Superfluid turbulence in a nonuniform circular channel

We have measured the dissipation associated with superfluid turbulence in a nonuniform channel of circular cross section in order to further explore the discrepancies with theory discovered previously in a nonuniform rectangular channels. Our data show that the two turbulent states supported in uniform circular channels (TI and TII) are also present in our experiments for either diverging or converging flow, indicating that this two-state structure is quite robust. The transition from laminar flow to the TI state and the transition from the TI to the TII state each occur at stationary turbulent fronts in the channel. One consequence of this phenomenon is that the TI/TII transition is substantially broadened. Our data for the TI state, when analysed assuming local uniformity, are in excellent agreement with previous results from uniform channels. The broadened TI/TII transition severely restricts our experimental access to the TII state. Nevertheless, our data are consistent with the same kind of modification to the vortex line density found for the nonuniform rectangular channels.