I don't know a whole lot about Zen meditation, but what I do know is that you breathe and let your thoughts run through you. You notice, let go, breathe.
It's a wonderful way to get distance from a busy mind. I recommend the Zen meditation to my psychic reading clients as a way to separate from their worry thoughts when they are going through a hard time.
Of course, I do the same myself, just breathe when a bunch of thoughts--for me usually way too many ideas of things I'd love to create--come up.
However, most recently something interesting has happened. Simply, it struck me as a real thing how useless most of my thoughts are. I kind of feel bad saying that. The reason is from another perspective, the therapy perspective, we do want to notice those thoughts and use them, constructively, one would hope. So I am talking about a slightly different context for my thoughts.
I have experienced a deeper layer of being. You might call it soul level, God level. At this level everything is productive and constructive.
Having experienced this level of being, and from this perspective, the casual thoughts that go nowhere really do appear as just static.
So, most recently I've learned to let them arise and disappear without investigating their meaning. In this context, and these types of thoughts, there isn't much to investigate, really. An investigation would just confuse things, take me away from the deeper truth. And it would lead nowhere.
The result of this change is that I feel hugely unburdened; I don't have to carry all that weight of my thoughts. I can let them go. Phew!