Following on from Lev D. Landau, Trevor Stuart is known for his work on nonlinear waves in the onset of turbulence in fluids. He also extended the work of Lord Rayleigh with research into steady streaming in unsteady viscous flows at high Reynolds numbers.

Trevor has received a number of awards and honours for his work, including the Senior Whitehead Prize of the London Mathematical Society in 1984 and the Otto Laporte Award of the American Physical Society in 1987. He was awarded honorary Doctor of Science degrees from Brown University in 1986 and the University of East Anglia in 1987.

He presented both the 1985 Stewartson and DiPrima memorial lectures in the United States, as well as the 1986 Ludwig Prandtl Memorial Lecture in Germany. He served as President of the LMS from 2000 to 2002. He has been the Editor of Royal Society publication Biographical Memoirs since 2012.