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.

scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

scholarly journals Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

2020 ◽  
Vol 634 ◽  
pp. A96
Author(s):  
E. Vickers ◽  
I. Ballai ◽  
R. Erdélyi
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Contact Discontinuity ◽  
Homogeneous Magnetic Field ◽  
Taylor Instability ◽  
Wide Range ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field ◽  
Theoretical Results

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit. Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation. Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.

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.

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.

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