Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations

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We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub ... continued below

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Mikaelian, K O September 28, 2009.

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We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.

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PDF-file: 65 pages; size: 2.3 Mbytes

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  • Journal Name: Physical Review E, vol. 81, no. 2, January 1, 2010, pp. 016325-1 to 016325-16; Journal Volume: 81; Journal Issue: 2

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  • Report No.: LLNL-JRNL-417610
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 978901
  • Archival Resource Key: ark:/67531/metadc927609

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  • September 28, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 6, 2016, 7 p.m.

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Mikaelian, K O. Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations, article, September 28, 2009; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc927609/: accessed April 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.