Richtmyer–Meshkov instability

The Richtmyer–Meshkov instability (RMI) occurs when two fluids of different density are impulsively accelerated. Normally this is by the passage of a shock wave. The development of the instability begins with small amplitude perturbations which initially grow linearly with time. This is followed by a nonlinear regime with bubbles appearing in the case of a light fluid penetrating a heavy fluid, and with spikes appearing in the case of a heavy fluid penetrating a light fluid. A chaotic regime eventually is reached and the two fluids mix. This instability can be considered the impulsive-acceleration limit of the Rayleigh–Taylor instability.[1]

Dispersion Relation

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For ideal MHD

 For Hall MHD

 For QMHD

 

History

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R. D. Richtmyer provided a theoretical prediction,[2] and E. E. Meshkov (Евгений Евграфович Мешков)(ru) provided experimental verification.[3] Materials in the cores of stars, like Cobalt-56 from Supernova 1987A were observed earlier than expected. This was evidence of mixing due to Richtmyer–Meshkov and Rayleigh–Taylor instabilities. [4]

Examples

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During the implosion of an inertial confinement fusion target, the hot shell material surrounding the cold DT fuel layer is shock-accelerated. This instability is also seen in magnetized target fusion (MTF).[5] Mixing of the shell material and fuel is not desired and efforts are made to minimize any tiny imperfections or irregularities which will be magnified by RMI.

Supersonic combustion in a scramjet may benefit from RMI as the fuel-oxidants interface is enhanced by the breakup of the fuel into finer droplets. Also in studies of deflagration to detonation transition (DDT) processes show that RMI-induced flame acceleration can result in detonation.

See also

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References

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  1. ^ Zhou, Ye (September 2021). "Rayleigh–Taylor and Richtmyer–Meshkov instabilities: A journey through scales". Physica D: Nonlinear Phenomena. 423: 132838. Bibcode:2021PhyD..42332838Z. doi:10.1016/j.physd.2020.132838. hdl:10871/124449. Retrieved 15 July 2022.
  2. ^ Richtmyer, Robert D. (1960). "Taylor Instability in a Shock Acceleration of Compressible Fluids". Communications on Pure and Applied Mathematics. 13 (2): 297–319. doi:10.1002/cpa.3160130207.
  3. ^ Meshkov, E. E (1969). "Instability of the Interface of Two Gases Accelerated by a Shock Wave". Soviet Fluid Dynamics. 4 (5): 101–104. Bibcode:1972FlDy....4..101M. doi:10.1007/BF01015969. S2CID 123494913.
  4. ^ "Richtmyer meshkov instability".
  5. ^ "On the collapse of a Gas Cavity by an Imploding Molten Lead Shell and Richtmyer–Meshkov Instability" Victoria Suponitsky, et al. General Fusion Inc, 2013
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