Motivation

Leaves drifting in streams and blowing in the wind belong amongst our root impressions of the natural world. Plumes discharging into streams and pumping from smoke stacks symbolize our impact on that world. Thus it is baffling when as students we discover that fluid dynamics is seemingly exclusively investigated by measuring pressure at fixed points. The manometers in our first fluids laboratories plainly measure total stagnation pressure; the mechanical flow meters less obviously strike a dynamical balance between the torque of the partial stagnation pressure on the turbine blades and the torque of friction in the turbine bearings. Our hands and faces do feel the rush of a stream or the sweep of the wind, but these are brute sensations in comparison to the incisive information processing at work when our eyes follows a flow marker.

This is a book about the role of kinematics in fluid dynamics. The most revealing mathematical framework for developing kinematics is the Lagrangian formulation, long ago discarded for being unwieldy compared to the Eulerian formulation (Tokaty, 1971). Yet the discarded unwieldiness owes precisely to the richness of the kinematical information. This book might have been written any time in the twentieth century; the motivation now is the emergence of Lagrangian observing technology. The emergence is of course a reemergence; meteorologists have been routinely tracking weather balloons with theodolites since the nineteenth century.