Engineering, 06.06.2020 01:57 Melleeroo

A straight and non-moving linear vortex of the initial circulation |-0, is submerged into a viscous fluid of viscosity mu and density p, thus kinematic viscosity of v (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. 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...