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In this work we first briefly review some of the mutual friction effects onvortex lines and rings that were obtained in the context of the truncatedGross-Pitaevskii equation in references Krstulovic \& Brachet [Phys.~Rev.~E\textbf{83}(6), 066311 and Phys.~Rev.~B \textbf{83}132506 (2011)], withparticular attention to the anomalous slowdown of rings produced by thermallyexcited Kelvin waves. We then study the effect of mutual friction on therelaxation and fluctuations of Kelvin waves on straight vortex lines bycomparing the results of full $3D$ direct simulations of the truncatedGross-Pitaevskii equation with a simple stochasticLocal-Induction-Approximation model with mutual friction and thermal noiseincluded. This new model allows us to determine the mutual friction coefficient$\alpha$ and $\alpha'$ for the truncated Gross-Pitaevskii equation.

Kelvin waves, mutual friction, and fluctuations in the Gross-Pitaevskii model