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We perform a numerical analysis of counterflow quantum turbulence ofsuperfluid 4He with nonuni- form flows by using the vortex filament model. Inrecent visualization experiments nonuniform laminar flows of the normal fluid,namely, Hagen-Poiseuille flow and tail-flattened flow, have been observed.Tail-flattened flow is a novel laminar flow in which the outer part of theHagen-Poiseuille flow becomes flat. In our simulation, the velocity field ofthe normal fluid is prescribed to be two nonuniform profiles. This workaddresses a square channel to obtain important physics not revealed in thepreceding numerical works. In the studies of the two profiles we analyze thestatistics of the physical quantities. Under Hagen-Poiseuille flow,inhomogeneous quantum turbulence appears as a statistically steady state. Thevortex tangle shows a characteristic space-time oscillation. Undertail-flattened flow, the nature of the quantum turbulence depends strongly onthat flatness. Vortex line density increases significantly as the profilebecomes flatter, being saturated above a certain flatness. The inhomogeneity issignificantly reduced in comparison to the case of Hagen-Poiseuille flow.Investigating the behavior of quantized vortices reveals that tail-flattenedflow is an intermedi- ate state between Hagen-Poiseuille flow and uniform flow.In both profiles we obtain a characteristic inhomogeneity in the physicalquantities, which suggests that a boundary layer of superfluid appears near asolid boundary. The vortex tangle produces a velocity field opposite to theapplied superfluid flow, and, consequently, the superfluid flow becomes smallerthan the applied one.

Counterflow quantum turbulence of He II in a square channel: Numerical analysis with nonuniform flows of the normal fluid