Turbulent dissipative coupling in nanoscale multimode superfluid acoustics

Superfluid helium, the inviscid low-temperature phase of liquid \4He, 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.