Engineering, 28.05.2020 20:57 sg3635939

A straight and non-moving linear vortex of the initial circulation 0 is submerged into a viscous fluid of viscosity  and density  , thus kinematic viscosity of  (think about a straight tornado just formed in air). Due to the viscous effects, the vorticity surrounding this vortex  evolves in time as a function of the above-mentioned parameters, the radial distance from the vortex center r and time t , i. e. 0  =  f r t ( , , , )  . 1. Using the concepts of dimensional analysis, find a dimensionless form of this function f. 2. Using the concept of self-similarity, find the self-similar form of this function f. 3. Explain why it is beneficial for an experimentalist to establish this form of self-similar function without solving Navier-Stokes equations or experimental measurements.

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A straight and non-moving linear vortex of the initial circulation 0 is submerged into a viscous fl...

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