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Shallow viscoplastic flow on an inclined plane

2002; Cambridge University Press; Volume: 470; Linguagem: Inglês

10.1017/s0022112002001660

1469-7645

N. J. Balmforth, R. V. Craster, Roberto Sassi,

Blood properties and coagulation

Evolving viscoplastic flows upon slopes are an important idealization of many flows in a variety of geophysical situations where yield stress is thought to play a role. For such models, asymptotic expansions suitable for slowly moving shallow fluid layers (lubrication theory) reduce the governing equations to a simpler problem in terms of the fluid thickness. We consider the version of the theory for fluids described by the Herschel–Bulkley constitutive law, and provide a variety of solutions to the reduced equation, both numerical and analytical. For extruded inclined domes, we derive the characteristic temporal behaviour of measures of the dome's dimensions.