Michael McIntyre has applied his fundamental theoretical research in geophysical fluid dynamics to the Earth's atmosphere and oceans and the Sun's interior. His contributions to the theory of stratified rotating fluid flow and the associated waves and instabilities have led to a unified view of the interaction of waves and mean flows. The theory has been used to illuminate a number of diverse phenomena, including Langmuir circulations, nonlinear baroclinic instabilities, jet streams, stratospheric sudden warmings, and the 27-month 'quasi-biennial' cycle in the equatorial stratosphere.

He has also worked on the magnetohydrodynamics of the solar tachocline, on musical acoustics, and on the connections between music, science, mathematics, and 'lucidity principles'. Recently, he has tried to synthesise a fresh view of the climate problem, now summarized in his 2022 book 'Science, Music, and Mathematics: The Deepest Connections' published by World Scientific.

Michael's work is widely regarded as seminal to our understanding of stratospheric dynamics and tracer transport, and has been recognised by the award of the Carl-Gustaf Rossby Research Medal, the highest honour of the American Meteorological Society, and the Julius Bartels Medal of the European Geophysical Society.