Linear velocity field 2026-10-25
An affine velocity field with zero uniform translation. It describes the relative motion about a comoving reference point even when the original velocity field has a nonzero spatially uniform component.
Past exam of the advanced fluid dynamics course of the University of Oxford 2024 2 c Solution 2026-10-25
Write the centre position as and the bead positions as . In the affine velocity field, . The midpoint follows the flow, so its two slip velocities areEach bead loses mechanical power times its squared slip speed. Adding the two powers proves the drag dissipation of a bead-spring pair:The factor one half comes from two equal-and-opposite bead slips, not from assigning only one bead a drag force.