The Inflection-point theorem

It follows that U must change sign at least once across the fluid - i.e., there has to be an inflection point in the undisturbed velocity profile. 

The existence of an inflection point is therefore a necessary condition for instability, but it is not a sufficient condition. Indeed, there are some quite simple velocity profiles with one or more inflection points that are actually stable. Nevertheless, the inflection-point theorem is a useful starting point in assessing the potential of an inviscid flow for instability. If there is no inflection point, an inviscid fluid will be stable. Subsequent researchers have 

There are two possibilities for the role of viscous effects. One is that the system is unstable in the absence of viscous effects, but the latter stabilizes the system whenever the Reynolds number is below some critical value (which depends, of course, on the problem). The second is that the inviscid fluid is stable, but viscous effects act in such a way as to produce instability. 

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