Sohail, Ayesha
(2012)
*Analysis of non-linear surface waves
induced by harmonic forcing in a flow cell.*
PhD
thesis, University of Sheffield.

## Abstract

An online measurement technique based on capacitance measurements has been used to study surface water waves induced by harmonic forcing propagating in a laboratory flow cell with dimensions of the order of a few centimeters. It has been postulated theoretically that such nonlinear dispersive waves propagating on an interface of length just a few multiples of the fluid depth satisfy an evolution equation with steeper nonlinearity than the conventional Korteweg-de Vries (KdV) equation for shallow water theory. In this thesis a nonlinear Fourier analysis is performed on time-series of surface displacement measurements made at two locations downstream of an oscillating membrane. Results from a discrete periodic inverse scattering transform based on the KdV equation, which decomposes a signal into soliton, cnoidal and sinusoidal components, indicate that whilst the amplitudes of linear modes are conserved as the disturbance propagates between the two sensors, the amplitudes of the nonlinear modes increase. This suggests that the nonlinearity of such surface waves is indeed stronger than that predicted by the KdV equation. The properties of harmonically induced surface waves propagating on surfactant solutions have also been studied. In particular the relationship between concentration and phase speed was investigated. A number of fluid samples were investigated, covering a range of concentrations from 0 to 10 mM. The effect of the physicochemical parameter β has also been considered. The phase speed of waves propagating on the surface of the liquid was found to decrease monotonically as the concentration of the solution considered was increased upto a limit of 4 mM, i.e. for 0 ≤ β ≤ 0.4. This was attributed to the corresponding decrease in Bond number. The phase speed of waves propagating on the surface of a liquid of concentration greater than 4 mM (0.4 < β < 1) was also investigated and the corresponding Marangoni effects relative to concentration gradients due to wave propagation were discussed.

Item Type: | Thesis (PhD) |
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Additional Information: | we need an embargo of 10 years |

Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |

Depositing User: | Mrs Ayesha Sohail |

Date Deposited: | 16 Oct 2012 10:22 |

Last Modified: | 08 Aug 2013 08:50 |

URI: | http://etheses.whiterose.ac.uk/id/eprint/2793 |