This is what we mean by waves. Many songbird species also migrate in loose flocks. There may be no robins in your area one day, and thousands the next morning. If these birds are passing through they may stay for a day or two or more, but then move on, more or less together. And then another group may arrive.
Weather needs to be part of the definition.
The sizes of migration waves relate directly to the intensity of the depression and strength of the favorable winds. This is why Laura says that suddenly seeing a bunch of robins one morning when there was no evidence of them the day before isn't really a wave in and of itself, but is evidence that a wave did pass. I've seen over 60,000 robins fly by in a single day along Lake Superior. This is a wave. Last time we saw that, in many areas, wintering robins feed mainly on dried up fruits and berries.