We present results for large scale linear stability analysis of buoyancy driven fluid flows using a parallel finite element CFD code (MPSalsa) along with a general purpose eigensolver (ARPACK). The goal of this paper is to examine both the capabilities and limitations of such an approach, with particular focus on solving large problems on massively parallel computers using iterative methods. We...

A forward-in-time splitting method for integrating the elastic equations is presented. A second-order Runge– Kutta time integrator (RK2) for the large-time-step integration is combined with the forward–backward scheme in a manner similar to the Klemp and Wilhelmson method. The new scheme produces fully second-order-accurate integrations for advection and gravity wave propagation. The RK2 scheme...

The fact that many small aquatic and marine organisms manage to persist in their native environments in the presence of constant advection into unfavorable habitat is known as the “drift paradox.” Although advection may determine large scale biological patterns, individual behavior such as predation or vertical/horizontal migration can dominate at smaller scales. Using both computational and an...

A finite volume scheme for transport and diffusion problems on evolving hypersurfaces is discussed. The underlying motion is assumed to be described by a fixed, not necessarily normal, velocity field. The ingredients of the numerical method are an approximation of the family of surfaces by a family of interpolating simplicial meshes, where grid vertices move on motion trajectories, a consistent...

The interaction between trace shortwave radiative absorbers and the dynamical circulation is shown to be linearly unstable for horizontally uniform basic states with a vertical gradient in the basic state absorber mixing ratio. Two types of instability are identified, described as the advective mode and the propagating mode. The advective mode is usually unstable when the basic state absorber m...

Fluids circulate through the Earth's crust perhaps down to depths as great as 5^15 km, based on oxygen isotope systematics of exhumed metamorphic terrains, geothermal fields, mesozonal batholithic rocks and analysis of obducted ophiolites. Hydrothermal flows are driven by both thermal and chemical buoyancy; the former in response to the geothermal gradient and the latter due to differences in s...

Contour crossings are a form of numerical error common to contour dynamical and contour-advective simulations of geophysical fluid flows. This thesis is devoted to the study of contour crossings that occur in simulations of fluid motion performed by the Contour-Advective Semi-Lagrangian (CASL) algorithm. Components of the CASL algorithm relevant to the study of contour crossings are discussed. ...