Abstract
The behavior of nucleated vortex loops and of remanent vortex filaments in idealized circular and slit-like orifices has been investigated by direct computation. It is found that such vortices can be stretched by the diverging flow on the exit side of the orifice. The energy needed to stretch the vortex is abstracted from the flow field and observed as “dissipation”. This occurs in the form of discrete phase-slip events in the case of nucleated vortex loops, and in the form of multiple-phase-slip cascades when a remanent vortex is involved.
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References
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It is assumed here that the volume of fluid lying outsideS ±∞ is large compared to Ω, so thatv a is not significantly affected by the energy lost in a phase slip. On the other hand, Ω is assumed large enough so that the vortex field makes a negligible contribution to energy changes outside of Ω. Our argument is easily generalized to situations where these conditions are violated, but the results are then more complicated than those usually quoted.
We note that, in order for Φ to be a single-valued quantity, the vortex as it moves must trace out a surface across which Φ has a discontinuity of κ. Thus an event in which a vortex crosses all of the streamlines andv a is not changed significantly results in a decrease of κ in the velocity potential difference betweenS + andS −, or equivalently, in a 2π change in the phase difference. Hence, such an event is often referred to as aphase slip.
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