A current flows at over adjacent slower water moving at in the same direction
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow
Fluid Dynamics, Ch Vorticity: its sources, its field and the motion of vortices
Problem
A current flows at 1.5ms−1 over adjacent slower water moving at 0.3ms−1 in the same direction. Model the thin boundary between them as a plane vortex sheet, treating the fluid as inviscid and ignoring the thickness of the boundary and any three-dimensional structure.
((a)) Find the strength qs of the sheet.
((b)) Find the velocity the sheet alone induces on each side, expressed as a departure from the mean of the two current speeds, and check that adding it to the mean recovers the two given speeds.