Fluid mechanics, one of the oldest branches of continuum mechanics, is still full of life. However, it is too often taught in a very formal way, with a heavy insistence on the analytical formulation and on peculiar solutions of the equations. But it has been recognized for a long time that many of the “classical results” are of little or no help for understanding real flows. This was to the great disappointment of G.I. Taylor who realized that the niceties of Rayleigh's stability theory of parallel flows were off the mark most of the time, but that made him happier at last to see his theory of the Taylor–Couette instability explain his experiments. Perhaps the best example of the irrelevance of classical stability theory is that it predicts the most simple shear flow –the plane Couette flow – to remain always linearly stable, although it becomes experimentally highly turbulent as soon as the Reynolds number goes beyond a few hundreds.

There is a curious example of what might be called conservatism in the exposition of fluid mechanics. Around the time of World War I, Henri Bénard in Paris did very careful experiments on the wake behind a cylinder. He basically showed that this wake changes around Reynolds 40–50 from stationary to time periodic, something now called a Poincaré– Andronov bifurcation.