Decay of two-dimensional superfluid turbulence over pinning surface

We report on the free decay of quasi-two-dimensional turbulence in superfluid ⁴He confined within nanofluidic channels. Using a pump-probe technique, we observe a complex decay of the vortex density $L(t)$ that deviates from a simple power law. The decay exhibits a universal fast transient, scaling as L∝ t⁻², followed by a slower non-universal regime that depends on the geometry and flow conditions. We demonstrate that this behavior is governed by the interplay between vortex pinning on the disordered topography of the channel walls and the mobilizing effect of the weak probe flow. A numerical model that treats pinning as a velocity-dependent effective mutual friction successfully reproduces the essential features of our experimental observations.