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Bubble and spike growth rate of Rayleigh Taylor and Richtmeyer Meshkov instability in finite layers

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Abstract

Growth rates of Rayleigh Taylor (RT) and Richtmeyer Meshkov (RM) instability arising at the perturbed interface of two fluid both of which are of finite extent (d h  = height of the upper heavier fluid and d l  = depth of the lower lighter fluid) are studied. It is found that the RT growth rate of bubble for a given height d h is nearly independent of d l but for RM, there exists a weak dependence. However, for both RT and RM spikes the dependence on d h and d l is quite appreciable. Analytic expressions of the growth rate for finite values of d h and d l are obtainable only in linear approximation and these agree with earlier results. Nonlinear approximation results are obtainable by numerical integration of set of nonlinear ordinary differential equations.

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Acknowledgments

This work is supported by the Council of Scientific and Industrial Research, Government of India under grant no. R-10/B/1/09.

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Authors and Affiliations

  1. St Paul’s Cathedral Mission College, 33/1, Raja Rammohan Roy Sarani, Kolkata, 700 009, West Bengal, India

    R. Banerjee

  2. Department of Instrumentation Science and Centre for Plasma Studies, Jadavpur University, Kolkata, 700 032, West Bengal, India

    R. Banerjee, L. Mandal, M. Khan & M. R. Gupta

Authors
  1. R. Banerjee
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  2. L. Mandal
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  3. M. Khan
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  4. M. R. Gupta
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Correspondence to M. Khan.

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Banerjee, R., Mandal, L., Khan, M. et al. Bubble and spike growth rate of Rayleigh Taylor and Richtmeyer Meshkov instability in finite layers. Indian J Phys 87, 929–937 (2013). https://doi.org/10.1007/s12648-013-0300-x

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  • DOI: https://doi.org/10.1007/s12648-013-0300-x

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