It will be shown how parameter-robust numerical methods can be used to solve equations that arise in the modelling of wave-current interactions. Two such models are presented: a complete flow model for wave-current interaction in the presence of weakly turbulent flow leading to an Orr-Sommerfeld type problem and a system of two singularly perturbed reaction-diffusion equations from a $k$-$\epsilon$ turbulence model.
The numerical results are compared with experimental data.