Quantum turbulence in the many-body regime

We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly interacting superfluids, often modelled by a mean-field theory governed by the Gross-Pitaevskii (GP) equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We indicate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.