Showing papers on "Convection published in 2012"

New perspectives in turbulent Rayleigh-Bénard convection.

Abstract: Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Benard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Benard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.

Thermal and electrical conductivity of iron at Earth/'s core conditions

Abstract: First principles calculations of the thermal and electrical conductivities of liquid iron mixtures under Earth's core conditions suggest a relatively high adiabatic heat flux of 15 to16 terawatts at the core–mantle boundary, indicating that the top of the core must be thermally stratified. The thermal and electrical properties of iron are important for understanding the thermal evolution of the deep Earth and the power available to drive the dynamo that generates Earth's magnetic field. These parameters have previously been estimated by extrapolating results from conditions with lower pressure or temperature, but Monica Pozzo and colleagues now present a calculation from first principles of these parameters at the pressure and temperature of Earth's outer core. Both conductivities are found to be two to three times higher than earlier estimates, prompting a re-evaluation of power estimates for the dynamo. The results greatly restrict models for powering the geodynamo, and indicate that the top of the core must be thermally stratified. The Earth acts as a gigantic heat engine driven by the decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing (as the solid inner core grows), and on chemical convection (due to light elements expelled from the liquid on freezing). The power supplied to the geodynamo, measured by the heat flux across the core–mantle boundary (CMB), places constraints on Earth’s evolution1. Estimates of CMB heat flux2,3,4,5 depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent experimental and theoretical difficulties. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles—unlike previous estimates, which relied on extrapolations. The mixtures of iron, oxygen, sulphur and silicon are taken from earlier work6 and fit the seismologically determined core density and inner-core boundary density jump7,8. We find both conductivities to be two to three times higher than estimates in current use. The changes are so large that core thermal histories and power requirements need to be reassessed. New estimates indicate that the adiabatic heat flux is 15 to 16 terawatts at the CMB, higher than present estimates of CMB heat flux based on mantle convection1; the top of the core must be thermally stratified and any convection in the upper core must be driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted, and future models of mantle evolution will need to incorporate a high CMB heat flux and explain the recent formation of the inner core.

Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth’s core

Abstract: Earth’s magnetic field is sustained by magnetohydrodynamic convection within the metallic liquid core. In a thermally advecting core, the fraction of heat available to drive the geodynamo is reduced by heat conducted along the core geotherm, which depends sensitively on the thermal conductivity of liquid iron and its alloys with candidate light elements. The thermal conductivity for Earth’s core is very poorly constrained, with current estimates based on a set of scaling relations that were not previously tested at high pressures. We perform first-principles electronic structure computations to determine the thermal conductivity and electrical resistivity for Fe, Fe–Si, and Fe–O liquid alloys. Computed resistivity agrees very well with existing shock compression measurements and shows strong dependence on light element concentration and type. Thermal conductivity at pressure and temperature conditions characteristic of Earth’s core is higher than previous extrapolations. Conductive heat flux near the core–mantle boundary is comparable to estimates of the total heat flux from the core but decreases with depth, so that thermally driven flow would be constrained to greater depths in the absence of an inner core.

Detailed Investigation of the Self-Aggregation of Convection in Cloud-Resolving Simulations

Abstract: In models of radiative–convective equilibrium it is known that convection can spontaneously aggregate into one single localized moist region if the domain is large enough. The large changes in the mean climate state and radiative fluxes accompanying this self-aggregation raise questions as to what simulations at lower resolutions with parameterized convection, in similar homogeneous geometries, should be expected to produce to be considered successful in mimicking a cloud-resolving model.The authors investigate this self-aggregation in a nonrotating, three-dimensional cloud-resolving model on a square domain without large-scale forcing. It is found that self-aggregation is sensitive not only to the domain size, but also to the horizontal resolution. With horizontally homogeneous initial conditions, convective aggregation only occurs on domains larger than about 200km and with resolutions coarser than about 2km in the model examined. The system exhibits hysteresis, so that with aggregated initial c...

Lake‐size dependency of wind shear and convection as controls on gas exchange

Abstract: [1] High-frequency physical observations from 40 temperate lakes were used to examine the relative contributions of wind shear (u*) and convection (w*) to turbulence in the surface mixed layer. Seasonal patterns of u* and w* were dissimilar; u* was often highest in the spring, while w*increased throughout the summer to a maximum in early fall. Convection was a larger mixed-layer turbulence source than wind shear (u*/w* < 0.75) for 18 of the 40 lakes, including all 11 lakes <10 ha. As a consequence, the relative contribution of convection to the gas transfer velocity (k, estimated by the surface renewal model) was greater for small lakes. The average k was 0.54 m day−1 for lakes <10 ha. Because u* and w*differ in temporal pattern and magnitude across lakes, both convection and wind shear should be considered in future formulations of lake-air gas exchange, especially for small lakes.

Air-Gap Convection in Rotating Electrical Machines

Abstract: This paper reviews the convective heat transfer within the air gap of both cylindrical and disk geometry rotating electrical machines, including worked examples relevant to fractional horsepower electrical machines. Thermal analysis of electrical machines is important because torque density is limited by maximum temperature. Knowledge of surface convective heat transfer coefficients is necessary for accurate thermal modeling, for example, using lumped parameter models. There exists a wide body of relevant literature, but much of it has traditionally been in other application areas, dominated by mechanical engineers, such as gas turbine design. Particular attention is therefore given to the explanation of the relevant nondimensional parameters and to the presentation of measured convective heat transfer correlations for a wide variety of situations from laminar to turbulent flow at small and large gap sizes for both radial-flux and axial-flux electrical machines.

Porphyry-Copper Ore Shells Form at Stable Pressure-Temperature Fronts Within Dynamic Fluid Plumes

Abstract: Porphyry-type ore deposits are major resources of copper and gold, precipitated from fluids expelled by crustal magma chambers. The metals are typically concentrated in confined ore shells within vertically extensive vein networks, formed through hydraulic fracturing of rock by ascending fluids. Numerical modeling shows that dynamic permeability responses to magmatic fluid expulsion can stabilize a front of metal precipitation at the boundary between lithostatically pressured up-flow of hot magmatic fluids and hydrostatically pressured convection of cooler meteoric fluids. The balance between focused heat advection and lateral cooling controls the most important economic characteristics, including size, shape, and ore grade. This self-sustaining process may extend to epithermal gold deposits, venting at active volcanoes, and regions with the potential for geothermal energy production.

Statistical and physical balances in low Rossby number Rayleigh–Bénard convection

Abstract: Rapidly rotating Rayleigh–Benard convection is studied using an asymptotically reduced equation set valid in the limit of low Rossby numbers. Four distinct dynamical regimes are identified: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Rayleigh numbers, followed for yet larger Rayleigh numbers by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced efficiency and finally by geostrophic turbulence. The transitions are quantified by examining the properties of the horizontally and temporally averaged temperature and thermal dissipation rate. The maximum of the thermal dissipation rate is used to define the width of the thermal boundary layer. In contrast to the non-rotating Rayleigh–Benard convection, the temperature drop across this layer decreases monotonically with increasing Rayleigh number and does not saturate. The breakdown of the convective Taylor column regime is attributed to the onset...

A new vision on giant planet interiors: the impact of double diffusive convection

Abstract: While conventional interior models for Jupiter and Saturn are based on the simplistic assumption of a solid core surrounded by a homogeneous gaseous envelope, we derive new models with an inhomogeneous distribution of heavy elements, i.e. a gradient of composition, within these planets. Such a compositional stratification hampers large scale convection which turns into double-diffusive convection, yielding an inner thermal profile which departs from the traditionally assumed adiabatic interior, affecting these planet heat content and cooling history. To address this problem, we develop an analytical approach of layered double-diffusive convection and apply this formalism to Solar System gaseous giant planet interiors. These models satisfy all observational constraints and yield a metal enrichment for our gaseous giants up to 30 to 60% larger than previously thought. The models also constrain the size of the convective layers within the planets. As the heavy elements tend to be redistributed within the gaseous envelope, the models predict smaller than usual central cores inside Saturn and Jupiter, with possibly no core for this latter. These models open a new window and raise new challenges on our understanding of the internal structure of giant (solar and extrasolar) planets, in particular on the determination of their heavy material content, a key diagnostic for planet formation theories.

Cyclic magnetic activity due to turbulent convection in spherical wedge geometry

Abstract: We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50° latitude, we find for the first time a pronounced equatorward branch at around 20° latitude, reminiscent of the solar cycle.

Observational Evidence for Relationships between the Degree of Aggregation of Deep Convection, Water Vapor, Surface Fluxes, and Radiation

Abstract: Tropical deep convection exhibits complex organization over a wide range of scales. This study investigates the relationships between the spatial organization of deep convection and the large-scale atmospheric state. By using several satellite datasets and reanalyses, and by defining a simple diagnostic of convective aggregation, relationships between the degree of convective aggregation and the amount of water vapor, turbulent surface fluxes, and radiation are highlighted above tropical oceans. When deep convection is more aggregated, the middle and upper troposphere are drier in the convection-free environment, turbulent surface fluxes are enhanced, and the low-level and midlevel cloudiness is reduced in the environment. Humidity and cloudiness changes lead to a large increase in outgoing longwave radiation. Cloud changes also result in reduced reflected shortwave radiation. Owing to these opposing effects, the sensitivity of the radiative budget at the top of the atmosphere to convective aggreg...

Magnetic Wreaths and Cycles in Convective Dynamos

Abstract: Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global 3D magnetohydrodynamic (MHD) simulations with the anelastic spherical harmonic (ASH) code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3$\Omega_\odot$), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed.

Anomalously Weak Solar Convection

Abstract: Convection in the solar interior is thought to comprise structures on a spectrum of scales. This conclusion emerges from phenomenological studies and numerical simulations, though neither covers the proper range of dynamical parameters of solar convection. Here, we analyze observations of the wavefield in the solar photosphere using techniques of time-distance helioseismology to image flows in the solar interior. We downsample and synthesize 900 billion wavefield observations to produce 3 billion cross-correlations, which we average and fit, measuring 5 million wave travel times. Using these travel times, we deduce the underlying flow systems and study their statistics to bound convective velocity magnitudes in the solar interior, as a function of depth and spherical-harmonic degree l. Within the wavenumber band l < 60, convective velocities are 20–100 times weaker than current theoretical estimates. This constraint suggests the prevalence of a different paradigm of turbulence from that predicted by existing models, prompting the question: what mechanism transports the heat flux of a solar luminosity outwards? Advection is dominated by Coriolis forces for wavenumbers l < 60, with Rossby numbers smaller than approximately 10-2 at r/R⊙ = 0.96, suggesting that the Sun may be a much faster rotator than previously thought, and that large-scale convection may be quasi-geostrophic. The fact that isorotation contours in the Sun are not coaligned with the axis of rotation suggests the presence of a latitudinal entropy gradient.

Heat transfer by rapidly rotating Rayleigh–Bénard convection

Abstract: Turbulent, rapidly rotating convection has been of interest for decades, yet there exists no generally accepted scaling law for heat transfer behaviour in this system. Here, we develop an exact scaling law for heat transfer by geostrophic convection, , by considering the stability of the thermal boundary layers, where , and are the Nusselt, Rayleigh and Ekman numbers, respectively, and is the critical Rayleigh number for the onset of convection. Furthermore, we use the scaling behaviour of the thermal and Ekman boundary layer thicknesses to quantify the necessary conditions for geostrophic convection: . Interestingly, the predictions of both heat flux and regime transition do not depend on the total height of the fluid layer. We test these scaling arguments with data from laboratory and numerical experiments. Adequate agreement is found between theory and experiment, although there is a paucity of convection data for low .

General-Relativistic Simulations of Three-Dimensional Core-Collapse Supernovae

Abstract: We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27-solar-mass star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a 3-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27-solar-mass progenitor was studied in 2D by B. Mueller et al. (ApJ 761:72, 2012), who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low-l-mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.

Possible links between long-term geomagnetic variations and whole-mantle convection processes

Abstract: The Earth's internal magnetic field varies on timescales of months to billions of years. The field is generated by convection in the liquid outer core, which in turn is influenced by the heat flowing from the core into the base of the overlying mantle. Much of the magnetic field's variation is thought to be stochastic, but over very long timescales, this variability may be related to changes in heat flow associated with mantle convection processes. Over the past 500 Myr, correlations between palaeomagnetic behaviour and surface processes were particularly striking during the middle to late Mesozoic era, beginning about 180 Myr ago. Simulations of the geodynamo suggest that transitions from periods of rapid polarity reversals to periods of prolonged stability — such as occurred between the Middle Jurassic and Middle Cretaceous periods — may have been triggered by a decrease in core-mantle boundary heat flow either globally or in equatorial regions. This decrease in heat flow could have been linked to reduced mantle-plume-head production at the core-mantle boundary, an episode of true polar wander, or a combination of the two.

An overview on heat transfer augmentation using vortex generators and nanofluids: Approaches and applications

Abstract: The subject of heat transfer enhancement has significant interest to develop the compact heat exchangers in order to obtain a high efficiency, low cost, light weight, and size as small as possible. Therefore, energy cost and environmental considerations are going on to encourage attempts to invent better performance over the existence designs. Streamwise vortices can be generated using small flow manipulators or protrusions such as wings and winglets configurations. Single-pair, single row, or two dimensional array of vortex generators (VGs) can be punched, mounted, attached or embedded in the boundary layer of flow channel. VGs generate longitudinal and transverse vortices, while longitudinal vortices are more efficient for heat transfer enhancement than transverse vortices. A dramatic augmentation in thermal performance of the thermal system can be achieved but pressure drop penalty is existed. Several parameters have been overviewed in this paper, which have pronounced effect on the convective heat transfer coefficient and pressure drop penalty. These parameters are: attack angle of VG, geometry of VG, standard and novel types of VG, spacing between the VG tips, number of pairs of VGs in the flow direction, rectangular or circular array arrangement of VGs, common-flow upper (CFU) or common-flow down (CFD) configuration of VG, pointing up (PU) or pointing down (PD) arrangement of VG with flow direction, Re number, channel aspect ratio, number of tubes of fin-tube heat exchanges (HE), circular or oval tubes of fin-tube HE, and location of VG respect to the tube of HE or from leading edge of the channel. This paper gives an overview about the early studies done in order to improve the performance of thermal systems with minimal pressure losses to derive systems with less negative impact on the environment and high level of energy economic. This study also provides an outlook for future work using nanofluids with vortex generators. This article is also summarizes the recent experimental and numerical developments on the thermal conductivity measurements of nanofluids, thermal conductivity enhancement, convection and conduction heat transfer, some applications, main problems and suggestions for future works.

Heat transport in low-Rossby-number Rayleigh-Bénard convection.

Abstract: We demonstrate, via simulations of asymptotically reduced equations describing rotationally constrained Rayleigh-Benard convection, that the efficiency of turbulent motion in the fluid bulk limits overall heat transport and determines the scaling of the nondimensional Nusselt number Nu with the Rayleigh number Ra, the Ekman number E, and the Prandtl number σ. For E << 1 inviscid scaling theory predicts and simulations confirm the large Ra scaling law Nu-1 ≈ C(1)σ(-1/2)Ra(3/2)E(2), where C(1) is a constant, estimated as C(1) ≈ 0.04 ± 0.0025. In contrast, the corresponding result for nonrotating convection, Nu-1 ≈ C(2)Ra(α), is determined by the efficiency of the thermal boundary layers (laminar: 0.28 ≤ α ≤ 0.31, turbulent: α ~ 0.38). The 3/2 scaling law breaks down at Rayleigh numbers at which the thermal boundary layer loses rotational constraint, i.e., when the local Rossby number ≈ 1. The breakdown takes place while the bulk Rossby number is still small and results in a gradual transition to the nonrotating scaling law. For low Ekman numbers the location of this transition is independent of the mechanical boundary conditions.

Mechanisms of Arctic Surface Air Temperature Change in Response to the Madden–Julian Oscillation

Abstract: Using lagged composites and projections with the thermodynamic energy equation, in this study the mechanisms that drive the boreal winter Arctic surface air temperature (SAT) change associated with the Madden–Julian oscillation (MJO) are investigated. The Wheeler and Hendon MJO index, which divides the MJO into 8 phases, where phase 1 (phase 5) corresponds to reduced (enhanced) convection over the Maritime Continent and western Pacific Ocean, is used. It is shown that the more zonally localized (uniform) tropical convective heating associated with MJO phase 5 (phase 1) leads to enhanced (reduced) excitation of poleward-propagating Rossby waves, which contribute to Arctic warming (cooling). Adiabatic warming/cooling, eddy heat flux, and the subsequent change in downward infrared radiation (IR) flux are found to be important for the Arctic SAT change. The adiabatic warming/cooling initiates the Arctic SAT change, however, subsequent eddy heat flux makes a greater contribution. The resulting SAT chan...

Cyclic magnetic activity due to turbulent convection in spherical wedge geometry

Abstract: We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50 degrees latitude, we find for the first time a pronounced equatorward branch at around 20 degrees latitude, reminiscent of the solar cycle.

The Influence of Pressure-dependent Viscosity on the Thermal Evolution of Super-Earths

Abstract: We study the thermal evolution of super-Earths with a one-dimensional (1D) parameterized convection model that has been adopted to account for a strong pressure dependence of the viscosity. A comparison with a 2D spherical convection model shows that the derived parameterization satisfactorily represents the main characteristics of the thermal evolution of massive rocky planets. We find that the pressure dependence of the viscosity strongly influences the thermal evolution of super-Earths—resulting in a highly sluggish convection regime in the lower mantles of those planets. Depending on the effective activation volume and for cooler initial conditions, we observe with growing planetary mass even the formation of a conductive lid above the core-mantle boundary (CMB), a so-called CMB-lid. For initially molten planets our results suggest no CMB-lids but instead a hot lower mantle and core as well as sluggish lower mantle convection. This implies that the initial interior temperatures, especially in the lower mantle, become crucial for the thermal evolution—the thermostat effect suggested to regulate the interior temperatures in terrestrial planets does not work for massive planets if the viscosity is strongly pressure dependent. The sluggish convection and the potential formation of the CMB-lid reduce the convective vigor throughout the mantle, thereby affecting convective stresses, lithospheric thicknesses, and heat fluxes. The pressure dependence of the viscosity may therefore also strongly affect the propensity of plate tectonics, volcanic activity, and the generation of a magnetic field of super-Earths.

Experimental investigation of the thermal dispersivity term and its significance in the heat transport equation for flow in sediments

Abstract: [1] A review of heat and solute transport in sediments demonstrates that the use of heat as a tracer has not been experimentally evaluated under the same experimental conditions as those used for the evaluation of solute as a tracer. Furthermore, there appears to be disagreement in the earth science literature over the significance of the thermal dispersivity term. To help resolve this disagreement, detailed experimentation with typical groundwater flow velocities (Darcy range, Re < 2.5) was conducted in a specifically designed hydraulic tank containing well-sorted saturated sand. The experiment enabled, for the first time, the precise monitoring of heat and solute tracer movement from a point source in separate runs under identical solid matrix and steady state flow conditions. Experimental results demonstrate that heat transport with natural groundwater flow velocities can reach a transition zone between conduction and convection (0.5 < Pet < 2.5). The thermal dispersion behavior can be described by using a thermal dispersivity coefficient and the square of the thermal front velocity. We propose an empirical formulation for thermal dispersion with Darcy flow in natural porous media and clarify the disagreement regarding its significance. Finally, it was observed that Darcy velocities independently derived from heat and solute experimentation show a systematic discrepancy of up to 20%, and that experimental thermal dispersion results contain significant scatter.