My use case was:
A button in a parent component triggers a method call in a child component.
I couldn't find a solution in the nuxtjs docs. Eventually, I stumbled upon this thread:
solved my problem.
Ideally, a new page explains the available options for component communication: (this.$root.$emit, eventBus, …)
The new page could be available at https://nuxtjs.org/api/component-communiction
If this is a valid feature request I could write that page.