In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the $k$ – $\unicode[STIX]{x1D714}$ closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models ( $k$ – $\unicode[STIX]{x1D714}$ and $k$ – $\unicode[STIX]{x1D700}$ variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above $k$ is the turbulent kinetic energy density, $\unicode[STIX]{x1D714}$ is the specific dissipation rate, and $\unicode[STIX]{x1D700}$ is the dissipation.)

The performance of interFoam (a widely used solver within OpenFOAM®) in simulating the propagation of a nonlinear (stream function solution) regular wave is investigated in this work. It is demonstrated that over time there is a tendency for surface elevations to increase, wiggles to appear in the free surface, and crest velocities to become (severely) overestimated. It is shown that increasing the temporal and spatial resolution can mitigate these undesirable effects, but that a relatively small Courant number is required and fine discretization is needed, indicating that many past simulations have not converged. It is further demonstrated that discretization schemes and solver settings (often treated as a “black box” by users) can have a major impact on the results. This impact is documented, and it is shown that obtaining a “diffusive balance” is crucial to accurately propagate a surface wave over long distances without requiring exceedingly high temporal and spatial resolutions. Finally, the new code isoAdvector is demonstrated to produce comparably accurate results to interFoam, while maintaining a sharper surface. It is hoped that the present study will raise awareness of potential shortcomings of interFoam and enable a more accurate and optimal use, in CFD simulation of free surface waves.