Viscous transfer of momentum across a shallow laminar flow

In a shallow channel, the flow transfers most of its momentum vertically. Based on this observation, one often neglects that is transferred across stream – core assumption shallow-water theory. context viscous flows, approximation referred to as ‘lubrication theory’, in which assumes shear stress exerted by fluid substrate over it flows proportional velocity. Here, we revise theory account for viscosity laminar flow, while keeping problem low-dimensional. We then test revised lubrication against analytical and numerical solutions exact problem. find that, at low computational cost, present represents actual more accurately than classical approximation. This theoretical improvement, devised with laboratory rivers mind, should also apply other geophysical contexts, such ice or forming lava domes.