Local convection theory makes the unphysical prediction that turbulent mixing terminates at the Schwarzschild stability boundary, and existing non-local convection theories have been criticized by Renzini (1987). Since the size of convecting cores bears upon stellar structure and evolution, a self-consistent treatment of non-local convection is needed. We have developed a theory of non-local mixing-length convection based upon a Boltzman transport theory for subsonic, turbulent fluid elements. The momentum and thermal energy excesses of fluid elements are dissipated on the scale of a mixing length. The distribution function, f(t,z,v,T), which is the mass density per velocity-temperature phase space volume, evolves according to the Boltzmann equation. The minimal non-local theory is obtained by taking moments of the Boltzmann equation, up to third order. The local limit of the moment equations reduces to standard mixing-length theory. We extend this moment method to local convection in a composition stratified fluid by considering the evolution of the distribution function, f(t,z,v,T,μ), in velocity-temperature-molecular weight phase space. The stability criteria for convection, semiconvection, and salt-finger instability are derived. To determine closure approximations and evaluate the validity of the moment theory, we have developed an algorithm called Generalized Smooth Particle Hydrodynamics (GSPH) that numerically simulates convection. The vertical structure of the background fluid is calculated by SPH averaging of particles on a grid. Forces on particles are calculated from the background grid and from the local deviations between particles and grid. Particles move vertically only, but the local deviation forces, which account for turbulent losses of momentum and energy, arise from horizontal interactions. GSPH simulations show that the fourth moments are approximately proportional to squares of the second moments in unstable regions, with a proportionality constant between 2 and 4. With this closure approximation, we show that solutions of the moment equations agree well with GSPH results. The closure relations lead to nearly correct second moments, even in overshooting regions where the closure approximations are poor. GSPH simulations of convective overshooting in plane parallel and spherical geometry typically give overshooting distances in the range dₒᵥₑᵣ ≈ 1 - 2ℓ(M). We discuss improvements that we would like to make to the GSPH code and to the analytic work to obtain more precise answers that are directly relevant to realistic stars.

The onset conditions and the behavior of the developed secondary flow were investigated for double-diffusive convection in a horizontal layer of porous medium. The work concentrated on the case in which the layer is heated from below and saturated with a fluid having a stabilizing concentration gradient. Because the component with the larger diffusivity (heat) is destabilizing and the component with the smaller diffusivity (solute) is stabilizing, the motion at onset is predicted to be oscillatory according to linear stability theory. Experiments were conducted in a rectangular tank 24 cm long x 12 cm wide x 4 cm deep filled with glass beads 3 mm in diameter. The saturating fluid was distilled water and NaCl was the solute. The basic state salinity profiles were slowly diffusing in time, because the salt concentration was not maintained fixed at the solid top and bottom boundaries. Sustained oscillations were not detected at onset in the experiments; instead, there was a dramatic increase in the heat flux at the critical temperature difference. After more than one thermal diffusion time, the heat flux reached a steady value, which increased monotonically if the temperature difference was increased further. When the temperature difference was reduced, the heat flux exhibited hysteresis. Flow visualization indicated that the convection pattern of the developed flow was three-dimensional. In order to better model the experiments, linear theory was extended to include the effects of temperature-dependent thermal expansion coefficient and viscosity for water and the actual solute boundary conditions in the experiment. These extensions of the linear theory required numerical solution procedures. In addition, nonlinear solutions were obtained using finite differences, assuming the problem is two-dimensional. In the nonlinear calculations, the oscillatory motion predicted by linear theory was found to be unstable at finite amplitude. The breakdown of the initial oscillatory motion is followed by a large increase in the heat transport, similar to what was observed in the experiments. Both steady and oscillatory nonlinear asymptotic solutions were found, depending on the governing parameter values. Hysteresis in the heat curve was also obtained.

Thesis (Ph.D.) -- University of Texas at Arlington, 2008.

Thesis (Ph. D.)--University of Chicago, Dept. of Astronomy and Astrophysics, March 2000. / Includes bibliographical references. Also available on the Internet.

Thesis presented in fulfilment of the requirements for the degree of Doctor of Philosophy at the University of the Witwatersrand, Johannesburg, 2017. / This thesis investigates in detail the structure of models of turbulent convec tion with phenomenological closures for the eddy-viscosity. It explores the merits of replacing the canonical Mixing Length Theory of stellar convection with more realistic models of fluid turbulence that take into account the full spectrum of eddy sizes. The author provides a detailed exposition of the fun damental assumptions and the modus operandi of various approaches to the treatment of convective energy-transfer in stars. He focuses in particular on spectral descriptions of the convective process. The structure of several clo sure models developed by various authors are investigated, and he identifies and elucidates those aspects of these closures that lead to an improved descrip tion of convective turbulence in the stellar interior. The author also develops an implementation within the public-domain code, called Modules for Experi ments in Stellar Astrophysics, of two of these models and reports and discusses the results of his numerical experiments. / XL2018

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Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 96-101). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Chicago, Dept. of Astronomy and Astrophysics, March, 2001. / Includes bibliographical references. Also available on the Internet.

La détection et la caractérisation d'exoplanètes apparaissent clairement comme des thèmes centraux de l'observation astronomique pour les années à venir. Les projets spatiaux ou au sol sont nombreux (HARPS, CoRoT, Kepler, JWST, SPHERE...), mais les études théoriques visant à l'analyse et à la compréhension des données recueillies et à venir sont nécessaires. Durant cette thèse j'ai étudié divers processus physiques affectant la structure interne et l'évolution des planètes géantes, aussi bien au sein, qu'à l'extérieur de notre système solaire. J'ai notamment modélisé en détail: -L'impact de l'irradiation intense émise par l'étoile sur l'atmosphère d'une planète à faible distance orbitale, et l'effet induit sur l'évolution interne de cette planète. -Le couplage par dissipation de marée de l'évolution orbitale et thermique d'une planète interagissant avec sa proche étoile parente. -L'effet de la déformation due aux marées sur les paramètres observables d'une planète en transit grâce au suivi photométrique de son passage devant l'étoile. -L'incidence sur la structure et l'évolution d'une diminution de l'efficacité du transport de chaleur par convection due à un gradient d'éléments lourd dans l'enveloppe gazeuse d'une planète géante, conduisant au phénomène de convection double-diffusive. A travers l'étude des ces divers processus, j'ai développé différents modèles analytiques et codes numériques qui sont à la fois flexibles et robustes, et qui permettent maintenant d'étudier certaines propriétés des nouveaux objets substellaires détectés à mesure qu'ils sont découverts. / The detection and characterization of extrasolar planets clearly appears as one of the main goals of observational astronomy for the coming years. Space and ground project are numerous, but theoretical studies aimed at analyzing and understanding available and future data are needed. During this thesis, I study various physical processes affecting the internal structure and evolution of both solar, and extrasolar giant planets. In particular I investigate : -the impact of the intense stellar irradiation received by a close in planet on its subsequent internal evolution. This allows me to quantify the radius anomaly of bloated Hot Jupiters and to constrain their internal composition. -the tidal and centrifugal distortion of a fluid planet. By using both analytical and numerical models, I show how non-sphericity of the planet affects transit measurements, yielding an underestimation of its radius. -how the presence of double-diffusive convection caused by a heavy elements gradient in the gaseous envelope of a planet can decrease the efficiency of its internal heat transport, and affect its structure and evolution. -the coupling between the orbital and the thermal evolution of a planet arising from the strong star-planet tidal interaction. Subsequently, I find that tidal heating alone is not a viable explanation for the observed radius anomaly of transiting planets. Through these different studies, I developed various analytical models and numerical codes that are both flexible and robust, and which now allow one to study the properties of new extrasolar planets and brown dwarfs as they are discovered.