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This study is motivated by observations of coordinated transversedisplacements in neighboring solar active region loops, addressing specificallyhow the behavior of kink motions in straight two-tube equilibria is impacted bytube interactions and tube cross-sectional shapes.We work with linear, ideal,pressureless magnetohydrodynamics. Axially standing kink motions are examinedas an initial value problem for transversely structured equilibria involvingtwo identical, field-aligned, density-enhanced tubes with ellipticcross-sections (elliptic tubes). Continuously nonuniform layers are implementedaround both tube boundaries. We numerically follow the system response toexternal velocity drivers, largely focusing on the quasi-mode stage of internalflows to derive the pertinent periods and damping times. The periods anddamping times we derive for two-circular-tube setups justify available modalresults found with the T-matrix approach. Regardless of cross-sectional shapes,our nonuniform layers feature the development of small-scale shears and energyaccumulation around Alf\'ven resonances, indicative of resonant absorption andphase-mixing. As with two-circular-tube systems, our configurational symmetriesmake it still possible to classify lower-order kink motions by the polarizationand symmetric properties of the internal flows; hence such mode labels as $S_x$and $A_x$. However, the periods and damping times for two-elliptic-tube setupsfurther depend on cross-sectional aspect ratios, with $A_x$ motionsoccasionally damped less rapidly than $S_x$ motions. We find uncertainties upto $\sim 20\%$ ($\sim 50\%$) for the axial Alfven time (the inhomogeneitylengthscale) if the periods (damping times) computed for two-elliptic-tubesetups are seismologically inverted with canonical theories for isolatedcircular tubes.

Damped kink motions in a system of two solar coronal tubes with elliptic cross-sections