The Fluid Dynamics of James Clerk Maxwell

We tend to think of Maxwell’s genius entirely in relation to his creation of electromagnetic theory (as summarised by Maxwell’s equations) on the one hand, and to his seminal development of the kinetic theory of gases (leading to the Maxwell-Boltzmann distribution, the derivation of transport coefficients like viscosity and thermal diffusivity for gases and associated validation of the continuum model) on the other. To do so is perhaps to neglect his extraordinary insights in other directions, notably in the dynamics of fluids, a field in which his publications were few but nevertheless groundbreaking in their originality. Some of these insights were not published at the time, but are now available through the wonderful three-volume publication of The Scientific Letters and Papers of James Clerk Maxwell (Harman 1990, 1995, 2003) on which I draw freely in the following discussion. Maxwell’s insights relate to centrifugal instability, to fluid-dynamical stability both in general and in particular application to the problem of Saturn’s rings, to Kelvin’s knotted vortices (in relation to which Maxwell played the role of amused commentator) and to the problem of Lagrangian particle displacement in an unsteady Eulerian flow, for which he provided perhaps the first explicit example. Fluiddynamical thinking was in fact intrinsic to Maxwell’s development of electromagnetic theory in the 1850s, and provided the initial framework upon which he constructed this theory, as evidenced by his first major paper in the subject On Faraday’s lines of force. His endeavours to express observed phenomena in mechanical terms lay at the heart of his thinking, and may help us to understand the development of a mind of extraordinary boldness and originality.