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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

AMLT - Anisotropic mixing length theory

The standard mixing length theory (MLT) assumes that the largest eddies are the only ones that contribute to convection and that they are isotropic. These two requirements are internally inconsistent since it is experimentally known that only small eddies are isotropic while large ones exhibit large degrees of anisotropy. A new model called anisotropic MLT (AMLT) is presented here, together with a model that relates the anisotropy to other quantities of the problem. The new AMLT equations are solved for two cases of stellar structure calculations.

Canuto, V. M.↗
NASA NTRS1985

Conjecture on superrotation in planetary atmospheres - A diffusion model with mixing length theory

The component of rigid shell superrotation on Venus is discussed in the context of comparative planetary atmospheres. A simplified, heuristic analysis, utilizing mixed length theory to describe the small scale nonlinear advections of energy and angular momentum, thereby providing a closure of the dynamic system, is presented, on the basis of which a crude estimate of zonal velocity is made. The rigid shell (global average) component on Venus was calculated to be 105 m/sec.

Mayr, H. G.↗
NASA NTRS1993

Improved solar models constructed with a formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations

We have updated a previous attempt to incorporate within a solar model a treatment of convection based upon numerical simulations of convection rather than mixing-length theory (MLT). We have modified our formulation of convection for a better treatment of the kinetic energy flux. Our solar model has been updated to include a complete range of OPAL opacities, the Debye-Hueckel correction to the equation of state, helium diffusion due to gravitational settling, and atmospheres by Kurucz. We construct a series of models using both MLT and our revised formulation of convection and the compared results to measurements of the solar radius, the solar luminosity, and the depth of the solar convection zone as inferred from helioseismology. We find X(solar) = 0.702 +/- 0.005, Y(solar) = 0.278 +/- 0.005, and Z(solar) = 0.0193 +/- 0.0005.

Lydon, Thomas J.↗
NASA NTRS1987

The generalization of mixing length theory to rotating convection zones and applications to the sun

The consequences of a balance between the Coriolis forces, pressure gradients, and buoyancy forces in a compressible medium are explored, and the generalization of mixing length theory to rotating convection zones is considered, with particular attention being given to the approximations involved. It is shown that if this balance holds, the latitudinally dependent part of the superadiabatic gradient is determined by the angular velocity. Reynolds stresses are found to transport angular momentum towards the equator and towards the deeper layers of the solar convection zone (SCZ). The behavior of the angular velocity at the boundaries of the SCZ is also studied.

Durney, Bernard R.↗
NASA NTRS1993

A formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations. II - Application to Alpha Centauri A and B

We have constructed a series of models of Alpha Centauri A and Alpha Centauri B for the purposes of testing the effects of convection modeling both by means of the mixing-length theory (MLT), and by means of parameterization of energy fluxes based upon numerical simulations of turbulent compressible convection. We demonstrate that while MLT, through its adjustable parameter alpha, can be used to match any given values of luminosities and radii, our treatment of convection, which lacks any adjustable parameters, makes specific predictions of stellar radii. Since the predicted radii of the Alpha Centauri system fall within the errors of the observed radii, our treatment of convection is applicable to other stars in the H-R diagram in addition to the sun. A second set of models is constructed using MLT, adjusting alpha to yield not the 'measured' radii but, instead, the radii predictions of our revised treatment of convection. We conclude by assessing the appropriateness of using a single value of alpha to model a wide variety of stars.

Lydon, Thomas J.↗
NASA NTRS1988

Venus' superrotation, mixing length theory and eddy diffusion - A parametric study

The concept of the Hadley mechanism is adopted to describe the axisymmetric circulation of the Venus atmosphere. It is shown that, for the atmosphere of a slowly rotating planet such as Venus, a form of the nonliner 'closure' (self-consistent solution) of the fluid dynamics system which constrains the magnitude of the eddy diffusion coefficients can be postulated. A nonlinear one-layer spectral model of the zonally symmetric circulation was then used to establish the relationship between the heat source, the meridional circulation, and the eddy diffusion coefficients, yielding large zonal velocities. Computer experiments indicated that proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. It was also found that, for large eddy diffusion coefficients, the meridional velocity is virtually constant; below a threshold in the diffusion rate, the meridional velocity decreases; and, for large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates.

Mayr, H. G.↗
NASA NTRS1992

A formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations. I - Application to the sun

The problem of treating convective energy transport without MLT approximations is approached here by formulating the results of numerical simulations of convection in terms of energy fluxes. This revised treatment of convective transport can be easily incorporated within existing stellar structure codes. As an example, the technique is applied to the sun. The treatment does not include any free parameters, making the models extremely sensitive to the accuracy of the treatments of opacities, chemical abundances, treatments of the solar atmosphere, and the equation of state.

Lydon, Thomas J.↗
NASA NTRS1980

Theoretical studies of solar oscillations

Possible sources for the excitation of the solar 5 minute oscillations were investigated and a linear non-adiabatic stability code was applied to a preliminary study of the solar g-modes with periods near 160 minutes. Although no definitive conclusions concerning the excitation of these modes were reached, the excitation of the 5 minute oscillations by turbulent stresses in the convection zone remains a viable possibility. Theoretical calculations do not offer much support for the identification of the 160 minute global solar oscillation (reported by several independent observers) as a solar g-mode. A significant advance was made in attempting to reconcile mixing-length theory with the results of the calculations of linearly unstable normal modes. Calculations show that in a convective envelope prepared according to mixing length theory, the only linearly unstable modes are those which correspond to the turbulent eddies which are the basic element of the heuristic mixing length theory.

Goldreich, P.↗
NASA NTRS1973

Linear convective modes and the energy transport in stellar convection zones.

Model stars whose convection zones had been prepared in accordance with the standard mixing-length theory were used as a basis for the computation of unstable convective modes. It was found that no superposition of statistically independent, nonviscous, adiabatic, convective modes can reproduce the radial dependence of the convective flux of the model. This implies that the representation of a stellar convection zone as a superposition of unstable adiabatic linear modes is inconsistent with the mixing-length theory, and that conclusions based upon such a representation should be regarded with caution. It is also shown that if the linear scale of convective motions is greater than (or of the same order as) the pressure scale height, then the fractional deviation of the pressure from equilibrium will generally not be negligible, as assumed in the mixing-length theory, but will be at least of the same order as the fractional deviation of the density from equilibrium.

Hart, M. H.↗
NASA NTRS1993

Why convective heat transport in the solar nebula was inefficient

The radial distributions of the effective temperatures of circumstellar disks associated with pre-main sequence (T Tauri) stars are relatively well-constrained by ground-based and spacecraft infrared photometry and radio continuum observations. If the mechanisms by which energy is transported vertically in the disks are understood, these data can be used to constrain models of the thermal structure and evolution of solar nebula. Several studies of the evolution of the solar nebula have included the calculation of the vertical transport of heat by convection. Such calculations rely on a mixing length theory of transport and some assumption regarding the vertical distribution of internal dissipation. In all cases, the results of these calculations indicate that transport by radiation dominates that by convection, even when the nebula is convectively unstable. A simple argument that demonstrates the generality (and limits) of this result, regardless of the details of mixing length theory or the precise distribution of internal heating is presented. It is based on the idea that the radiative gradient in an optically thick nebula generally does not greatly exceed the adiabatic gradient.

Cassen, P.↗
NASA NTRS1995

Tests of two convection theories for red giant and red supergiant envelopes

Two theories of stellar envelope convection are considered here in the context of red giants and red supergiants of intermediate to high mass: Boehm-Vitense's standard mixing-length theory (MLT) and Canuto & Mazzitelli's new theory incorporating the full spectrum of turbulence (FST). Both theories assume incompressible convection. Two formulations of the convective mixing length are also evaluated: l proportional to the local pressure scale height (H(sub P)) and l proportional to the distance from the upper boundary of the convection zone (z). Applications to test both theories are made by calculating stellar evolutionary sequences into the red zone (z). Applications to test both theories are made by calculating stellar evolutionary sequences into the red phase of core helium burning. Since the theoretically predicted effective temperatures for cool stars are known to be sensitive to the assigned value of the mixing length, this quantity has been individually calibrated for each evolutionary sequence. The calibration is done in a composite Hertzsprung-Russell diagram for the red giant and red supergiant members of well-observed Galactic open clusters. The MLT model requires the constant of proportionality for the convective mixing length to vary by a small but statistically significant amount with stellar mass, whereas the FST model succeeds in all cases with the mixing lenghth simply set equal to z. The structure of the deep stellar interior, however, remains very nearly unaffected by the choices of convection theory and mixing lenghth. Inside the convective envelope itself, a density inversion always occurs, but is somewhat smaller for the convectively more efficient MLT model. On physical grounds the FST model is preferable, and seems to alleviate the problem of finding the proper mixing length.

Stothers, Richard B.↗
NASA NTRS1990

The mixing length parameter alpha

The standard mixing length theory, MLT, treats turbulent eddies as if they were isotropic, while the largest eddies that carry most of the flux are highly anisotropic. Recently, an anisotropic MLT was constructed, and the relevant equations derived. It is shown that these new equations can actually be cast in a form that is formally identical to that of the standard isotropic MLT, provided the mixing length parameter, derived from stellar structure calculations, is interpreted as an intermediate, auxiliary function alpha(x), where x, the degree of anisotropy is given as a function of the thermodynamic variables of the problem. The relation between alpha(x) and the physically relevant alpha(l = Hp) is also given. Once the value alpha is deduced, it is found to be a function of the local thermodynamic quantities, as expected.

Canuto, V. M.↗
NASA NTRS1980

Linear modes of convection in the solar envelope

The structure of the solar convective envelope calculated according to mixing-length theory is not consistent with the transport of the convective heat flux by any superposition of the fundamental linear convective modes. If the amplitudes of these modes can be estimated by consideration of the most important nonlinear terms in the equations of motion, it becomes possible to find solar models which are consistent with mode transport of the heat through the convective zone. These models may be characterized by a mixing length which varies from point to point through the envelope. The linear modes in such models show peaks in velocity at certain preferred length scales, but these scales do not necessarily correspond to those of the solar motions, such as the supergranulation.

Bogart, R. S.↗
NASA NTRS1993

Test of a new theory for stellar convection using helioseismology

Two evolutionary models of the sun have been tested using helioseismological data. The two models use the same input microphysics (nuclear reaction rates, opacity, equation of state) and the same numerical evolutionary code, but differ in the treatment of turbulent convection. The first model employs the standard mixing - length theory of convection, while the second one employs a new turbulent convection model which overcomes some basic inconsistencies of the standard theory of convection. The test rests on the calculation of p-mode eigenfrequencies and on the comparison with the helioseismological data. The comparison shows an overall improvement of the eigenfrequencies calculated with the new model with respect to those calculated with the standard model, although it appears that both models still suffer from inaccuracies especially in the treatment of the surface layers.

Paterno, L.↗
NASA NTRS1994

Convection, nucleosynthesis, and core collapse

We use a piecewise parabolic method hydrodynamics code (PROMETHEUS) to study convective burning in two dimensions in an oxygen shell prior to core collapse. Significant mixing beyond convective boundaries determined by mixing-length theory brings fuel (C-12) into the convective regon, causing hot spots of nuclear burning. Plumes dominate the velocity structure. Finite perturbations arise in a region in which O-16 will be explosively burned to Ni-56 when the star explodes; the resulting instabilities and mixing are likely to distribute Ni-56 throughout the supernova envelope. Inhomogeneities in Y(sub e) may be large enough to affect core collapse and will affect explosive nucleosynthesis. The nature of convective burning is dramatically different from that assumed in one-dimensional simulations; quantitative estimates of nucleosynthetic yields, core masses, and the approach to core collapse will be affected.

Bazan, Grant↗
NASA NTRS1991

Stellar turbulent convection - A new model and applications

Improvements of the mixing-length theory (MLT) of turbulent convection in stellar atmospheres are developed theoretically. It is pointed out that inaccuracies are introduced into MLT by the approximating assumptions of a single large eddy (rather than many eddies of different sizes) and of incompressibility. In the proposed new model, the full spectrum of turbulent eddies is determined using more recent turbulence models (e.g., the eddy-damped quasi-normal Markovian model of Orszag, 1977), and a new formula for the convective flux is obtained which gives values up to 10 times greater than those of the MLT at high convective efficiencies. The problem of compressibility is addressed by adding one of two new expressions (one with no free parameters) for the mixing length. Numerical results from simulations of a solar-type star and a 0.8-solar-mass globular-cluster star are presented in tables and graphs and discussed in detail; the agreement with observations is found to be better than with the MLT.

Canuto, V. M.↗
NASA NTRS2003

Subgrid Scale Modeling in Solar Convection Simulations using the ASH Code

The turbulent solar convection zone has remained one of the most challenging and important subjects in physics. Understanding the complex dynamics in the solar con- vection zone is crucial for gaining insight into the solar dynamo problem. Many solar observatories have generated revealing data with great details of large scale motions in the solar convection zone. For example, a strong di erential rotation is observed: the angular rotation is observed to be faster at the equator than near the poles not only near the solar surface, but also deep in the convection zone. On the other hand, due to the wide range of dynamical scales of turbulence in the solar convection zone, both theory and simulation have limited success. Thus, cutting edge solar models and numerical simulations of the solar convection zone have focused more narrowly on a few key features of the solar convection zone, such as the time-averaged di erential rotation. For example, Brun & Toomre (2002) report computational finding of differential rotation in an anelastic model for solar convection. A critical shortcoming in this model is that the viscous dissipation is based on application of mixing length theory to stellar dynamics with some ad hoc parameter tuning. The goal of our work is to implement the subgrid scale model developed at CTR into the solar simulation code and examine how the differential rotation will be a affected as a result. Specifically, we implement a Smagorinsky-Lilly subgrid scale model into the ASH (anelastic spherical harmonic) code developed over the years by various authors. This paper is organized as follows. In x2 we briefly formulate the anelastic system that describes the solar convection. In x3 we formulate the Smagorinsky-Lilly subgrid scale model for unstably stratifed convection. We then present some preliminary results in x4, where we also provide some conclusions and future directions.

Young, Y.-N.↗
DOE OSTI2025

Neutrino heating in 1D, 2D, and 3D core-collapse supernovae: characterizing the explosion of high-compactness stars

Massive stars can end their lives with a successful supernova explosion (leaving behind a neutron star or, more rarely, a black hole), or a failed explosion that leaves behind a black hole. The density structure of the pre-collapse progenitor star already encodes much of the information regarding the outcome and properties of the explosion. However, the complexity of the collapse and subsequent shock expansion phases prevents drawing a straightforward connection between the pre-collapse and post-explosion properties. In order to derive such a connection several explodability studies have been performed in recent years. However, different studies can predict different explosion outcomes. In this article, we show how compactness, which is related to the average density of the star’s core, has an important role in determining the efficiency of neutrino heating, and therefore the outcome of the explosion. Commonly, high-compactness progenitors are assumed to yield failed explosions, due to their large mass accretion rates, preventing the shock from expanding. We show by analysing ~150 2D flash and F ornax simulations and 20 3D F ornax simulations that this is not the case. Instead, due to the rapid increase of neutrino heating with compactness, high-compactness progenitors lead to successful shock revival. We also show that 1D+ simulations that include v-driven convection using a mixing-length theory approach correctly reproduce this trend. Finally, we compare 1D+ models, which we show can reproduce some aspects of multi-D simulations with reasonable accuracy, with other widely used 1D models in the literature.

neutrinos↗