- Perturbation theory
- Strongly nonlinear analysis
- Acoustic cavitation
Warren has pioneered the application of strongly nonlinear analysis to the Navier-Stokes equations. This analysis has succeeded in demonstrating that viscous effects always represent a singular perturbation for rotational flows even in the absence of interior/boundary layers.
Throughout his academic career, Warren has sought after multi-scale industrial topics. These allow the application of regular perturbation theory (for example, in laser percussion drilling) or singular perturbation theory (for example, in acoustic cavitation). The European Study Groups with Industry (ESGI), links with ECMI and interdisciplinary collaboration have provided sources for these projects. During his career, he has collaborated with mechanical engineers (Brunel, Oxford), electrical engineers (Nottingham), chemical engineers (Cornell, Eindhoven), physicists (Eindhoven) and biomedical engineers (Birmingham).