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Whilst there are observational indications that transverse MHD waves carryenough energy to maintain the thermal structure of the solar corona, it is notclear whether such energy can be efficiently and effectively converted intoheating. Phase-mixing of Alfv\'en waves is considered a candidate mechanism, asit can develop transverse gradient where magnetic energy can be converted intothermal energy. However, phase-mixing is a process that crucially depends onthe amplitude and period of the transverse oscillations, and only recently havewe obtained a complete measurement of the power spectrum for transverseoscillations in the corona. We aim to investigate the heating generated byphase-mixing of transverse oscillations triggered by buffeting of a coronalloop that follows from the observed coronal power spectrum as well as theimpact of these persistent oscillations on the structure of coronal loops. Weconsider a 3D MHD model of an active region coronal loop and we perturb itsfootpoints with a 2D horizontal driver that represents a random buffetingmotion of the loop footpoints. Our driver is composed of 1000 pulsessuperimposed to generate the observed power spectrum. We find that the heatingsupply from the observed power spectrum in the solar corona through phasemixing is not sufficient to maintain the million degree active region solarcorona. We also find that the development of Kelvin-Helmholtz instabilitiescould be a common phenomenon in coronal loops that could affect their apparentlife time. This study concludes that is unlikely that phase-mixing of Alfv\'enwaves resulting from an observed power spectrum of transverse coronal looposcillations can heat the active region solar corona. However, transverse wavescould play an important role in the development of small scale structures.

Contribution of observed multi frequency spectrum of Alfv\'en waves to coronal heating