Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

- We propose a subgrid approach to efficiently resolve wave-induced currents in nonhydrostatic models.
- Model predictions are compared with laboratory experiments of surf zone waves.
- The model captures the wave evolution and mean flow profiles throughout the surf zone.
- The subgrid approach makes 3D applications of non-hydrostatic models feasible at field scales.

Wave-induced currents are an ubiquitous feature in coastal waters that can spread material over the surf zone and the inner shelf. These currents are typically under resolved in non-hydrostatic wave-flow models due to computational constraints. Specifically, the low vertical resolutions adequate to describe the wave dynamics - and required to feasibly compute at the scales of a field site - are too coarse to account for the relevant details of the three-dimensional (3D) flow field. To describe the relevant dynamics of both wave and currents, while retaining a model framework that can be applied at field scales, we propose a two grid approach to solve the governing equations. With this approach, the vertical accelerations and non-hydrostatic pressures are resolved on a relatively coarse vertical grid (which is sufficient to accurately resolve the wave dynamics), whereas the horizontal velocities and turbulent stresses are resolved on a much finer subgrid (of which the resolution is dictated by the vertical scale of the mean flows). This approach ensures that the discrete pressure Poisson equation - the solution of which dominates the computational effort - is evaluated on the coarse grid scale, thereby greatly improving efficiency, while providing a fine vertical resolution to resolve the vertical variation of the mean flow. This work presents the general methodology, and discusses the numerical implementation in the SWASH wave-flow model. Model predictions are compared with observations of three flume experiments to demonstrate that the subgrid approach captures both the nearshore evolution of the waves, and the wave-induced flows like the undertow profile and longshore current. The accuracy of the subgrid predictions is comparable to fully resolved 3D simulations - but at much reduced computational costs. The findings of this work thereby demonstrate that the subgrid approach has the potential to make 3D non-hydrostatic simulations feasible at the scale of a realistic coastal region.