text: In the larger context of the Navier-Stokes equations (and especially in the context of potential theory), elementary flows are a collection of basic flows from which it is possible to construct more complex flows with different techniques. 
  In this article the term flows is used interchangeably to the term solutions due to historical reasons.
  The techniques involved to create more complex solutions can be 
  for example by superposition, by techniques such as topology or considering them as local solutions on a certain neighborhood, subdomain or boundary layer and to be patched together. Elementary flows can be considered the basic building blocks (Fundamental solutions, local solutions and solitons) of the different types of equations derived from the Navier-Stokes. Some of the flows reflect specific cases  constraints such as incompressible or irrotational flows, or both, as in the case of potential flow, and some of the flows are often limited in the case of 2 dimensions.
  Due to the relation from fluid dynamics to all field theory it is important to understand how all these flows are relevant not only to aerodynamics but to all field theory in general. To put it in perspective boundary layers can be interpreted as topological defects on generic manifolds, and considering fluid dynamics analogies and limit cases in electromagnetism, quantum mechanics and general relativity one can see how all these solutions are at the core of  recent developments in  theoretical physics such as the ads/cft duality, the SYK model, the physics of nematic liquids, strongly correlated systems and even to quark gluon plasmas.