Vortex dynamics in the two-fluid model - art. no. 224504

We have used two-fluid dynamics to study the discrepancy between the work o f Thouless, Ao, and Niu (TAN) and that of Iordanskii. In TAN no transverse force on a vortex due to normal fluid flow was found, whereas the earlier w ork found a transverse force proportional to normal fluid velocity u(n) and normal fluid density rho (n). We have linearized the time-independent two- fluid equations about the exact solution for a vortex, and find three solut ions that are important in the region far from the vortex. Uniform superflu id flow gives rise to the usual superfluid Magnus force. Uniform normal flu id how gives rise to no forces in the linear region, but does not satisfy r easonable boundary conditions at short distances. A logarithmically increas ing normal fluid Row gives a viscous force. As in classical hydrodynamics, and as in the early work of Hall and Vinen, this logarithmic increase must be cut off by nonlinear effects at large distances; this gives a viscous fo rce proportional to u(n)/ln u(n), and a transverse contribution that goes l ike u(n)/(ln u(n))(2), even in the absence of an explicit Iordanskii force. In the limit u(n)-->0 the TAN result is obtained, but at nonzero u(n) ther e are important corrections that were not found in TAN. We argue that the M agnus force in a superfluid at nonzero temperature is an example of a topol ogical relation for which finite-size corrections may be large.