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The coupled dynamics of the two-fluid model of superfluid $^4$He isnumerically studied for quantum turbulence of the thermal counterflow in asquare channel. We combine the vortex filament model of the superfluid and theNavier-Stokes equations of normal fluid. Simulations of the coupled dynamicsshow that the velocity profile of the normal fluid is deformed significantly bysuperfluid turbulence as the vortices become dense. This result is consistentwith recently performed visualization experiments. We introduce a dimensionlessparameter that characterizes the deformation of the velocity profile.

Three-Dimensional Coupled Dynamics of Two-Fluid Model in Superfluid $^4$He: Deformed Velocity Profile of Normal Fluid in Thermal Counterflow