Humpbacks sometimes extend their pectoral fins nearly straight up, above the surface. They are barely moving forward when they do it and it's just as though they are floating nearly motionless at the surface with their fins projecting high out of the water. It can be visually striking since each pectoral fin can be about eight feet long.
There's no reason to think the whales are really waving, at least, not at us; after all, their medium is the ocean, and if one pectoral fin is nearly straight up, the other is probably extended well below the whale. It seems more likely the lower pectoral is actually the "active" fin for the whale's purposes.
But on this early evening, when many of the photos in these whale posts were taken, after all the bubble-net feeding episodes, the participating whales seemed to be much more active than usual, displaying an assortment of gymnastic moves (including the synchronized spy hops shown in the last post). There were a lot of people watching, on perhaps ten whale boats of different sizes. So maybe the whales were waving at their admirers. Or maybe they were just celebrating a very successful feeding. It is an indication of the human tendency to be human-centric, even when watching a remarkably non-human animal, that many of the human observers audibly exclaimed that the whales "must be" engaging in gymnastic displays to entertain us and show their appreciation for our attention.
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Humpback pectorals, like flukes and other humpback surfaces, can bear various marks and distinguishing features, including barnacles, that sometimes allow the whales to be identified. Much closer crops of a photo show the distinctive marks on this whale's exposed pectoral fin.
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After a lifetime of mainly expressing myself with words, my postings here will mainly rely on images. They will speak for themselves to some extent, but I'll usually add a few comments of explanation. I've taken photographs for decades, since the 1950's, inspired in part by my father's photographic skill. Four years of photo assignments and quality darkroom time eventually gave way to decades of casual and family picture-taking. I re-immersed myself when I left film and turned to digital.