Rayleigh-Bénard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use threedimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning 3 × 10−7 ≤ E ≤ 10−1, Rayleigh number...

A conducting spherical shell with a circular orifice of half angle θ0 is at electric potential V0. Show that the difference between the charge densities on the inner and outer surfaces is independent of position, and estimate the ratio of the electric charge on the inner surface to that on the outer. Correct results can be inferred from “elementary” arguments based on superposition, and more “e...

RE PR INT The helicity constraint in spherical shell dynamos A. Brandenburg, P. J. Käpylä, D. Mitra, D. Moss, and R. Tavakol 1 NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden 2 Observatory, University of Helsinki, PO Box 14, FI-00014 University of Helsinki, Finland 3 School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK 4 School of Mathem...

The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modul...

The Casimir energy for a conducting spherical shell of radius a is computed using a direct mode summation approach. An essential ingredient is the implementation of a recently proposed method based on Cauchy's theorem for an evaluation of the eigenfrequencies of the system. It is shown, however, that this earlier calculation uses an improper set of modes to describe the waves exterior to the sp...

In this work, we study the formation and evolution of dark matter halos by means of the spherical infall model with shell-crossing. We present a framework to tackle this effect properly, that does not involve the adiabatic approximation, and is based on the numerical follow-up, with time, of that individual shell of matter that contains always the same fraction of mass with respect to the total...

Pneumatic pressure cells with thin metallic spherical diaphragm of shallow spherical shell configuration linked with vibrating wire pickup or vibrating cantilever pickup were reported in the past. In order to enhance the sensitivity of the pressure cell this work considers dual diaphragm structure fitted with cantilever pickup. The design and development of the pressure cell with this dual diap...

Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to 1/r(5). This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at the International Space Station where t...

Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in th...

Ill PREFACE This Memorandum is part of RAND's continuing search for new ways of utilizing the modern digital computer. The authors present a method for numerically Integrating nonlinear partial differential integral equations, which occur In such fields as radiative transfer and mathematical biology. The method Is then specifically applied to solving a basic equation of transport In a spherical...