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Kelvin's theorem of minimum kinetic energy

Kelvin has established the remarkable theorem that Laplacian flow has less kinetic energy than any other motion consistent with the same normal motion of the boundaries of the fluid. The proof is given by Lamb (Art. 45, p. 47).

A practical criterion can be immediately inferred from this theorem in connection with the foregoing example (Art. 1.13): the effective added mass, , is a minimum in the case of Laplacian flow around a cylinder. In the more usual case where turbulent flow exists in the neighborhood of the cylinder, we should expected to find that

for a circular cylinder.


next up previous contents
Next: Addition of velocity potentials Up: Kinematics of Fluids Previous: Application of the boundary

Steve Baum
Mon Dec 1 08:50:29 CST 1997