15,729 research outputs found
Metastability of solitary roll wave solutions of the St. Venant equations with viscosity
We study by a combination of numerical and analytical Evans function
techniques the stability of solitary wave solutions of the St. Venant equations
for viscous shallow-water flow down an incline, and related models. Our main
result is to exhibit examples of metastable solitary waves for the St. Venant
equations, with stable point spectrum indicating coherence of the wave profile
but unstable essential spectrum indicating oscillatory convective instabilities
shed in its wake. We propose a mechanism based on ``dynamic spectrum'' of the
wave profile, by which a wave train of solitary pulses can stabilize each other
by de-amplification of convective instabilities as they pass through successive
waves. We present numerical time evolution studies supporting these
conclusions, which bear also on the possibility of stable periodic solutions
close to the homoclinic. For the closely related viscous Jin-Xin model, by
contrast, for which the essential spectrum is stable, we show using the
stability index of Gardner--Zumbrun that solitary wave pulses are always
exponentially unstable, possessing point spectra with positive real part.Comment: 42 pages, 9 figure
Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling
We have developed a model of diffusive and decompressive growth of a bubble in a finite region of melt which accounts for the energetics of volatile degassing and melt deformation as well as the interactions between magmatic system parameters such as viscosity, volatile concentration, and diffusivity. On the basis of our formulation we constructed a numerical model of bubble growth in volcanic systems. We conducted a parametric study in which a saturated magma is instantaneously decompressed to one bar and the sensitivity of the system to variations in various parameters is examined. Variations of each of seven parameters over practical ranges of magmatic conditions can change bubble growth rates by 2–4 orders of magnitude. Our numerical formulation allows determination of the relative importance of each parameter controlling bubble growth for a given or evolving set of magmatic conditions. An analysis of the modeling results reveals that the commonly invoked parabolic law for bubble growth dynamics R∼t1/2 is not applicable to magma degassing at low pressures or high water oversaturation but that a logarithmic relationship R∼log(t) is more appropriate during active bubble growth under certain conditions. A second aspect of our study involved a constant decompression bubble growth model in which an initially saturated magma was subjected to a constant rate of decompression. Model results for degassing of initially water‐saturated rhyolitic magma with a constant decompression rate show that oversaturation at the vent depends on the initial depth of magma ascent. On the basis of decompression history, explosive eruptions of silicic magmas are expected for magmas rising from chambers deeper than 2 km for ascent rates \u3e1–5 m s−1
Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation
Transcritical flow of a stratified fluid past a broad localised topographic
obstacle is studied analytically in the framework of the forced extended
Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible
signs for the cubic nonlinear term in the Gardner equation corresponding to
different fluid density stratification profiles. We identify the range of the
input parameters: the oncoming flow speed (the Froude number) and the
topographic amplitude, for which the obstacle supports a stationary localised
hydraulic transition from the subcritical flow upstream to the supercritical
flow downstream. Such a localised transcritical flow is resolved back into the
equilibrium flow state away from the obstacle with the aid of unsteady coherent
nonlinear wave structures propagating upstream and downstream. Along with the
regular, cnoidal undular bores occurring in the analogous problem for the
single-layer flow modeled by the forced KdV equation, the transcritical
internal wave flows support a diverse family of upstream and downstream wave
structures, including solibores, rarefaction waves, reversed and trigonometric
undular bores, which we describe using the recent development of the nonlinear
modulation theory for the (unforced) Gardner equation. The predictions of the
developed analytic construction are confirmed by direct numerical simulations
of the forced Gardner equation for a broad range of input parameters.Comment: 34 pages, 24 figure
An Experimental and Analytical Approach to Understanding the Dynamic Leaching from Municipal Solid Waste Combustion Residue
This paper describes an experimental technique involving the use of small columns for generating significant quantities of leachate data from municipal solid waste (MSW) solid residues within a relatively short amount of time. Data analysis using the discretized mass balance equations descriptive of the system results in best estimates of governing transport parameters that can, in turn, be used to predict the long-term release of leachable components (As, Cd, Cu, Fe, Ni, Pb, Zn, Ca, Mg, Na, K, Cl, SO4) from the solid matrix. Results indicate that both chemical solubility and physical transport are important factors affecting the flux of contaminants from the solid to the solution phase
Effects of Changes in Surface Water Regime and/or Land Use on the Vertical Distribution of Water Available for Wetland Vegetation: Dynamic Model of the Zone of Aeration (Part 1 of Completion Report for Project A-023-ARK)
A mathematical model by Green, simulating one-dimensional vertical ground-water movement in unsaturated soils of the prairie region of Kansas, has been adapted for use in a wetlands environment typified by the wetlands forest of Eastern Arkansas. The model consists of two second-order, non-linear, partial differential equations and an algorithm for their numerical solution. The original model was extended to include functions for seasonal changes in transpiration and for drainage of excess precipitation. Before the addition of the two functions, the model reliability was limited to one growth season
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