Abstract
Fluid fibres and jets are described, in general, by free boundary Navier Stokes problems. If the ratio of the cross section of the jet is small compared to the axial length scale of the jet or fibre, then the free boundary problem can be significantly simplified, and a greatly simplified system of (nonlinear) partial differential equations obtained. In this paper, the broad outline of the method will be discussed, with reference to the problem of tapering optical fibres of arbitrary cross sectional shape and with reference to symmetric fluid jets. In the latter case, further analysis is possible by looking for transformations that reduce the partial differential equations to ordinary differential equations.
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