In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex lines. These theorems apply to inviscid flows and flows where the influence of viscous forces are small and can be ignored.
Helmholtz's three theorems are as follows:[1]
Helmholtz's theorems apply to inviscid flows. In observations of vortices in real fluids the strength of the vortices always decays gradually due to the dissipative effect of viscous forces.
Alternative expressions of the three theorems are as follows:
Helmholtz's theorems have application in understanding:
Helmholtz's theorems are now generally proven with reference to Kelvin's circulation theorem. However Helmholtz's theorems were published in 1858,[3] nine years before the 1867 publication of Kelvin's theorem.