There are a number of dualities in science, the wave vs. particle duality of quantum physics being the best known. Other dualities include continuous vs. granular, deterministic vs. stochastic and rationalist vs. empiricist. In recent times the advent of digital devices has favoured the continuous, the deterministic, and the rationalist elements of these dualities. Despite the fundamentally granular nature of digital devices, it is commonly assumed that continuous descriptions of natural phenomena can always be well-described by numerical models. This assumption has led, in turn, to the present predominance of deterministic and rationalist views of the physical world, i.e. to the belief that a Newtonian description of the physical world in terms of differential equations is the epitome of scientific discovery. The predictions of numerical models based on such equations always seems to trump observations, whose sole function is the post hoc validation of the model.
The failure of Maxwell’s Equations of Electromagnetism at high energy densities, The Ultraviolet Catastrophe, led to the new Quantum Physics of Boltzmann and Planck and to the understanding that a granular and stochastic description was required under these circumstances. However, one branch of Physics, Fluid Dynamics, experienced no such paradigm shift. In the present era, the failure of digital models based on the Navier-Stokes equations has become increasingly evident. These equations cannot account for turbulence nor for the increased entropy associated with turbulence. This is The Fluid Catastrophe.
Only by abandoning the smooth, deterministic “continuum” of rationalism and adopting an empirical approach to fluid behaviour can we understand turbulence.
Chapter 16 of The Fluid Catastrophe by John Reid