Kelvin's minimum energy theorem

In fluid mechanics, Kelvin's minimum energy theorem (named after William Thomson, 1st Baron Kelvin who published it in 1849^[1]) states that the steady irrotational motion of an incompressible fluid occupying a simply connected region has less kinetic energy than any other motion with the same normal component of velocity at the boundary (and, if the domain extends to infinity, with zero value values there).^[2]^[3]^[4]^[5]

^ Thomson, W. (1849). Notes on hydrodynamics. V. On the vis-viva of a liquid in motion. Camb. Dubl. Math. J, 4, 90-94.
^ Kelvin, W. T. B., & Tait, P. G. (1867). Treatise on natural philosophy (Vol. 1). Clarendon Press.
^ Lamb, H. (1932). Hydrodynamics. Cambridge university press.
^ Batchelor, G. K. (2000). An introduction to fluid dynamics. Cambridge university press.
^ Truesdell, C. (1954). The kinematics of vorticity (Vol. 954). Bloomington: Indiana University Press.

[1] Thomson, W. (1849). Notes on hydrodynamics. V. On the vis-viva of a liquid in motion. Camb. Dubl. Math. J, 4, 90-94.

[2] Kelvin, W. T. B., & Tait, P. G. (1867). Treatise on natural philosophy (Vol. 1). Clarendon Press.

[3] Lamb, H. (1932). Hydrodynamics. Cambridge university press.

[4] Batchelor, G. K. (2000). An introduction to fluid dynamics. Cambridge university press.

[5] Truesdell, C. (1954). The kinematics of vorticity (Vol. 954). Bloomington: Indiana University Press.

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