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We report preliminary results of the complementary experimental and numericalstudies on spatiotemporal tangle development and streamwise vortex line density(VLD) distribution in counterflowing $^4$He. The experiment is set up in a longsquare channel with VLD and local temperature measured in three streamwiselocations. In the steady state we observe nearly streamwise-homogeneous VLD.Experimental second sound data as well as numerical data (vortex filamentmethod in a long planar channel starting with seeding vortices localized inmultiple locations) show that the initial build up pattern of VLD displayscomplex features depending on the position in the channel, but the some tangleproperties appear uniform along its length.

Transition to turbulence and streamwise inhomogeneity of vortex tangle in thermal counterflow