Turbulent dissipative coupling in nanoscale multimode superfluid acoustics

Abstract Superfluid helium, the inviscid low-temperature phase of liquid 4 He, enables investigation of flows with reduced dimensionality since, due to the vanishing viscosity, sub-micron flow channels can be constructed. In such strongly confined volumes filled with superfluid, the longitudinal acoustic wave is a coupled fluctuation of pressure and entropy density called fourth sound. In this work, we use multiple 4th sound acoustic modes inside a nano-superfluidic acoustic resonator in a pump–probe arrangement to observe localized clusters of quantized vortices leading to two-dimensional turbulence. The localised turbulence enables controllable and asymmetric dissipative coupling between acoustic modes. Furthermore, we derive a general procedure for analytically estimating the superfluid acoustic resonance frequencies inside a volume with mechanically compliant walls. Our work confirms earlier assumptions that turbulence in similar nanofluidic systems initially develops in localized areas of high shear. The multimode pump–probe methods presented here will allow future experiments to study the dynamics of two-dimensional quantum turbulence, e.g. the free decay.