Helmholtz minimum dissipation theorem
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In fluid mechanics, Helmholtz minimum dissipation theorem (named after Hermann von Helmholtz who published it in 1868[1][2]) states that the steady Stokes flow motion of an incompressible fluid has the smallest rate of dissipation than any other incompressible motion with the same velocity on the boundary.[3][4] The theorem also has been studied by Diederik Korteweg in 1883[5] and by Lord Rayleigh in 1913.[6]
This theorem is, in fact, true for any fluid motion where the nonlinear term of the incompressible Navier-Stokes equations can be neglected or equivalently when , where is the vorticity vector. For example, the theorem also applies to unidirectional flows such as Couette flow and Hagen–Poiseuille flow, where nonlinear terms disappear automatically.