Abstract
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 language | English |
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Pages (from-to) | 16-36 |
Number of pages | 21 |
Journal | Journal of Fluids and Structures |
Volume | 52 |
Early online date | 7 Nov 2014 |
DOIs | |
Publication status | Published - Jan 2015 |
Keywords
- Flexural waves
- Channel flow
- Nonlinear waves
Profiles
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Emilian Parau
- School of Mathematics - Professor of Applied Mathematics & Head of School
- Fluid and Solid Mechanics - Member
Person: Research Group Member, Academic, Teaching & Research
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Richard Purvis
- School of Mathematics - Associate Professor
- Fluid and Solid Mechanics - Member
Person: Research Group Member, Academic, Teaching & Research
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Robert Whittaker
- School of Mathematics - Lecturer in Applied Mathematics
- Fluid and Solid Mechanics - Member
Person: Research Group Member, Academic, Teaching & Research