Theory Of Convection Research Articles

Beryllium depletion in the solar atmosphere

Using a non-local convection theory for chemically inhomogeneous stars, the beryllium depletion of the Sun is calculated. The results show that Be is slightly depleted (∼5%) in the evolutionary model for the Sun.

Formation of large-scale semiorganized structures in turbulent convection.

A new mean-field theory of turbulent convection is developed by considering only the small-scale part of spectra as "turbulence" and the large-scale part, as a "mean flow," which includes both regular and semiorganized motions. The developed theory predicts the convective wind instability in a shear-free turbulent convection. This instability causes formation of large-scale semiorganized fluid motions in the form of cells. Spatial characteristics of these motions, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This study predicts also the existence of the convective shear instability in a sheared turbulent convection. This instability causes formation of large-scale rolls and generation of convective shear waves which have a nonzero hydrodynamic helicity. Increase of shear promotes excitation of the convective shear instability. Applications of the obtained results to the atmospheric turbulent convection and the laboratory experiments on turbulent convection are discussed.

The extent of the solar overshooting zone deduced from Li abundance

Using a non-local convection theory for chemically inhomogeneous stars, a set of models of the solar convective envelope is presented in this work. The (7) Li depletion as a result of convective overshooting is calculated. A model for the solar convective envelope is found which meets the observational constraints from both the Li abundance and depth of the convection zone determined by helioseismology. We argue that there is no general overshooting distance that holds for all physical quantities, and the differences between them can be factors of a few. In the case of solar lithium depletion, the effective overshooting distance at the low convective boundary can be extended to 1.07H(P) (where H-P is the local pressure scaleheight at the boundary), while the corresponding super-radiative temperature zone overshoots to 0.2H(P) in the sense of helioseismology, and the e-folding length for turbulent velocity and temperature is about 0.38H(P) for this solar model.

The Chemical Composition of White Dwarfs as a Test of Convective Efficiency during Core Helium Burning

Pulsating white dwarfs provide constraints to the evolution of progenitor stars. We revise He-burning stellar models, with particular attention to core convection and to its connection with the nuclear reactions powering energy generation and chemical evolution. Theoretical results are compared to the available measurements for the variable white dwarf GD 358, which indicate a rather large abundance of central oxygen (Metcalfe and coworkers). We show that the attempt to constrain the relevant nuclear reaction rate by means of the white dwarf composition is faced with a large degree of uncertainty related to evaluating the efficiency of convection-induced mixing. By combining the uncertainty of the convection theory with the error on the relevant reaction rate, we derive that the present theoretical prediction for the central oxygen mass fraction in white dwarfs varies between 0.3 and 0.9. Unlike previous claims, we find that models taking into account semiconvection and a moderate 12C(α,γ)16O reaction rate are able to account for a high central oxygen abundance. The rate of the 12C(α,γ)16O used in these models agrees with the one recently obtained in laboratory experiments by Kunz and coworkers. On the other hand, when semiconvection is inhibited, as in the case of classical models (bare Schwarzschild criterion) or in models with mechanical overshoot, an extremely high rate of the 12C(α,γ)16O reaction is needed to account for a large oxygen production. Finally, we show that the apparent discrepancy between our result and those reported in previous studies depends on the method used to avoid the convective runaways (the so-called breathing pulses) that are usually encountered in modeling late stage of core He-burning phase.

On the Red Edge of the δ Scuti Instability Strip

The delta Scuti star catalogue is used to derive the observational locations of such stars on the HR diagram. The theoretical and observational instability strips are compared to check the theoretical red edge obtained by considering non-local time-dependent convection theory. The observational instability strip almost overlaps with the theoretical one, but the observed blue and red envelopes are hotter than the theoretical edges. The distribution of delta Scuti stars in the pulsation strip is not uniform.

Modeling dynamic flavor release from water.

A mathematical model derived from the convective mass transfer theory was developed to predict dynamic flavor release from water. A specific mass transfer correlation including a new term for volatile permeability was applied. The model was entirely based on physicochemical constants of flavor compounds and on some parameters of an apparatus used for validation. The model predicted a linear pattern of release kinetics during the first 30 s and large differences of absolute release for individual compounds. Both calculated and experimentally determined release profiles of a test mixture of flavors showed good agreement.

Theory and simulation of buoyancy-driven convection around growing protein crystals in microgravity.

We present an order-of-magnitude analysis of the Navier-Stokes equations in a time-dependent, incompressible and Boussinesq formulation. The hypothesis employed of two different length scales allows one to determine the different flow regimes on the basis of the geometrical and thermodynamical parameters alone, without solving the Navier-Stokes equations. The order-of-magnitude analysis is then applied to the field of protein crystallization, and to the flow field around a crystal, where the driving forces are solutal buoyancy-driven convection, from density dependence on species concentration, and sedimentation caused by the different densities of the crystal and the protein solution. The main result of this paper is to provide predictions of the conditions in which a crystal is growing in a convective regime, rather than in the ideal diffusive state, even under the typical microgravity conditions of space platforms.

On the effective temperatures and surface gravities of superficially normal main sequence band B and A stars

Eective temperatures and surface gravities for 48 main sequence band B and A stars were found by matching optical region spectrophotometry and H profiles with the predictions of ATLAS9 solar composition model atmospheres. When these values were compared with those found using Stromgren uvby photometry based on ATLAS6 model atmospheres, we found a dierence (photometry-spectrophotometry) of 25118 K for 29 stars with 8000 K Te 10 050 K compared to 76 105 K for 14 stars with 10 050 K Te 17 000 K. The surface gravity scales are in agreement. These stars are suciently hot that their eective temperatures and surface gravity determinations are unaected by discrepancies due to the choice of Mixing-Length or Canuto-Mazzitelli convection theories.

강원도 정선군 운치리 얼음골의 여름철 결빙현상에 관한 연구

The meteorological elements were measured to investigate cause of summertime ice formation at Unchiri, Gangwon Province. The cause of freezing at valley was conformed as adiabatic expansion theory, latent heat of evaporation, natural convective theory, cold air remain theory, and convective freezing theory according to former study. However nither theory produced a satisfactory explanation. This studying area is not valley but ridge, and underground water surface exists at below than freezing height. wintertime temperature drop and summertime cold air spouting were explain as natural convective theory, generation of water drop on the rock was explained as cooling theory by air expansion, and ice formation on the rock was explained as adiabatic expansion theory. In conclusion, formation of ice valley at Unchiri was formed by natural convective theory, adiabatic expansion theory, and latent heat of evaporation successively.

A Statistical Theory for the “Patchiness” of Open-Ocean Deep Convection: The Effect of Preconditioning

Within basins that exhibit open-ocean convection, convectively mixed fluid is often observed in regions of upward-doming isopycnal surfaces, preconditioned by either cyclonic circulation and/or bottom topography. Here, an equilibrium statistical theory for open-ocean convection, developed in the context of two-layer heton models, is adapted to study the outcome of basinwide cooling events over preexisting large-scale ambient flow. A range of prototype ambient flows is studied—including cyclonic and anticyclonic gyres, purely barotropic circulations, and topographically induced flow about a localized seamount and within a broad bowl-like depression. The critical element of these elementary ambient flows is the position of the fluid interface separating the upper and lower layers; it is displaced upward within the cyclonic gyre and the upwelling seamount, downward within the anticyclonic gyre and the bowl-like depression, and is flat for purely barotropic flow. The authors then consider the effect of applying cooling by introducing cold hetons over the preconditioned flow. The most probable postconvection state is found by maximizing the entropy contained in the coarse-grained vorticity field subject to key large-scale constraints. Consistent with observations, the most probable distribution of the coldtemperature anomalies, introduced by the convective overturning that follows a basin-scale surface cold-air outbreak, is indeed concentrated about the peaks of upwelling isopycnals. In contrast, ambient flows with isopycnal surfaces that slope downward fail to confine the cold-temperature anomalies as hetons tend to cluster along the edges and corners of the basin with much weaker displacements.

Convective motions in the mantle

Key subjects related to the present status of mantle convection theory are reviewed in this paper. Rheology of the polycrystalline mantle material is known from laboratory experiments. Diffusion and dislocation creeps must predominate in the long-term deformation of the mantle at high temperatures; their effective viscosities can be estimated from measured creep parameters. Inhomogeneities in the chemical and phase composition of the mantle can influence the convective pattern considerably. Perhaps the most significant heterogeneities in this respect are those produced by the phase changes of the transition zone. The endothermic spinel-perovskite transition at 660 km depth can create an efficient obstacle to vertical flow. Available seismic tomographic images show clear signs of such an obstacle in some subduction zones, at other places however the downwellings seem to be unimpeded. The exact degree of flow layering caused by the 660 km discontinuity is not known, but some sort of flow stratification is strongly suggested by the isotopic and trace element geochemistry which shows that different chemical reservoirs must exist in the mantle on the geological time scale. Equations and the main governing forces are analyzed, and the basic structures of the convective flow are demonstrated in examples of numerical solutions. In particular, recent modelling results are discussed with regard to the plume forms allowed by a semi-permeable internal phase boundary. It is shown that three different kinds of plumes can reach the surface and produce hotspots; those arising from the internal phase boundary, those coming from the basal boundary layer of the mantle, and a recently described new plume type which breaks through the phase transition starting from a diffuse volume below the transition zone.

A Model of Time-Dependent and Non-Local Convection Included in a Stellar Evolution Code

AbstractThe Kuhfuß theory of convection is derived from the exact hydrodynamic equations by means of anelastic approximation and diffusion approximation. In the local and time-independent limit the result is identical to the MLT case. In the more general case the theory includes overshooting and convective mixing as well as time-dependence. We present test calculations in a simple box model and first steps toward the implementation in a stellar code.

Diffusion Impedance of Electrodes of Different Size in Isothermal and Nonisothermal Natural Convection Conditions

The impedance for a reversible K3[Fe(CN)6 ]/K4[Fe(CN)6 ] system is measured at vertical platinum disk electrodes of different diameter in isothermic natural convection conditions and during nonisothermal heating of the electrode. The frequency dependence of the diffusion impedance is described by a classic formula for a finite Warburg impedance. The dimensionless frequency ωδ2/D in the extreme point of the impedance spectrum approached 2.5, in accordance with the theory. Under isothermic conditions near equilibrium, for large-diameter (d > 1 mm) electrodes, the characteristic frequency that corresponds to the extreme point, ω*, is proportional to the square root of the redox-component concentration, overvoltage, and d–1/2. In nonisothermal systems, this frequency is proportional to the square root of the temperature gradient at the electrode/solution interface. These regularities agree with the theory of natural convection. For microelectrodes, the impedance frequency spectrum conforms to the Fleischmann–Pons theory and ω* is proportional to d–2.

Optimal Controls of 3-Dimensional Navier--Stokes Equations with State Constraints

This work is concerned with the maximum principles for optimal control problems governed by 3-dimensional Navier--Stokes equations. Some types of state constraints (time variables) are considered.

Hydrodynamic Simulations of Convection

Convection is one of the most problematic components of almost every model of a pulsating star. RR Lyrae stars, in particular, have a narrow convection zone at the outer layers, and a model without convection cannot get the red edge of the instability strip (see for example Kollath et al., 2000).In recent years, the common approach is to use non-local time-dependent extensions to the Mixing Length Theory of convection (Bono et al., 1997; Feuchtinger, 1999). These models have many free parameters that need to be calibrated. In this paper we report on a preliminary work in which a different approach is used: 2D hydro simulations similar to the red giant model in Asida (2000). This approach was used by Deupree (1975, 1977) but we used a much better numerical resolution and focused on comparison with MLT results.

The structure of the solar convective overshooting zone

Using a non-local theory of convection, we calculated the structure of the solar convection zone, paying special attention to the detailed structure of the lower overshooting zone. Our results show that an extended transition zone exists near the bottom of the convection zone, where the temperature gradient turns smoothly from adiabatic in the convection zone to radiative in solar interior. A super-radiative temperature region is found in the overshooting zone under the solar convection zone, where and . The extension of the super-radiative region (defined by l is about 0.63-HP (0.053-R⊙). A careful comparison of the distribution of adiabatic sound speed and density with the local one is carried out. It is found, strikingly, that the distribution of adiabatic sound speed and density of our model is roughly consistent with the results of reversion from solar oscillation observations.

A simple constitutive equation for entangled polymers with chain stretch

We propose a simple way of including chain stretch effects in convective constraint release theories for entangled polymers. The main idea is that the characteristic time of orientational relaxation depends in a series-parallel way on all three relevant mechanisms, i.e., reptation, constraint release (thermal and convective), and Rouse relaxation. As usual, a separate equation describes chain stretch, which however is assumed not to be affected by constraint release. The model is further simplified by writing the orientational equation in differential form. For step strains, the successful damping function of the Doi–Edwards theory is exactly preserved. Predictions in steady shear also favorably compare with typical data of nearly monodisperse polymers.

Lithium depletion in the solar atmosphere

Using a complete non-local convection theory, we carried out the theoretical calculations of 7 Li depletion of the solar convective envelope models with different convective parameters c 1 and c 2, and got a model of the solar convection zone consistent with the observed 7 Li abundance and the depth of the solar convection zone determined by helioseismic techniques. The overshooting distance of effective non-local convective mixing of 7 Li is very extensive, which is about 1.07 H P or 0.09 R ⊙. However, the super-radiative temperature zone is much narrower, and it is only 0.20 H P or 0.016 R ⊙ .

The Evolutionary Timescale of Sakurai’s Object: A Test of Convection Theory?

Sakurai's Object (V4334 Sagittarii) is a born-again asymptotic giant branch star following a very late thermal pulse. So far, no stellar evolution models have been able to explain the extremely fast evolution of this star, which has taken it from the pre-white dwarf stage to its current appearance as a giant within only a few years. A very high stellar mass can be ruled out as the cause of the fast evolution. Instead, the evolution timescale is reproduced in stellar models by making the assumption that the efficiency for element mixing in the He-flash convection zone during the very late thermal pulse is smaller than predicted by the mixing-length theory (MLT). As a result, the main energy generation from fast proton capture occurs closer to the surface, and the expansion to the giant state is accelerated to a few years. Assuming a mass of V4334 Sgr of 0.604 M☉—which is consistent with a distance of 4 kpc—a reduction of the MLT mixing efficiency by a factor of ~100 is required to match its evolutionary timescale. This value decreases if V4334 Sgr has a smaller mass and, accordingly, a smaller distance. However, the effect does not disappear for the smallest possible masses. These findings may present a semiempirical constraint on the element mixing in convective zones of the stellar interior.

Turbulent convection and pulsational stability of variable stars -- IV. The red edge of the Scuti instability strip

Using a non-local time-dependent statistical theory of convection, we made a linear pulsational instability analysis for stars in the mass range 1.4–3.0 M⊙. The results define a red edge for the δ Scuti instability strip, which fits the observational boundary very well. It is found that the dynamic coupling between convection and oscillation together with the turbulent viscosity are the two main damping mechanisms for low-temperature stars.