  Finite-temperature quantum turbulence is often described in terms of two
immiscible fluids that can flow with a non-zero mean relative velocity. Such
out-of-equilibrium state is known as counterflow superfluid turbulence. We
report here the emergence of a counterflow-induced inverse energy cascade in
three-dimensional superfluid flows by performing extensive numerical
simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of
the mean counterflow is increased, an abrupt transition, from a fully
three-dimensional turbulent flow to a quasi two-dimensional system exhibiting a
split cascade, is observed. The findings of this work could motivate new
experimental settings to study quasi two-dimensional superfluid turbulence in
the bulk of three-dimensional experiments. They might also find applications
beyond superfluids in systems described by more than one fluid component.
