scholarly journals An Elementary Model for a Self-Accelerating Outward Propagating Flame Subject to the Rayleigh–Taylor Instability: Transition to Detonation

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 196
Author(s):  
Leonid Kagan ◽  
Gregory Sivashinsky
Keyword(s):  
Critical Level ◽  
Boussinesq Approximation ◽  
Taylor Instability ◽  
The Self ◽  
Pressure Shock ◽  
Elementary Model ◽  
Thermonuclear Supernovae ◽  
Rayleigh Taylor Instability ◽  
Detonation Transition ◽  
Transition To Detonation

Within the Boussinesq approximation, an elementary model for the deflagration-to-detonation transition triggered by self-acceleration of an expanding flame is formulated and explored. The self-acceleration is sustained by the intrinsic Rayleigh–Taylor instability until the Deshaies–Joulin deflagrability threshold is reached, followed by an abrupt transition to detonation. Emergence of the threshold is caused by positive feedback between the accelerating flame and the flame-driven pressure shock that results in the thermal runaway when the flame speed reaches a critical level. The model offers a simple mechanism that may be responsible for the transition to detonation in thermonuclear supernovae.

Rayleigh-Taylor Instability of a Stratified Plasma

1974 ◽  
Vol 29 (3) ◽  
pp. 518-523 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Boussinesq Approximation ◽  
Short Wave ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Disturbances ◽  
Magnetic Field Gradients ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

We have investigated the effect of finite Larmor radius on the Rayleigh-Taylor instability of a semi-infinite, compressible, stratified and infinitely conducting plasma. The plasma is assumed to have a one dimensional density and magnetic field gradients. The eigenvalue problem has been solved under Boussinesq approximation for disturbances parallel to the magnetic field. It has been established that for perturbation parallel to the magnetic field, the system is stable for both stable and unstable stratification. For perturbation perpendicular to the magnetic field, the problem has been solved without Boussinesq approximation. The dispersion relation has been discussed in the two limiting cases, the short and long wave disturbances. It has been observed that the gyroviscosity has a destabilizing influence from k = 0 to k = 4.5 for ß* = 0.1 and for ß* = 0.1 up to k* = 2.85 and then onwards it acts as a stabilizing agent. It has a damping effect on the short wave disturbances. For some parameters, the largets imaginary part has been shown in Figs. 1 and 2

Rotational suppression of Rayleigh–Taylor instability

2002 ◽  
Vol 457 ◽  
pp. 181-190 ◽  
Author(s):  
G. F. CARNEVALE ◽  
P. ORLANDI ◽  
YE ZHOU ◽  
R. C. KLOOSTERZIEL
Keyword(s):  
Coriolis Force ◽  
Boussinesq Approximation ◽  
Taylor Instability ◽  
Vortex Rings ◽  
Mixing Zone ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

It is demonstrated that the growth of the mixing zone generated by Rayleigh–Taylor instability can be greatly retarded by the application of rotation, at least for low Atwood number flows for which the Boussinesq approximation is valid. This result is analysed in terms of the effect of the Coriolis force on the vortex rings that propel the bubbles of fluid in the mixing zone.

scholarly journals Magnetic fields generated by the Rayleigh-Taylor instability

1986 ◽  
Vol 4 (3-4) ◽  
pp. 325-328 ◽  
Author(s):  
R. G. Evans
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Magnetic Fields ◽  
Taylor Instability ◽  
The Self ◽  
Magnetic Diffusion ◽  
Rayleigh Taylor Instability

In the absence of magnetic diffusion the self-generated magnetic field in a plasma is proportional to the fluid vorticity. The ratio of magnetic to fluid energy then shows that self-generated magnetic fields can only affect the Rayleigh Taylor growth rate for large k (wavelengths less then a few microns).

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