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 numerical analysis of thermal convection in porous media, heated from below, and assuming Darcy flow conditions, involves the solving of a set of non-linear equations for the temperature and flow fields. The condition of criticality determining the onset of convection is obtained by linearization and the solving of an eigenvalue problem of the fourth order. The smallest eigenvalue represents the critical Rayleigh number. The shape of the critical temperature and flow fields is then obtained from the linear set. In most practical cases, the problem setting is such that closed analytical solutions cannot be derived. The difficulties of solving the convection equations can be overcome by using the Galerkin finite-element method. The method allows the solution of both the linear set and also the more complete non-linear set of equations at various boundary conditions and taking variations in the material parameters into account. In this thesis, the Galerkin method is used to solve the convection equations for infinitely long porous vertical or semi-vertical slabs with prescribed temperatures at the top and bottom surfaces. The first set of models investigated involve boundary walls that are impermeable to the fluid but perfectly conducting to heat. The critical Rayleigh numbers and critical temperature and flow fields are obtained for such slabs with various aspect ratios. The results show that the critical number is raised by 200 to 400% as compared with published data for similar slabs with thermally non-conducting walls. The results are generalized by investigating cases of slabs with (1) three types of vertically varying permeability, (2) by taking the temperature dependence of the fluid properties into account, (3) by including non-linear terms, and finally, (4) a few cases of slabs with boundary walls of finite thermal conductivity are investigated. The results are applicable to a number of situations in geothermal areas. A brief discussion of two such cases is given, that is, (1) the estimating of the critical permeability profile for the East geothermal field in the Imperial Valley and (2) the computation of a temperature cross section in the Cumali geothermal field in Turkey. / Graduation date: 1979

Variations in characteristics of tropical deep convection are examined for an association with the stratospheric quasi-biennial oscillation (QBO). Eight years (1998-2005) of Tropical Rainfall Measuring Mission (TRMM) Lightning Imaging Sensor (LIS) flash densities and ten years (1998-2007) of TRMM Precipitation Radar (PR) deep convective and stratiform rainfall and convective echo top heights are analyzed. The QBO can be linked to deep convection through two hypothesized mechanisms: 1) modulation of tropopause height, which may affect the altitude that convection can penetrate; and 2) modulation of cross-tropopause shear, which may affect the vertical development of convection via shearing of cloud tops. Tropopause height and cross-tropopause shear is measured by National Centers for Environmental Prediction (NCEP) reanalysis 100 hPa temperatures and 50-200 hPa zonal wind shear, respectively. When partitioned by QBO east and west phases, zonal monthly mean anomalies and anomalous monthly mean difference maps illustrate a QBO signal in lightning flash rates, convective and stratiform rain amounts, and the number of convective echo tops > 12 km. QBO modulation of cross-tropopause shear causes 50-200 hPa shear east (west) phase anomalies to decrease (increase) about the equator and increase (decrease) in off-equator regions. QBO modulation of tropopause height induces a higher/colder (lower/warmer) tropopause near the equator during the east (west) phase. While the expectation was that decreases in cross-tropopause shear and tropopause temperatures at monthly time scales during the QBO would result in an increase of deep convective properties near the equator, observations suggest that deep convective properties may increase or decrease depending on the location and season. Similar to the QBO results, the increase or decrease of deep convective properties with general variations in cross-tropopause shear and tropopause temperatures depends on the location and season.

Dissertation--Fachbereich Geowissenschaften--Universität Hamburg, 2001. / Bibliogr. p. 113-123.

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ix, 174 leaves : ill. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mechanical Engineering, 1972

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 72-75).

Thesis (M.S.)--University of Wisconsin--Madison, 1982. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 68-69).

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 125-129).