In a straight pipe flow, secondary flow patterns (i.e. perpendicular to the axis of the pipe) arise due to gravity in the form of two counterrotating vortices (or so I heard). But why is the dynamics at all changed in the presence of a gravitational field? Why isn't the pressure just modified in such a way that gravity is effectively cancelled? Gravity is a conservative force after all, so can be written as the gradient of a scalar field. Why isn't this scalar field just added to the pressure, resulting in a modified pressure, leaving the dynamics unchanged? Is this a stability issue, with the sketched scenario possible, but unstable?