1. Introduction Given the title of this paper, it is incumbent on the authors to assure the reader that we do not claim to have done the impossible. A viscous fluid is, after all, a non-Hamiltonian system (Millikan Reference Millikan1929; Finlayson Reference Finlayson1972a,Reference Finlaysonb). There is no action integral for which Hamilton's principle (Hamilton Reference Hamilton1833, Reference Hamilton1834, Reference Hamilton1835) yields the Navier–Stokes equations (Stokes Reference Stokes184...