FAMILIES OF SALT DOMES IN THE GULF COASTAL PROVINCE

Geophysics ◽  
1966 ◽  
Vol 31 (4) ◽  
pp. 726-740 ◽  
Author(s):  
Franz Selig ◽  
E. G. Wermund
Keyword(s):  
Viscosity Ratio ◽  
Hydrodynamic Instability ◽  
Coastal Region ◽  
Taylor Instability ◽  
Initial Disturbance ◽  
Salt Domes ◽  
Two Fluids ◽  
The Family ◽  
Coastal Province ◽  
Rayleigh Taylor Instability

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 examples provide a framework for examining the disturbance of Gulf Coastal salt domes.

The Rayleigh–Taylor instability of a viscous liquid layer resting on a plane wall

1990 ◽  
Vol 217 ◽  
pp. 615-638 ◽  
Author(s):  
Lori A. Newhouse ◽  
C. Pozrikidis
Keyword(s):  
Surface Tension ◽  
Liquid Layer ◽  
Viscosity Ratio ◽  
Taylor Instability ◽  
Creeping Flow ◽  
Plane Wall ◽  
Ambient Fluid ◽  
Initial Thickness ◽  
Two Fluids ◽  
Rayleigh Taylor Instability

The nonlinear Rayleigh–Taylor instability of a liquid layer resting on a plane wall below a second liquid of higher density is considered. Under the assumption of creeping flow, the motion is studied as a function of surface tension and the ratio of the viscosities of the two fluids. The flow induced by the deformation of the layer is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind is derived for the density of the distribution, and is solved by successive iteration. The results show that for small and moderate surface tension, the instability of the layer leads to the formation of a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of these plumes strongly depends upon the viscosity ratio and surface tension. When the viscosity of the overlying fluid is comparable with or larger than that of the layer, the plumes are composed of a well-defined leading drop on top of a narrow stem. When the viscosity of the overlying fluid is smaller than that of the layer, the plumes take the form of a compact column of rising fluid. The size of the drop leading a plume is roughly proportional to the initial thickness of the layer. When surface tension is sufficiently small, ambient fluid is entrained into the leading drop and circulates in a spiral pattern. Convection currents generated by the rising plumes are visualized with streamline patterns, and the rate of thinning of the remnant layer, as well as the speed of the rising drop or plumes, are discussed.

Spouting and planform selection in the Rayleigh–Taylor instability of miscible viscous fluids

1998 ◽  
Vol 377 ◽  
pp. 27-45 ◽  
Author(s):  
N. M. RIBE
Keyword(s):  
Viscosity Ratio ◽  
Initial Perturbation ◽  
Taylor Instability ◽  
Viscous Layer ◽  
Weakly Nonlinear ◽  
Subexponential Growth ◽  
Weakly Nonlinear Analysis ◽  
Salt Domes ◽  
Initial Evolution ◽  
Rayleigh Taylor Instability

A weakly nonlinear analysis is used to study the initial evolution of the Rayleigh–Taylor instability of two superposed miscible layers of viscous fluid between impermeable and traction-free planes in a field of gravity. Analytical solutions are obtained to second order in the small amplitude of the initial perturbation of the interface, which consists of either rolls or squares or hexagons with a horizontal wavenumber k. The solutions are valid for arbitrary values of k, the viscosity ratio (upper/lower) γ, and the depth ratio r, but are presented assuming that k=kmax(γ, r), where kmax is the most unstable wavenumber predicted by the linear theory. For all planforms, the direction of spouting (superexponential growth of interfacial extrema) is determined by the balance between the tendency of the spouts to penetrate the less viscous layer, and a much stronger tendency to penetrate the thicker layer. When these tendencies are opposed (i.e. when γ>1 with r>1), the spouts change direction at a critical value of r=rc(γ). Hexagons with spouts at their centres are the preferred planform for nearly all values of γ and r, followed closely by squares; the most slowly growing planform is hexagons with spouts at corners. Planform selectivity is strongest when γ[ges ]10 and r[ges ]γ1/3. Application of the results to salt domes in Germany and Iran show that these correspond to points (γ, r) below the critical curve r=rc(γ), indicating that the domes developed from interfacial extrema having subexponential growth rates.

scholarly journals Experimental investigation into inertial properties of Rayleigh–Taylor turbulence

1997 ◽  
Vol 15 (1) ◽  
pp. 25-31 ◽  
Author(s):  
Yu.A. Kucherenko ◽  
S.I. Balabin ◽  
R. Cherret ◽  
J.F. Haas
Keyword(s):  
Experimental Investigation ◽  
Kinetic Energy ◽  
Turbulent Mixing ◽  
Average Density ◽  
Taylor Instability ◽  
X Ray ◽  
Two Fluids ◽  
Time Space ◽  
Rayleigh Taylor Instability ◽  
Region Size

An experimental investigation into inertial properties of the developed Rayleigh–Taylor instability with the different initial values of the kinetic energy of turbulence has been performed. The experiments were performed by using two fluids having different densities with density ration n = 3. Fluids were placed in an ampoule. At the unstable stage of motion, the ampoule was moving under an acceleration. At a certain instant of time the acceleration was removed and the ampoule moved under the force of inertia. By means of pulsed X-ray photography, the mixing region size and the time-space distributionof the average density of matter in the turbulent mixing region have been determined at different instants of time. The time-space distributions are compared with those obtained by semiempirical theories of mixing.

Numerical studies of some nonlinear hydrodynamic problems by discrete vortex element methods

1978 ◽  
Vol 84 (3) ◽  
pp. 433-453 ◽  
Author(s):  
J. C. S. Meng ◽  
J. A. L. Thomson
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Gravity Current ◽  
Vortex Sheet ◽  
Taylor Instability ◽  
Green’S Function Method ◽  
Discrete Vortex ◽  
Two Fluids ◽  
Rayleigh Taylor Instability

A class of nonlinear hydrodynamic problems is studied. Physical problems such as shear flow, flow with a sharp interface separating two fluids of different density and flow in a porous medium all belong to this class. Owing to the density difference across the interface, vorticity is generated along it by the interaction between the gravitational pressure gradient and the density gradient, and the motion consists of essentially two processes: the creation of a vortex sheet and the subsequent mutual induction of different portions of this sheet.Two numerical methods are investigated. One is based upon the well-known Green's function method, which is a Lagrangian method using the Biot-Savart law, while the other is the vortex-in-cell (VIC) method, which is a Lagrangian-Eulerian method. Both methods treat the interface as sharp and represent it by a distribution of point vortices. The VIC method applies the FFT (fast Fourier transform) to solve the stream-function/vorticity equation on an Eulerian grid, and computational efficiency is further improved by using the reality properties of the physical variables.Four specific problems are investigated numerically in this paper. They are: the Rayleigh-Taylor instability, the Saffman-Taylor instability, transport of aircraft trailing vortices in a wind shear, and the gravity current. All four problems are solved using the VIC method and the results agree well with results obtained by previous investigators. The first two problems, the Rayleigh-Taylor instability and the Saffman-Taylor instability, are also solved by the Green's function method. Comparisons of results obtained by the two methods show good agreement, but, owing to its computational economy, the VIC method is concluded to be the better method for treating the class of hydrodynamic problems considered here.

Effects of Heat and Mass Transfer on Rayleigh-Taylor Instability

1972 ◽  
Vol 94 (1) ◽  
pp. 156-160 ◽  
Author(s):  
D. Y. Hsieh
Keyword(s):  
Mass Transfer ◽  
Phase Transformation ◽  
Dispersion Relation ◽  
Temperature Gradient ◽  
Thermal Effect ◽  
Taylor Instability ◽  
Interfacial Wave ◽  
Interfacial Conditions ◽  
Two Fluids ◽  
Rayleigh Taylor Instability

The effect on the interfacial gravity wave between two fluids is studied when there is a temperature gradient in the fluids. It is found that the thermal effect is closely related to the phase transformation across the interface. The interfacial conditions with mass flow are first derived. Then the dispersion relation for the interfacial wave is obtained. It is found that the effect of evaporation is to damp the interfacial wave and to enhance the Rayleigh-Taylor instability. It is also found that the system will be stabilized or destabilized depending on whether the vapor is hotter or colder than the liquid.

Numerical Simulation of Rayleigh–Taylor Instability by Multiphase MPS Method

2018 ◽  
Vol 16 (02) ◽  
pp. 1846005
Author(s):  
Xiao Wen ◽  
Decheng Wan
Keyword(s):  
Numerical Simulation ◽  
Hydrodynamic Instability ◽  
Phase Interface ◽  
Industrial Applications ◽  
Taylor Instability ◽  
Transitional Region ◽  
Two Phase ◽  
Mps Method ◽  
Evolutionary Features ◽  
Rayleigh Taylor Instability

The Rayleigh–Taylor instability (RTI) problem is one of the classic hydrodynamic instability cases in natural scenarios and industrial applications. For the numerical simulation of the RTI problem, this paper presents a multiphase method based on the moving particle semi-implicit (MPS) method. Herein, the incompressibility of the fluids is satisfied by solving a Poisson Pressure Equation (PPE) and the pressure fluctuation is suppressed. A single set of equations is utilized for fluids with different densities, making the method relatively simple. To deal with the mathematical discontinuity of density in the two-phase interface, a transitional region is introduced into this method. For particles in the transitional region, a density smoothing scheme is applied to improve the numerical stability. The simulation results show that the present MPS multiphase method is capable of capturing the evolutionary features of the RTI, even in the later stage when the two-phase interface is quite distorted. The unphysical penetration in the interface is limited, proving the stability and accuracy of the proposed method.

scholarly journals Study of Rayleigh Taylor Instability with the Help of CFD Simulation

2020 ◽  
Author(s):  
Indrashis Saha
Keyword(s):  
Cfd Simulation ◽  
Classical Method ◽  
Nonlinear Partial Differential Equations ◽  
Mesh Size ◽  
Transient State ◽  
Taylor Instability ◽  
Multiphase Model ◽  
Element Analysis ◽  
Two Fluids ◽  
Rayleigh Taylor Instability

The purpose of this paper is to simulate a two-dimensional Rayleigh-Taylor instability problem using the classical method of Finite Element analysis of a multiphase model using ANSYS FLUENT 19.2. The governing equations consist of a system of coupled nonlinear partial differential equations for conservation of mass, momentum and phase transport equations. The study focuses on the transient state simulation of Rayleigh Taylor waves and subsequent turbulent mixing in the two phases incorporated in the model. The Rayleigh Taylor instability is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid in a gravitational field. The problem was governed by the Navier-Stokes and Cahn-Hilliard equations in a primitive variable formulation. The Cahn- Hilliard equations were used to capture the interface between two fluids systems. The objective of this article is to perform grid dependency test on Rayleigh Taylor Instability for 2 different mesh size and compare the results for the variation in Atwood Number. The results were validated with the observations from previous published literatures.

scholarly journals Nonlinear stage in the development of hydrodynamic instability in laser targets

1990 ◽  
Vol 8 (3) ◽  
pp. 399-407 ◽  
Author(s):  
E. G. Gamaly ◽  
A. P. Favorsky ◽  
A. O. Fedyanin ◽  
I. G. Lebo ◽  
E. E. Myshetskaya ◽  
...  
Keyword(s):  
Growth Rate ◽  
Laser Irradiation ◽  
Hydrodynamic Instability ◽  
Short Wave ◽  
Taylor Instability ◽  
Numerical Code ◽  
Linear Stage ◽  
Nonlinear Stage ◽  
Rayleigh Taylor Instability

The development of hydrodynamic instability in laser targets is studied by means of the 2D numerical code “ATLANT.” At the linear stage, perturbations grow as At the nonlinear stage, the growth rate of Rayleigh-Taylor instability is reduced and new harmonics are generated. The effect of the nonuniformity of laser irradiation has been investigated for long- and shortwave perturbations. The growth rate of short-wave perturbations may be effectively decreased by means of symmetrical prepulses.

scholarly journals A New Approach to the Rayleigh–Taylor Instability

2021 ◽  
Author(s):  
Björn Gebhard ◽  
József J. Kolumbán ◽  
László Székelyhidi
Keyword(s):  
Turbulent Mixing ◽  
Taylor Instability ◽  
General Criterion ◽  
New Approach ◽  
Two Fluids ◽  
Flat Interface ◽  
Rayleigh Taylor Instability ◽  
Incompressible Euler ◽  
Atwood Number ◽  
High Range

AbstractIn this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the constitutive laws we formulate a general criterion for the existence of infinitely many weak solutions which reflect the turbulent mixing of the two fluids. Our criterion can be verified in the case that initially the fluids are at rest and separated by a flat interface with the heavier one being above the lighter one—the classical configuration giving rise to the Rayleigh–Taylor instability. We construct specific examples when the Atwood number is in the ultra high range, for which the zone in which the mixing occurs grows quadratically in time.

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