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Abstract In some recent publications (Taylor 1937; Taylor and Green 1937) the author has put forward the view that the high average vorticity which is known to exist in turbulent motion is caused by the extension of vortex filaments in an eddying fluid. Let A and B be two particles a short distance, d0, apart on a vortex line where the vorticity is ω0. At a subsequent time when the distance between A and B has changed from d0 to d and the vorticity from ω0 to ω then, neglecting the effects of viscosity, the equation representing the conservation of circulation is ω/ω0 = d/d0. (1) Turbulent motion is found to be diffusive, so that particles which were originally neighbours move apart as the motion proceeds. In a diffusive motion the average value of d2/d20 continually increases. It will be seen therefore from (1) that the average value of ω2/ω20 continually increases. An equation for the average rate of increase in ω2 has been given by v. Karman (1937) which contains the term ω2 ∂u3/∂x3, where the bar shows that the average value has been taken and ∂u3/∂x3 represents the rate of stretching of vortex filaments.
Geoffrey Ingram Taylor (Fri,) studied this question.