Pulse interactions in falling liquid films

Round, Alexander Luigi (2024). Pulse interactions in falling liquid films. PhD thesis The Open University.


Thin liquid films are often found in many physical settings and thus fully understanding the dynamics and learning how to predict the behaviours that arise can become vital. Moreover, we see the emergence of coherent structures, namely solitary pulses which are found to be interacting in the system along the surface of the flat film. This thesis highlights work around solitary pulses along a falling liquid film by making use of a Weighted Integral Boundary Layer (WIBL) model to show the behaviour. We make use of numerical and analytical methods to analyse the interactions between these solitary pulses to better distinguish what occurs when these structures arise. By looking locally in the area around the pulses we can simplify models and provide the ability to lower computational cost of coding because we can isolate the mechanism that is responsible for the behaviours. This method also allows for analytical statements to hold true. This work focusses on a relatively strong interaction between the pulses that exist on the surface of these flows and this is the main difference to the previous work that focus on interactions between the pulses. It can be shown through spectral properties, namely a linearised operator, that we can isolate eigenvalue behaviours that identify a Hopf bifurcation within the system. Numerical work provides a method to systematically change parameters within the system to isolate the emergence of oscillatory behaviour alongside decaying oscillations. These behaviours can be observed to occur over stability branches that can be found using an energy potential function which allows for further predictions on the stability of the system. Finally we discuss the effects that can be seen when multiple pulses are considered in the system. We locate a regime in which chaotic behaviour is observed that can be quantified in terms of positive Lyapunov exponents.

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