scholarly journals The Rayleigh–Taylor instability in a porous medium

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Lawrence K. Forbes ◽  
Catherine A. Browne ◽  
Stephen J. Walters
Keyword(s):  
Porous Medium ◽  
Nonlinear Model ◽  
Taylor Instability ◽  
Curvature Singularity ◽  
Heavy Fluid ◽  
Two Fluids ◽  
Partially Saturated ◽  
Linearized Theory ◽  
Rayleigh Taylor Instability ◽  
Horizontal Interface

AbstractThe classical Rayleigh–Taylor instability occurs when a heavy fluid overlies a lighter one, and the two fluids are separated by a horizontal interface. The configuration is unstable, and a small perturbation to the interface grows with time. Here, we consider such an arrangement for planar flow, but in a porous medium governed by Darcy’s law. First, the fully saturated situation is considered, where the two horizontal fluids are separated by a sharp interface. A classical linearized theory is reviewed, and the nonlinear model is solved numerically. It is shown that the solution is ultimately limited in time by the formation of a curvature singularity at the interface. A partially saturated Boussinesq theory is then presented, and its linearized approximation predicts a stable interface that merely diffuses. Nonlinear Boussinesq theory, however, allows the growth of drips and bubbles at the interface. These structures develop with no apparent overturning at their heads, unlike the corresponding flow for two free fluids.

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.

Density driven natural convection in a porous medium associated with Rayleigh-Taylor instability

2016 ◽  
Vol 2016 (0) ◽  
pp. I123
Author(s):  
Tetsuya Suekane ◽  
Yuji Nakanishi ◽  
Alexis Daniel Van Hoang Teston ◽  
Lei Wang
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Taylor Instability ◽  
Rayleigh Taylor Instability

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.

Rayleigh-Taylor Instability of Newtonian and Oldroydian Viscoelastic Fluids in Porous Medium

1994 ◽  
Vol 49 (10) ◽  
pp. 927-930
Author(s):  
R. C. Sharma ◽  
V. K. Bhardwaj
Keyword(s):  
Porous Medium ◽  
Interfacial Tension ◽  
Viscoelastic Fluids ◽  
Taylor Instability ◽  
Horizontal Boundary ◽  
Wave Numbers ◽  
Unstable Configuration ◽  
Rayleigh Taylor Instability

AbstractThe Rayleigh-Taylor instability of viscous and viscoelastic (Oldroydian) fluids, separately, has been considered in porous medium. Two uniform fluids separated by a horizontal boundary and the case of exponentially varying density have been considered in both viscous and viscoelastic fluids. The effective interfacial tension succeeds in stabilizing perturbations of certain wave numbers (small wavelength perturbations) which were unstable in the absence of effective interfacial tension, for unstable configuration/stratification.

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