Mathermatical modelling of gravity-driven flows in environmental settings

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It has been observed that, under certain conditions, the steady discharge of fluid in an open inclined channel does not result in the flow of a uniform fluid layer. Instead, the flow exhibits a series of intermittent bores along its surface, a pattern referred to as "roll waves". The occurrence of this phenomenon has important consequences in artificial conduits such as open aqueducts, run-off channels, and spillways from dams. The associated bores can damage flow control and flow measuring devices, and may be sufficiently high to raise the fluid level beyond the constraints of the channel. Naturally occurring flows along inclined surfaces can also involve roll waves. Mudflows, for example, generated in mountainous regions after intense rainy periods or initiated by volcanic eruptions can develop large intermittent bores that surge downhill with enough force to inflict extensive property damage and even loss of life. Furthermore, soil erosion is exacerbated by the significant increase in shear stress at the bottom of the fluid layer associated with the appearance of roll waves.