Floquet Stability Analysis of a Two-Layer Oscillatory Flow near a Flexible Wall

  • Barcenas-Luque, Antonio Jose (Universidad de Granada)
  • Martinez-Bazan, Carlos (Universidad de Granada)
  • Gutierrez-Montes, Cándido (Universidad de Jaén)
  • Coenen, Wilfried (Universidad Calos III de Madrid)

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Floquet stability analysis of a two-layer oscillatory flow near a flexible wall has been carried out. Two layers of the same fluid are separated by a flexible wall whose deformation is taken to be linearly proportional to the pressure difference across it. An oscillatory linear pressure gradient per unit of length drives an oscillatory motion parallel to the walls. The critical Reynolds number at which the problem becomes unstable and the corresponding wave number are characterized as a function of the control parameters, namely the membrane stiffness, and the dimensionless widths, $H_1$ and $H_2$. The occurrence of the instability strongly depends on the value of the dimensionless stiffness $\mathcal{K}$.