Free surface flows over submerged obstructions

Page, Charlotte (2015) Free surface flows over submerged obstructions. Doctoral thesis, University of East Anglia.

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Abstract

Steady and unsteady two-dimensional free surface flows subjected to one or multiple disturbances
are considered. Flow configurations involving either a single fluid or two layers
of fluid of different but constant densities, are examined. Both the effects of gravity and
surface tension are included. Fully nonlinear boundary integral equation techniques based
on Cauchy’s integral formula are used to derive integro-differential equations to model
the problem. The integro-differential equations are discretised and solved iteratively using
Newton’s method.
Both forced solitary waves and critical flow solutions, where the flow upstream is
subcritical and downstream is supercritical, are obtained. The behaviour of the forced
wave is determined by the Froude and Bond numbers and the orientation of the disturbance.
When a second disturbance is placed upstream in the pure gravity critical case,
trapped waves have been found between the disturbances. However, when surface tension
is included, trapped waves are shown only to exist for very small values of the Bond
number. Instead, it is shown that the disturbance must be placed downstream in the
gravity-capillary case to see trapped waves. The stability of these critical hydraulic fall
solutions is examined. It is shown that the hydraulic fall is stable, but the trapped wave
solutions are only stable in the pure gravity case.
Critical, flexural-gravity flows, where a thin sheet of ice rests on top of the fluid are
then considered. The flows in the flexural-gravity and gravity-capillary cases are shown
to be similar. These similarities are investigated, and the physical significance of both
configurations, examined.
When two fluids are considered, the situation is more complex. The rigid lid approximation
is assumed, and four types of critical flow are investigated. Trapped wave
solutions are found to exist in some cases, depending on the Froude number in the lower
layer.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: Vailele Chittock
Date Deposited: 29 Jan 2016 12:29
Last Modified: 29 Jan 2016 12:29
URI: https://ueaeprints.uea.ac.uk/id/eprint/56892
DOI:

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