependent convection. In a pure shear flow the inverse of the rate of deformation of a viscous blob is, to a first approximation, a linear function of the ratio λ/AR, where AR is the aspect ratio of the blob. For a viscous blob in a steady convection cell a periodic deformation is superimposed on the long‐term deformation. The period corresponds to an overturn time along the streamline followed by the blob. The strains of this periodic deformation obey the laws found for pure shear. In a time‐dependent flow, more representative of the mantle flow, we find that the average distance a* between two tracers situated within a viscous blob obeys the relationship ln(a*/a0)=At/(1+λ)2 and that it is independent of the aspect ratio of the blob. These two results are well explained by a simple model of successive strains in arbitrary directions. The viscosity contrast controls the mixing efficiency, and it has an effect much larger than predicted by earlier studies. Blobs of matter more viscous than the average mantle can therefore persist unmixed in the mantle over Earth's history.

A comparison of methods for the modeling of thermochemical convection

We have compared several methods of studying thermochemical convection in a Boussinesq fluid at infinite Prandtl number. For the representation of chemical heterogeneity tracer, marker chain, and field methods are employed. In the case of an isothermal Rayleigh‐Taylor instability, good agreement is found for the initial rise of the unstable lower layer; however, the timing and location of the later smaller‐scale instabilities may differ between methods. For a simulation of entrainment by thermal convection of a dense layer at the bottom of the mantle we found good agreement for a few overturn times. After this, differences between the results can be large. We propose intrinsic differences between the methods and possibly chaotic mixing effects may be the cause of the lack of detailed agreement. The comparison shows that high resolution is necessary for a reasonable thermochemical study. This will pose severe restrictions on the applicability of these methods to three‐dimensional situations.

The Theoretical Calculation of the Rossby Number and the ``Nonlocal'' Convective Overturn Time for Pre-Main-Sequence and Early Post-Main-Sequence Stars

This paper provides estimates of convective turnover timescales for Sun-like stars in the pre-main-sequence and early post-main-sequence phases of evolution, based on up-to-date physical input for the stellar models. In this first study, all models have solar abundances, which is typical of the stars in the Galactic disk, where most of the available data have been collected. A new feature of these models is the inclusion of rotation in the evolutionary sequences, thus making it possible to derive theoretically the Rossby number for each star along its evolutionary track, based on its calculated rotation rate and its local convective turnover time near the base of the convection zone. Global turnover times are also calculated for the complete convection zone. This information should make possible a new class of observational tests of stellar theory that were previously impossible with semiempirical models, particularly in the study of stellar activity and in research related to angular momentum transfer in stellar interiors during the course of stellar evolution.

Some effects of a dry crustal flow law on numerical simulations of coupled crustal deformation and mantle convection on Venus

Models of coupled crustal deformation and mantle convection on Venus are reevaluated in light of recent experimental evidence suggesting that the strength of dry basalt is comparable to that of olivine. A previous model which assumed a relatively weak basalt flow law, more appropriate for hydrated crust, is compared to a similar model that assumes a strong basalt flow law, more appropriate for dry crust. A principal difference is the timescale for significant crustal thickening, of the order of 108 years for the weak basalt model and 109 years for the strong basalt model. These results can be understood in the context of theoretical scaling relations for convecting temperature dependent media which imply that in the absence of concentrated zones of near‐surface weakness, of the type associated with plate margins on Earth, the lithospheric overturn time, which sets the timescale required for convective thickening of crust, scales dominantIy with the Rayleigh number defined by the average viscosity of the lithosphere. Theoretical scalings, as well as numerical models, suggest crustal thickening timescales of the order of 108 years remain possible for high bulk mantle Rayleigh numbers and effective viscosity contrasts from lithosphere to interior mantle of the order of 103. Such timescales imply a relatively thin lithosphere and heat loss comparable to that of the present‐day Earth. The large values inferred for the thickness of the mechanical lithosphere on Venus, if correct, would thus tend to favor timescales of the order of 109 years, if one assumes relatively low convective mantle heat loss over an equivalent time. This, in turn, would argue against the likelihood of highland plateaus being manifestations of crustal thickening above mantle downflows. If, instead, one assumes that convective heat removal and implied lithospheric overturn rates were significantly higher over the last several hundred million years, then highland formation due to crustal thickening cannot be ruled out based solely on the strength of dry crust.

Correction to “Processes involved in the formation of magnesian‐suite plutonic rocks from the highlands of the Earth's Moon” by Gregory A. Snyder, Clive R. Neal, and Lawrence A. Taylor

Models of coupled crustal deformation and mantle convection on Venus are reevaluated in light of recent experimental evidence suggesting that the strength of dry basalt is comparable to that of olivine. A previous model which assumed a relatively weak basalt flow law, more appropriate for hydrated crust, is compared to a similar model that assumes a strong basalt flow law, more appropriate for dry crust. A principal difference is the timescale for significant crustal thickening, of the order of 108 years for the weak basalt model and 109 years for the strong basalt model. These results can be understood in the context of theoretical scaling relations for convecting temperature dependent media which imply that in the absence of concentrated zones of near‐surface weakness, of the type associated with plate margins on Earth, the lithospheric overturn time, which sets the timescale required for convective thickening of crust, scales dominantIy with the Rayleigh number defined by the average viscosity of the lithosphere. Theoretical scalings, as well as numerical models, suggest crustal thickening timescales of the order of 108 years remain possible for high bulk mantle Rayleigh numbers and effective viscosity contrasts from lithosphere to interior mantle of the order of 103. Such timescales imply a relatively thin lithosphere and heat loss comparable to that of the present‐day Earth. The large values inferred for the thickness of the mechanical lithosphere on Venus, if correct, would thus tend to favor timescales of the order of 109 years, if one assumes relatively low convective mantle heat loss over an equivalent time. This, in turn, would argue against the likelihood of highland plateaus being manifestations of crustal thickening above mantle downflows. If, instead, one assumes that convective heat removal and implied lithospheric overturn rates were significantly higher over the last several hundred million years, then highland formation due to crustal thickening cannot be ruled out based solely on the strength of dry crust.

Geomagnetic polarity reversals: A connection with secular variation and core‐mantle interaction?

Geomagnetic polarity reversal remains one of Nature's most enigmatic phenomena. Dynamo theory admits solutions in pairs with reversed magnetic fields B and −B, but detailed calculations are required to understand how the field can change sign. Theory also admits separate solutions with different symmetry across the equatorial plane, the symmetric (ES) “quadrupole” and the antisymmetric (EA) “dipole” solutions, which may be important in the reversal process and which offer a simple framework for interpreting small paleomagnetic data sets. Ordinary secular variation leads to very large changes in the magnetic field over several centuries and could easily develop into full reversal; the theory of secular variation, which is relatively well developed, may therefore help in understanding reversals. Other clues to geomagnetic reversals come from the Sun, whose magnetic field reverses every 11 years. Paleomagnetic data show the Earth’s magnetic field reverses every million years or so, with each transition taking about a thousand years, during which the intensity may fall by as much as 1 order of magnitude. Reversal frequency undergoes a modulation on the long timescale (107 years) of mantle convection, and there have been two long intervals in the past with no reversals. Such behavior is typical of a highly nonlinear dynamical system, but the very long timescale of changes in reversal frequency, and its close proximity to the overturn time of mantle convection, suggests some control of the dynamo by the mantle. Short‐term phenomena, such as change in the length of day and secular variation, have been studied extensively for evidence of core‐mantle interactions, and we may draw on this body of evidence in order to understand long‐term effects. Three physical mechanisms have been proposed: topographic, electromagnetic, and thermal, with the last two being most significant for long‐term effects. Symmetries allow the dynamo to generate an EA field, with the major component a dipole, but lateral variations on the core‐mantle boundary may lead to magnetic fields with no symmetry, reflecting the structure of the boundary anomalies. Changes in reversal frequency on the mantle convection timescale could arise either from changes in total heat flux from the core to the mantle or from instabilities associated with lateral variations at the core‐mantle boundary. Neither mechanism is well understood, but the former involves significant changes to the Earth's overall heat budget, whereas the latter must always arise as a natural consequence of deep‐mantle convection. Recent measurements of transition fields show pole paths that lie close to two preferred longitudes near 90°W and 90°E; if substantiated, the result would provide the first definitive evidence of long‐term mantle control of the geomagnetic field. Further evidence suggests that the geomagnetic pole during stable polarity also lies along these two longitudes and that magnetic flux at the core surface tends to concentrate along the same longitudes, as does the present field. A simple theory is proposed relating changes in the core field to apparent transition paths measured at the Earth's surface. The model shows that longitude confinement of the transition paths can occur for quite complicated core fields and that surface intensities can drop by 1 order of magnitude, on average, simply because of the reduction in length scale of the transitional field. Simple transition paths may be an indication of some organization of flux at the core surface but not of large‐scale or small‐amplitude core fields.

Stellar analogs of solar magnetic activity

The techniques and principal results of observational studies of stellar activity are summarized. Both chromospheric and coronal emission clearly track surface magnetic field properties, but it is not well known how the detailed relation between the emission and surface magnetic fields varies with spectral type. For lower Main-Sequence stars of the same spectral type, there is clear evidence of a close relationship between mean activity level and rotation period P rot. There is also less definitive evidence for a similar dependence on convective overturn time τc, such that activity depends on the single parameter Ro = P rot/τc. For single stars, stellar rotation, and magnetic activity both decline smoothly with age. This implies a feedback between angular momentum loss rate and activity level. Temporal variations in mean stellar activity level mimic the solar cycle only for old stars like the Sun, being much more irregular for younger stars. The characteristic timescale of the variations (the ‘cycle period’) appears to depend on Ro for old stars, but shows no clear dependence on either rotation rate or spectral type for younger stars. Further data on mean activity and its variation for a large number of lower Main-Sequence stars should contribute significantly to our understanding of the causes of stellar magnetic activity.

A parameterized model for the evolution of isotopic heterogeneities in a convecting system

Laboratory experiments are used to illustrate how steady convective flows, while efficient at stirring an initial heterogeneity within a single cell, do not produce dispersal of heterogeneous material over scales large compared to the depth. Long-range dispersal requires that the flow be time dependent on a time scale comparable to the overturn time. Convection in an internally heated layer has this property and numerical solutions are used to study the way in which it disperses a set of neutrally buoyant particles that were initially confined to a small space. The horizontal dispersal of these particles is reasonably well represented by an effective diffusivity of 0.3 cm 2/s for a Rayleigh number of 10 6. The concept of an effective diffusivity is then applied to the isotopic evolution of the Sm-Nd and Rb-Sr systems with spatial variations generated by horizontal variations in degree of melting 1.8×10 9 years ago. The present-day average ε value one would measure in such a system depends on the average degree of melting, the amplitude and length scale of variations in partial melt, and the effective diffusivity assumed. Especially in the case of Nd the differences in average ε value between a uniform and a spatially variable (but with the same average) melting case can be significant. The range of ε values about the average is controlled by the competing effects of generation by the differences in enrichment factor and decay due to the effective diffusivity.

Non-ionic surfactants and the membrane transport of barbiturates in goldfish

The effect of a series of polyoxyethylene non-ionic surfactants on the membrane transport of barbiturates in goldfish has been assessed using the overturn time technique. The surfactants, ranging in polyoxyethylene chain length from 2 to 60 and alkyl chain length from 4 to 18, were used at concentrations ranging from 0.001 to 0.1% w/v. Presence of the surfactants in the bathing medium caused a concentration-dependent alteration in the absorption of secobarbitone and thiopentone. The greatest enhancement of absorption for each barbiturate occurred with surfactants with 10 to 20 ethylene oxide moieties, alkyi chain lengths of C 12-C 16 and molecular areas of between 1.00 and 1.60 nm 2. The results are comparable with data obtained with the same surfactants using other epithelial membranes.

Membrane damage by bile salts: the protective function of phospholipids.

The direct toxicity of sodium deoxycholate (SDC) and lysophosphatidylcholine (LPC) to biological membranes was assessed by measurement of goldfish overturn time. When phosphatidylcholine (PC) was incorporated into the aqueous media, the toxicity of both SDC and LPC was reduced, as indicated by increased overturn time. Fish were also pretreated for various times in media containing (a) 1 mM SDC and (b) 1 mM SDC with 1 mM PC. Subsequent transfer to solution, 100 mg litre-1 quinalbarbitone sodium showed that reciprocal overturn times for fish treated using method (a) increased linearly with duration of pretreatment up to a limiting value, obtained after 20 min exposure; 40 min exposure to 1 mM SDC was directly toxic. Fish pretreated using regimen (b) survived longer when challenged with barbiturate, and the reciprocal overturn times were a linear function of time of pretreatment up to at least 40 min. PC also provided protection against membrane damage caused by the synthetic surfactant sodium dodecyl sulphate. Mixed micelle formation between PC and surfactant is thought to account for the protective effects. The results are of significance in the consideration of reflux hypothesis for the aetiology of gastric ulceration and also the possible formulation of drug delivery systems intended to enhance absorption whilst minimizing gastrointestinal damage.

Convection with decaying heat sources: constant viscosity

Summary. A series of two-dimension+ numerical convection models with time-dependent radioactive heating rates are studied in order to investigate the role of convective adjustment in the thermal evolution of the mantle. For uniform viscosity models it is found that two time-scales are important. Some disturbances act on an overturn time-scale, which is on the order of 100 Myr for the upper mantle. This is typical of processes affecting only the thermal boundary layers. Convective adjustment to decaying heat sources, which is a process involving changes in the temperature of the layer as a whole, acts on a time-scale that is long compared to an overturn time (- 1 x lo9 yr for the upper mantle). This results in large time lags between surface heat loss and instantaneous heat production.

A thermal history model for the Earth with parameterized convection

Summary. A thermal history model for the Earth is described in which the energetically important effects of convection are parameterized through the Nusselt number. The validity of the resulting quasi-steady-state thermal model is shown to depend upon the separation of two time-scales—a dynamic time-scale associated with the overturn time for an assumed mantle-wide convective circulation, and a thermal time-scale associated with the cooling of the planet. Provided the initial thermal state of the Earth was ‘hot’, the assumption of a time-scale separation can be shown under certain conditions, to be valid throughout the Earth's history. In this connection, the temperature-dependent mantle rheology plays a key role in regulating the thermal history. It is shown that the present-day, gross thermal structure of the Earth can be understood within the context of a quasi-steady-state model which is driven mainly by primordial heat. The notion of whole-mantle convection is shown to be consistent with several additional observational constraints, including the observed mean lithospheric thickness and the mean plate velocities. We briefly consider the extension of the parameterized thermal model to Venus.

Effect of Lidocaine and Derivatives on Time of Death and Overturn in Goldfish

The effect of lidocaine and five derivatives on the time of overturn and time of death was examined in goldfish. A relationship between the minimum effective concentration of drug necessary to produce the pharmacological response and the partition coefficient between n-heptane or n-octanol and pH 7.4 buffer was found. Further investigations confirmed that, in goldfish, the nonionized local anesthetic agent is solely responsible for the observed effects on overturn time and time of death. Experiments performed to determine the amount of drug in the goldfish at the time of pharmacological response indicated that, for five of the six compounds studied, the same concentration of drug was found in the fish at the time of response. This finding supports the observation that, for the compounds studied, the critical concentration of drug in the goldfish necessary to produce a given response is identical, the difference in time of response being due to differences in absorption rate. The relationship between overturn time and time of death in goldfish was examined, and linear regression of l/time of death versus l/overturn time yielded 1/TD=0.2860(1/TO)+0.0001 (r=0.9648). The relationship between overturn and death may simply be a function of the amount of drug in the fish at the time of the pharmacological response, and the relationship between the amounts of the drug in the fish at the two endpoints may be constant regardless of the derivative evaluated.

The influence of some biological surfactants on the overturn time in goldfish.

The influence of some biological surfactants on the overturn time in goldfish.

Use of the Overturn End Point for the Estimation of Absorption and Elimination Kinetics in Goldfish

The advantages of overturn time as a pharmacologic end point for studies of biologic membrane permeation in goldfish are presented. Studies with both pentobarbital and ethanol showed good reproducibility. Redeterminations of overturn time after 18 hr. provided excellent agreement with initial determinations with both drugs. Evidence is presented to suggest a complex mechanism of action of ethanol in goldfish. A kinetic model is derived which relates overturn time and recovery time and permits the estimation of an elimination rate constant from pharmacologic response data alone.

Convection currents in the Earth's mantle

Recent measurements by J. A. O'Keefe, A. Eckels, and R. K. Squires of the third zonal harmonic component of the earth's gravitational potential are used to determine the characteristics of a hypothetical convection current in the earth's mantle. The calculations are based on a convection theory developed by F. A. Vening Meinesz. The current's velocity is found to be 3.6 cm/yr, corresponding to an overturn time of 1.75×108 yr. The temperature perturbation is found to be 9.7°C. The flow is found to impose a distortion of 159 meters on the earth's crust and a distortion of 237 meters on the surface of the core. The mass loadings associated with these distortions were calculated as 5.3×107 dyne/cm2 at the top, and 8.9×107 dyne/cm2 at the bottom of the mantle. It is believed that the Vening Meinesz theory is capable of qualitatively explaining the results of O'Keefe and his co-workers. However, the required thermal efficiency is about 70 per cent, as compared with an estimated maximum of 4 per cent. It is considered improbable that convective efficiencies could be so large.