Experiments are described in which a heat current in a wide channel is suddenly increased from a small value
W
1
to a large value
W
2
; the time characterizing the build-up of the Gorter-Mellink mutual friction to its equilibrium value in the heat current
W
2
is studied as a function of
W
1
. Interpretation of the results on the basis of the idea that the mutual friction is associated with turbulence (in the form of vortex lines) in the superfluid shows that some mutual friction exists in the heat current
W
1
even when the latter is less than the critical value described in parts I and II, and that, as the channel width is increased or the temperature raised, the magnitude of the subcritical mutual friction increases until the critical heat current ceases to exist. It is shown that these observations on mutual friction in small heat currents can be described semi-quantitatively if a single term is added to the expression obtained in part III for the length of vortex line per unit volume in a heat current in a channel of infinite width, and that this term can probably arise either from an annihilation of vortex lines at the walls of the channel or from interference by the walls with the mechanisms of growth and decay of superfluid turbulence discussed in part III. Finally, an explanation is suggested of some of the results described in part II on the decay of mutual friction in the presence of a subcritical heat current.
Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels
