  Shear-driven turbulence in the superfluid interior of a neutron star exerts a
fluctuating torque on the rigid crust, causing the rotational phase to walk
randomly. The phase fluctuation spectrum is calculated analytically for
incompressible Kolmogorov turbulence and is found to be red; the half-power
point is set by the observed spin-down rate, the crust-superfluid lag, and the
dynamical response time of the superfluid. Preliminary limits are placed on the
latter quantities using selected time- and frequency-domain data. It is found
that measurements of the normalization and slope of the power spectrum are
reproduced for reasonable choices of the turbulence parameters. The results
point preferentially to the neutron star interior containing a turbulent
superfluid rather than a turbulent Navier-Stokes fluid. The implications for
gravitational wave detection by pulsar timing arrays are discussed briefly.
