Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

This textbook provides a basic understanding of the formative processes of igneous and metamorphic rock through quantitative applications of simple physical and chemical principles. The book encourages a deeper comprehension of the subject by explaining the petrologic principles rather than simply presenting the student with petrologic facts and terminology. Assuming knowledge of only introductory college-level courses in physics, chemistry, and calculus, it lucidly outlines mathematical derivations fully and at an elementary level, and is ideal for intermediate and advanced courses in igneous and metamorphic petrology. The end-of-chapter quantitative problem sets facilitate student learning by working through simple applications. They also introduce several widely-used thermodynamic software programs for calculating igneous and metamorphic phase equilibria and image analysis software. With over 350 illustrations, this revised edition contains valuable new material on the structure of the Earth's mantle and core, the properties and behaviour of magmas, recent results from satellite imaging, and more.

Principles of igneous and metamorphic petrology

The low Reynolds number dynamics of a thin layer of fluid bounded below by a flat horizontal boundary and moving buoyantly through a fluid of another viscosity and density is observed by means of model experiments and is described theoretically. Three distinct stages of growth were observed. The first stage is described by a linearized Rayleigh-Taylor instability, for which previous literature, present theory, and experiments exhibit close agreement. In this stage, disturbances of one specific wave number are found to grow most rapidly. In the second stage, distortion of the interface is large enough to invalidate the linearized analysis. It is found experimentally that the fluid moves upward as circular columns surrounded by relatively broad regions of descending material. A theory is advanced that attributes an accelerated growth to a structure of this kind through a resonant triad interaction. In the third stage, fully matured structures are formed. If the upwelling material has greater viscosity than the surrounding material, the structure is a long vertical column with gradually decreasing diameter; if the upwelling material has less viscosity than the surrounding material, the structure develops a rim syncline and a pronounced overhang and eventually ascends as a spherical pocket of fluid fed by a pipe. Dynamic explanations for these features are advanced, and some possible implications for geological and geophysical processes are discussed.

Dynamics of laboratory diapir and plume models

Rheological and tectonic modeling of salt provinces

We investigate the behavior of a spherical blob of buoyant fluid as gravity forces it toward either a rigid horizontal boundary or a free surface. The diapir fluid is assumed much less viscous than the ambient fluid. This fundamental problem is the simplest unsteady model relevant to the ascent of hot plumes of buoyant material toward Earth's surface or the base of the lithosphere and closely models the heads of starting plumes. As the diapir approaches the boundary, it collapses in the vertical and spreads horizontally while a layer of the surrounding mantle is slowly squeezed out from betweeen the diapir and the surface. Experimental results for the thinning and lateral spreading of the bouyant fluid, and for the thinning of the squeeze layer, are given for both the case of a rigid, nonslip boundary and that of a free surface. These are compared with similarity scaling laws based on a balance between the bouyancy of the diapir and viscous stresses in the diapir's surroundings. We also observe that the squeeze layer can become gravitationally unstable, leading to a bifurcation from convection on the scale of the original plume to convection on scales much smaller than the diapir. The vertical exchange on smaller horizontal scales enables the plume to more rapidly approach the boundary. At the time instability occurs the diapir has spread to roughly twice its initial diameter. Application of these results, and previous results from surface uplift, to the plumes responsible for continental flood basalts is subject to knowledge of the local value of upper mantle viscosity. If this is taken to be 3×1020 Pa s, most uplift takes place ovcer approximately 5 m.y. Eruption of voluminous basalts will not take place until at least 5–10 m.y. after the surface has reached its maximum elevation. If small-scale instabilities do develop within mantle plume heads, they may be an essential mechanism allowing the top of the plume to ascend to the shallow depths required for extensive melting. It may also explain the observation of Hooper (1990) that volcanism in the Deccan and Columbian Plateau begins before the onset of crustal extension.

Interaction of mantle plume heads with the Earth's surface and onset of small‐scale convection

Z. F. Danes’s mathematical formulation of salt dome dynamics was modified to the extent that explicit solutions can be obtained. For both the two‐dimensional and three‐dimensional model, a formula is derived relating the rate of growth and the wavenumber of a fundamental mode with the physical and geometrical parameters. It is shown that there exists one wavenumber for which the rate of growth reaches a maximum. In time this component will dominate and control the final pattern.

a Theoretical Prediction of Salt Dome Patterns

A straightforward mathematical procedure allows the calculation of the isogeothermal pattern in and about a salt intrusion. Temperature anomalies are controlled not only by the thermal properties of the media, but also are indicative of the geometry and history of the system. As a simple example, an axially symmetrical structure was chosen to illustrate the kind of inferences one can make from the temperature data, such as discrimination between connected and disconnected domes, and the estimation of the vertical velocity of the intrusion. The numerical results confirm and extend the observations in electrolytic scale models (Hubert Guyod, 1946), and augment W. Heroy’s comments on thermal properties of salt, given at the International Conference on Saline Deposits, Houston, 1962.

Temperature distribution in salt domes and surrounding sediments

If two fluids of different densities are superposed one over the other, the plane interface between the two fluids becomes unstable if the heavy fluid overlays the lighter one. This type of hydrodynamic instability is called Rayleigh‐Taylor instability. The theory of Rayleigh‐Taylor instability is a useful tool to study the distribution of salt domes in the coastal region of the Gulf Coastal Province. In spite of a drastic simplification of the geologic situation, the model shows: a) that the spacing of salt domes about an initial disturtbance depends upon the thickness of the mother salt and viscosity ratio of overlying sediment to salt; b) that domes not only grow upward from the initial disturbance, but domes are also triggered in the vicinity of the primary disturbance, forming a family of incipient domes with a regular pattern; c) that the family of incipient domes develops out of the initial disturbance starting at the location of maximal instability and spreading radially. Several numerical example...

Families of salt domes in the gulf coastal province

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Franz Selig

Author Tools

Chat about Author

Papers

a Theoretical Prediction of Salt Dome Patterns

Temperature distribution in salt domes and surrounding sediments

Families of salt domes in the gulf coastal province