Sunspots and the physics of magnetic flux tubes. V - Mutual hydrodynamic forces between neighboring tubes

The mutual hydrodynamic forces between parallel cylinders in a moving fluid are illustrated through several formal examples. Parallel tubes in a uniform flow are attracted or repelled depending on whether they are side by side or one ahead of the other, respectively. A pulsating or undulating tube attracts all other neighboring tubes toward itself. These hydrodynamic effects suggest that the separate flux tubes beneath the sunspots exert significant attractive forces on each other.