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We study non-axisymmetric oscillations of a straight magnetic tube with anelliptic cross-section and density varying along the tube. The governingequations for kink and fluting modes in the thin tube approximation arederived. We found that there are two kink modes, polarised along the large andsmall axes of the elliptic cross-section. We have shown that the ratio offrequencies of the first overtone and fundamental harmonic is the same for bothkink modes and independent of the ratio of the ellipse axes. On the basis ofthis result we concluded that the estimates of the atmospheric scale heightobtained using simultaneous observations of the fundamental harmonic and firstovertone of the coronal loop kink oscillations are independent of theellipticity of the loop cross-section.

Non-axisymmetric oscillations of stratified coronal magnetic loops with elliptical cross-sections