Woods spent two years as a research fellow at St John's College and as a Green Scholar at the University of California, San Diego before taking up a lectureship for 5 years at the Institute of Theoretical Geophysics, Cambridge. After three years as professor of applied mathematics at University of Bristol, he was appointed BP Professor and head of the BP Institute, University of Cambridge.
His work is characterised by the development of simplified mathematical and experimental models of complex fluid flow processes covering a wide range of phenomena from the dynamics of explosive volcanic eruptions, to geothermal power generation, carbon sequestration and enhanced oil recovery in heterogeneous porous rocks. His work on the dynamics of mixing in turbulent buoyant plumes and gravity currents has led to new insights about the ascent height of volcanic eruption columns and the run-out distance of pyroclastic flow, as well as constraints on the dynamics of hydrothermal and oil plumes in the deep sea.[7]
He has also developed fundamental understanding of ventilation flows in buildings, developing strategies to minimise heat loss associated with low-energy natural ventilation, as well as exploring the controls on the dispersal of air-borne infection.[8] Other work has included modelling the dynamics of traffic flows, to elucidate controls on the collective behaviour of individual vehicles and strategies to regulate the flow.[8]