Helen Silverman, whose graduate work included a study of the social organization and behavior of narwhals, describes as typical the following scene, from her observations in Lancaster Sound. "On one occasion a group of five narwhals consisting of two adult males, one adult female, one [calf] and one juvenile were moving west with the males in the lead. The group stopped and remained on the surface for about 30 [seconds]. One male turned, moved under the [calf], and lifted it out of the water twice. There was no apparent reaction from the mother. The male then touched the side of the female with the tip of its tusk and the group continued westward."-- from Arctic Dreams by Barry Lopez (1986). I've had the good fortune to reread parts of this book over the last couple of days.