Title: A contemporary look at Hermann Hankel's 1861 pioneering work on Lagrangian fluid dynamics,
Abstract: The present paper is a companion to the paper by Villone and Rampf (2017),
titled "Hermann Hankel's On the general theory of motion of fluids, an essay
including an English translation of the complete Preisschrift from 1861"
together with connected documents. Here we give a critical assessment of
Hankel's work, which covers many important aspects of fluid dynamics considered
from a Lagrangian-coordinates point of view: variational formulation in the
spirit of Hamilton for elastic (barotropic) fluids, transport (we would now say
Lie transport) of vorticity, the Lagrangian significance of Clebsch variables,
etc. Hankel's work is also put in the perspective of previous and future work.
Hence, the action spans about two centuries: from Lagrange's 1760-1761 Turin
paper on variational approaches to mechanics and fluid mechanics problems to
Arnold's 1966 founding paper on the geometrical/variational formulation of
incompressible flow. The 22-year old Hankel - who was to die 12 years later -
emerges as a highly innovative master of mathematical fluid dynamics, fully
deserving Riemann's assessment that his Preisschrift contains "all manner of
good things."