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MHD waves permeate the solar atmosphere and constitute potential coronalheating agents. Yet, the waves detected so far may be but a small subset of thetrue existing wave power. Detection is limited by instrumental constraints, butalso by wave processes that localise the wave power in undetectable spatialscales. In this study we conduct 3D MHD simulations and forward modelling ofstanding transverse MHD waves in coronal loops with uniform and non-uniformtemperature variation in the perpendicular cross-section. The observedsignatures are largely dominated by the combination of the Kelvin-Helmholtzinstability (KHI), resonant absorption and phase mixing. In the presence of across-loop temperature gradient we find that emission lines sensitive to theloop core catch different signatures than those more sensitive to the loopboundary and the surrounding corona, leading to an out-of-phase intensitymodulation produced by the KHI mixing. Common signatures to all consideredmodels include an intensity and loop width modulation at half the kink period,fine strand-like structure, a characteristic arrow-shaped structure in theDoppler maps, overall line broadening in time but particularly at the loopedges. For our model, most of these features can be captured with a spatialresolution of $0.33\arcsec$ and spectral resolution of 25~km~s$^{-1}$, althoughsevere over-estimation of the line width is obtained. Resonant absorption leadsto a significant decrease of the observed kinetic energy from Doppler motionsover time, which is not recovered by a corresponding increase in the line widthfrom phase mixing and the KHI motions. We estimate this hidden wave energy tobe a factor of $5-10$ of the observed value.

Observational signatures of transverse MHD waves and associated dynamic instabilities