Who can submit papers to peer-reviewed journals? Financial terms, content quality, etc, is not a problem. The author has a contribution that will significantly impact the advancement of human knowledge about a particular topic.

Can anyone submit a paper? Or does it require some affiliation with a larger group such as an educational/governmental/corporate institution?

I am talking about journals of such clout as the Journal of Fluid Mechanics, Physics of Fluids, etc.
Anyone can submit a manuscript to a peer reviewed journal. The challenge that face persons without training in scientific writing through, for example, a PhD, is that the manuscript is probably far more likely to be rejected because of poor writing or other mistakes. The key issues for authoring a good paper is to have a good grip on the literature in the field, knowing the sources that should be referenced to provide the basis for the own work, to know how to write clearly, concisely and precisely, and to understand any specific publishing aspects of the field. 

It is not rocket science but usually requires both good coaching and training. Approaching the authoring with care is therefore a good strategy.