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

Transition from a continental to an oceanic rift occurs in the Red Sea by initial emplacement of oceanic crust in regularly spaced ‘hot points’, which serve as nuclei for axial propagation into segments of oceanic crust accretion and for initiation of seafloor spreading. Hot points develop above upwelling mantle diapirs caused by density / viscosity inversion beneath continental and oceanic rifts.

Punctiform initiation of seafloor spreading in the Red Sea during transition from a continental to an oceanic rift

Experimentally determined steady state flow properties and processes of important rock-forming materials are reviewed in reference to those of metals and ceramics and to physical conditions in the earth's crust and upper mantle. Dislocation motion controls the creep rate over a wide range of steady state conditions in the experiments, and the observation that the same processes have operated during natural deformations permits extrapolations of the mechanical data. Under these conditions, strain rate is related to stress raised to the power 2–9, depending on the material and conditions, and the resulting flow stresses and equivalent viscosities are compared at a representative geological strain rate of 10−14/s. The results are applied in brief discussions of diapirism, growth of folds, and flow in the upper mantle.

Steady state flow of rocks

The Geophysics of the Pacific Ocean Basin and Its Margin: Sutton/The Geophysics of the Pacific Ocean Basin and Its Margin

The gravitational instability of a simple two‐layered medium resting on a rigid base has been treated in terms of the analog model of Biot. In order to avoid complications of purely mathematical nature which are unrelated to the physics of the process of instability and do not affect the results significantly, the analysis is presented for the two‐dimensional case. It is shown that such a system is unstable if the density contrast Δρ between the top layer (overburden) and the bottom layer (salt) is positive. The physically important parameters of the instability are the viscosity ratio and the thickness ratio between overburden and salt and the relative density contrast Δρ/ρ1. These parameters determine the amplification rate of a given initial sinusoidal perturbation of wavelength L of the overburden‐salt interface. For the purpose of isolating the role of each parameter and to provide an understanding of the underlying mechanics, several tables are presented which show the influence of each of these par...

/pdf/theory-of-gravity-instability-with-variable-overburden-and-3mdo46rryf.pdf

Theory of gravity instability with variable overburden and compaction

An experimental check has been obtained for the stability theory of stratified viscoelastic media in compression. Model tests have been conducted for both an elastic layer and a viscous layer embedded in a viscous medium and subject to a compression parallel with the layer. The appearance of the folds and the measured wavelengths are in good agreement with the theoretical predictions. For a better interpretation of the tests, the writers present a theoretical evaluation of the time history of deformation for a layer whose folding develops from a given initial departure from perfect flatness. The calculated folding of the layer at various intervals is plotted for different values of the significant parameter.

Experimental Verification of the Theory of Folding of Stratified Viscoelastic Media

The exact solution is given for the folding by compression of a visco- elastic layer embedded in a viscoelastic medium, under the assumption that there is perfect adherence between layer and medium. This solution agrees closely with the earlier result obtained by Biot which was based on the assumption that layer and medium could slip over each other. In a previous publication, Biot (l) has discussed the case of folding a layered visco- elastic medium under initial stress. An exact solution was presented for the folding, due to instability, of a viscoelastic layer of thickness h embedded in a viscoelastic medium extending infinitely far in both directions perpendicular to the layer; the assumption was made that layer and medium did not adhere and could slip over one another as if perfectly lubricated. An approximate solution for the case of perfect adherence was developed in a second publication of the same year by Biot (2). The influence of the adherence was found to be small. The purpose of this note is to check this conclusion by an exact solution for the case when perfect adherence exists between layer and medium. The method is the same as that in Ref. (l) and it combines two distinct developments contained in earlier work by the same author. One of these developments is the theory of elasticity of a medium under initial stress (1934-1941). The other was introduced as a correspondence principle (1954-56) by which elastic moduli are replaced by corre- sponding operators (3, 4, 51. Results are therefore applicable to either elastic or visco- elastic media of a very general nature. It was shown at the same time that the corre- spondence extends to problems which involve anisotropy, dynamics, wave propagation, and variational procedures. The mathematical restrictions on the operators were also derived from thermodynamics (3). The horizontal and vertical displacements u and v, in the layer representing the departure of the displacement from an initial steady state, satisfy the equations

/pdf/on-the-folding-of-a-viscoelastic-medium-with-adhering-layer-4qsyk37jr3.pdf

On the folding of a viscoelastic medium with adhering layer under compressive initial stress

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Theory of gravity instability with variable overburden and compaction

Experimental Verification of the Theory of Folding of Stratified Viscoelastic Media

On the folding of a viscoelastic medium with adhering layer under compressive initial stress