A body of water is a contiguous group of adjacent water sites, regardless of who controls those sites.
If a card refers to "its body of water" or "this body of water" (e.g. or ), it means the body of water occupied by that card. If that card doesn't currently occupy a body of water, then it doesn't have a body of water.
To choose a body of water (e.g. ), choose one water site. Every water site (regardless of controller) that's connected to the chosen site via adjacent water sites is in that body of water. If a site becomes disconnected from the chosen water site (e.g. in the middle of the turn), the disconnected site is no longer in the body of water. If the chosen site is no longer a water site (e.g. in the middle of the turn), then the "chosen body of water" no longer exists.