Nonlinear flexural waves in fluid–filled elastic channels

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Nonlinear waves on liquid sheets between thin infinite elastic plates are studied analytically and numerically. Linear and nonlinear models are used for the elastic plates coupled to the Euler equations for the fluid. One-dimensional time dependent equations are derived based on a long-wavelength approximation. Inertia of the elastic plates is neglected, so linear perturbations are stable. Symmetric and mixed-mode travelling waves are found with the linear plate model and symmetric travelling waves are found for the nonlinear case. Numerical simulations are employed to study the evolution in time of initial disturbances and to compare the different models used. Nonlinear effects are found to decrease the travelling wave speed compared with linear models. At sufficiently large amplitude of initial disturbances, higher order temporal oscillations induced by non-linearity can lead to thickness of the liquid sheet approaching zero.
Original languageEnglish
Pages (from-to)16-36
Number of pages21
JournalJournal of Fluids and Structures
Early online date7 Nov 2014
Publication statusPublished - Jan 2015


  • Flexural waves
  • Channel flow
  • Nonlinear waves

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