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We study the coupled dynamics of normal and superfluid components of thesuperfluid $^4$He in the channel considering the counterflow turbulence withlaminar normal component. In particular, we calculated profiles of the normalvelocity, the mutual friction, the vortex line density and other flowproperties and compared them to the case when the dynamic of the normalcomponent is "frozen". We have found that the coupling between the normal andsuperfluid components leads to flattening of the normal velocity profile,increasingly more pronounced with temperature, as the mutual friction, andtherefore coupling, becomes stronger. The commonly measured flow propertiesalso change when the coupling between two components is taken into account.

Coupled dynamics for superfluid $^4$He in the channel