He is notable for theoretical and experimental contributions in various subjects such as wave motion, oceanography, magneto-hydrodynamics, rotating fluids, bio-fluid dynamics, mixtures, centrifugal separation and multi-phase flows.
Along his career, Greenspan was a member of the American Academy of Arts and Sciences (1966), a Visiting Professor and Fairchild Scholar at the Caltech (1987), received an Honorary Doctorate at the Royal Institute of Technology in Stockholm (1991), and was a long time consultant to industry and government and an editor of the 'Studies in Applied Mathematics' journal.
The result of this investigation, a now classical exact solution of the nonlinear theory, established conditions for the breaking of waves and as such remains a key element of tsunami research.
His study of the interaction of fluids and electromagnetism, was among the earliest in the field of magneto-hydrodynamics to describe the structure and role of the complex boundary layers, and the upstream precursor caused by the propagation of Alfvén waves.
[3] Scientific interests and industrial experience was synthesized in a patent for a centrifuge that separates, sorts and fractionates different particle species of a mixture in a truly continuous manner by means of an internal cascade of particle/flow diversions.