Yes, sometimes the younger birds and their potential new mates and even family members from several years will try to return. Sometimes not always, but sometimes the returnees will be tolerated during the migratory/winter season when food and other resources are limited. However, once mating and nesting season begins, they will once again be chased from the area.

The flapping in the water could be bathing, chasing or fighting. Without seeing the behavior or the context of the actions, it is difficult to distinguish exactly what was occurring. But, any of these behaviors associated with flapping wings is certainly normal and frequent behavior in the world of a swan. The Regal Swan