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Weakly Nonlinear Rayleigh–Taylor Instability in Incompressible Fluids with Surface Tension

Funds: Supported by the National Natural Science Foundation of China under Grant Nos 11275031, 11475034, 11575033 and 11274026, and the National Basic Research Program of China under Grant No 2013CB834100.
  • Received Date: November 11, 2016
  • Published Date: March 31, 2017
  • A weakly nonlinear model is established for incompressible Rayleigh–Taylor instability with surface tension. The temporal evolution of a perturbed interface is explored analytically via the third-order solution. The dependence of the first three harmonics on the surface tension is discussed. The amplitudes of bubble and spike are greatly affected by surface tension. The saturation amplitude of the fundamental mode versus the Atwood number A is investigated with surface tension into consideration. The saturation amplitude decreases with increasing A. Surface tension exhibits a stabilizing phenomenon. It is shown that the asymmetrical development of the perturbed interface occurs much later for large surface tension effect.
  • Article Text

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