I'm curious if these scientists try to make the connection between the flow and the focused attention meditation. It seems to me that by trying to meditate, you are actually trying to get to the state of flow.
1. Samadhi/samatha or single pointed focus that calms or concentrates the mind.
2. vipashana/mindfullness/awareness that is looking inside the functioning mind and gains insight.
These two are not completely orthogonal. Even those who do pure awareness meditation develop the ability to keep their mind focused in this moment. In many traditions practitioners start with concentrative practice until they gain the so called 'access concentration' where they have the ability to stay in present moment without mind wandering too much. This access concentration is what I would call 'the flow'. You can go much deeper in concentration or use the flow to look into your mind. The flow itself is not the task. It's the first step.
In many/most Buddhist meditation traditions dedicated concentration practices are seen as tools and insight meditation seen as being more directly towards the goal of Buddhist meditation.
In Mahayana tradition developing deep concentration states is called Sharpening Manjusri’s sword. Using the sword is different than sharpening it.
I don't think the quiet mind phase is flow however. It is just that time disappears.
Meditation makes me peaceful and can provide me with more energy reserves for the rest of the day. Flow makes me satisfied but usually tired and at the same time wanting more flow.
So how do you HN participants see these different states?
For an obvious example, consider the kasina practice of old-school Theravada Buddhism.
http://web.archive.org/web/20031230220324/http://www.birken....
Breath concentration is done in a similar way, but with the sensation of the breath as the object of fixation rather than a colored disc.
In the case of mindfulness that is triggering some dismissiveness on your part, there is also abstract, settled, or awareness typed meditation. The latter, focusing on abstract, awareness of awareness (being a witness to your thoughts) without directing them can be just as useful to unlock creativity in day to day life.
Some meditative experiences are very similar to flow and allows the ability to slip into flow that much easier. Some folks can slip into meditation just sitting at their desk by closing their eyes and come out a few minutes later settled and focus in hand for something.