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Titolo:
A THEORY OF NONLOCAL MIXING-LENGTH CONVECTION .1. THE MOMENT FORMALISM
Autore:
GROSSMAN SA; NARAYAN R; ARNETT D;
Indirizzi:
UNIV TORONTO,CITA,60 ST GEORGE ST TORONTO M5S 1A1 ONTARIO CANADA UNIV ARIZONA,STEWARD OBSERV TUCSON AZ 85721 CTR ASTROPHYS CAMBRIDGE MA 02138
Titolo Testata:
The Astrophysical journal
fascicolo: 1, volume: 407, anno: 1993,
parte:, 1
pagine: 284 - 315
SICI:
0004-637X(1993)407:1<284:ATONMC>2.0.ZU;2-H
Fonte:
ISI
Lingua:
ENG
Soggetto:
TURBULENT COMPRESSIBLE CONVECTION; MASSIVE STARS; STELLAR CONVECTION; DEEP ATMOSPHERE; CORES; EVOLUTION; VALIDITY; MODELS; TESTS;
Keywords:
CONVECTION; HYDRODYNAMICS; STARS, INTERIORS; TURBULENCE;
Tipo documento:
Article
Natura:
Periodico
Citazioni:
51
Recensione:
Indirizzi per estratti:
Citazione:
S.A. Grossman et al., "A THEORY OF NONLOCAL MIXING-LENGTH CONVECTION .1. THE MOMENT FORMALISM", The Astrophysical journal, 407(1), 1993, pp. 284-315

Abstract

Nonlocal theories of convection that have been developed for the study of convective overshooting often make unwarranted assumptions which preordain the conclusions. We develop a flexible and potentially powerful theory of convection, based on the mixing length picture, which isdesigned to make unbiased, self-consistent predictions about overshooting and other complicated phenomena in convection. In this paper we set up the basic formalism and demonstrate the power of the method by showing that a simplified version of the theory reproduces all the standard results of local convection. The mathematical technique we employis a moment method, where we develop a Boltzmann transport theory forturbulent fluid elements. We imagine that a convecting fluid consistsof a large number of independent fluid blobs. The ensemble of blobs is described by a distribution function, f(A)(t, z, v, T), where t is the time, z is the vertical position of a blob, v is its vertical velocity, and T is its temperature. The distribution function satisfies a Boltzmann equation, where the physics of the interactions of blobs is introduced through dynamical equations for v and T. We assume horizontal pressure equilibrium. The equation for v includes terms due to buoyancy, microscopic viscosity, and turbulent viscosity. The latter effectis modeled with a turbulent viscosity coefficient, v(turb) = sigmal(w), where sigma is the local velocity dispersion of the blobs and l(w) is the mixing length corresponding to momentum exchange between blobs. Similarly, the equation for T includes adiabatic heating, radiative diffusion of heat, and turbulent diffusion of heat, which is modeled through a diffusion coefficient, chi(turb) = sigmal(theta), where l(theta) is the thermal mixing length. By taking various moments of the Boltzmann equation, we generate a series of equations which describe the evolution of the mean fluid and various moments of the turbulent fluctuations. The equations, taken to various orders, are useful for describing turbulent fluids at corresponding levels of complexity. In this picture, fluid blobs define the background, and the background tells theblobs how to move through v-T phase space. We consider the second-order equations of our theory in the limit of a steady state and vanishing third moments, and show that they reproduce all the standard resultsof local mixing-length convection. We find that there is a particularvalue of the superadiabatic gradient, DELTAdelT(crit), below which the only possible steady state of a fluid is nonconvecting. Above this critical value, a fluid is convectively unstable. We identify two distinct regimes of convection which we identify as efficient and inefficient convection. The equations we derive for convection in these regimesare very similar to the standard equations employed in stellar astrophysics. We also develop the theory of local convection in a composition-stratified fluid. We reproduce the various known regimes of convection in this problem, including semiconvection and the ''salt fingers'' phenomena. Surprisingly, we find that the well-known Ledoux criterion has no bearing at all on the physics of convection in a stratified medium, except in certain limits that are not of interest in astrophysics. To investigate nonlocal effects like convective overshooting, it is necessary to consider third-order equations. We write down the appropriate equations and see that they involve fourth moments in a nontrivial way. Closure relations for the fourth moments and the solution of the full nonlocal equations are the topics of future papers.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 27/11/20 alle ore 16:12:31