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

Abstract

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.

Wave‐Driven Mean Flow Dynamics in Submerged Canopies

“…The nonhydrostatic (RANS‐based) wave‐flow model SWASH (version 5.01) was used, which is effectively a direct numerical implementation of the three‐dimensional Navier‐Stokes equations within a terrain following framework (Rijnsdorp et al, ; Smit et al, ; Zijlema et al, ). Here, the model was used in 2DV mode, for which the governing equations (momentum and continuity) are given by where f v , x is the (instantaneous) vegetation force, and ζ is the water surface elevation.…”

Numerical simulations of surf zone wave dynamics using Smoothed Particle Hydrodynamics

“…were obtained using laser Doppler anemometry (LDA) at 100 Hz at several cross-shore locations (8 and 7 locations for the spilling and plunging cases, respectively); note that due to the intermittent wetting / drying and presence of air bubbles during breaking, valid current measurements could not be obtained over the entire crest-to-trough region (only the lower portion). An additional advantage of the TK94 dataset is its historical use to assess the performance of a number of different models, which range from applications using Boussinesq wave models (e.g., Tissier et al, 2012, Cienfuegos et al, 2010, non-hydrostatic RANS models (e.g., Derakhti et al, 2016a, Rijnsdorp et al, 2017, Smit et al, 2013, and mesh-based CFD models such as OpenFOAM (e.g., Jacobsen et al, 2012, Brown et al, 2016, thereby providing an opportunity to place the present SPH simulations in the context of prior studies using other classes of models. was followed by a 1:8 beach covered with a porous mat to dissipate wave energy.…”

“…These studies include those using 3D / 2DV phase-resolving wave-flow models solved on fixed grids using the same TK94 experiments to benchmark model performance, which can therefore provide valuable context to the present SPH results. Rijnsdorp et al (2017) and Derakhti et al (2016a) applied the multi-layered non-hydrostatic model approach to evaluate its ability to reproduce the mean current profiles observed in TK94 (see Figure 6 in the first, and Figure 3 and 4 in the latter study). While both studies found that the nonhydrostatic approach could reproduce the main features of the current profiles reasonably well, the results deviated significantly more than in the present study, with both an overprediction of the onshore transport in the crest region (by a factor of 2 for the plunging case) and with a similar overprediction of the offshore undertow transport (i.e., defined by more exaggerated belly-shaped profiles).…”

“…For both the spilling and plunging cases, the model agrees reasonably well with the observations within the inner surf zone region (i.e., x>9 m and 10 m for the spilling and plunging cases, respectively); however, within the outer surf zone towards the break point, the model overpredicts the mean TKE. A number of CFD and non-hydrostatic model applications of TK94 have also compared TKE predictions (e.g., Jacobsen, 2011, Larsen and Fuhrman, 2018, Rijnsdorp et al, 2017, Brown et al, 2016, and have similarly found TKE to be significantly overpredicted when using conventional turbulence closure schemes within RANS-based models. This has motivated the application of more sophisticated closure models (e.g., Devolder et al, 2017, Brown et al, 2016 that consider, for example, the stabilizing effects of buoyancy due to entrained air, which has helped to improve model agreement; nevertheless, it is still widely recognized that there is considerable scope to further improve parameterization of sub-grid scale turbulence within surf zone applications within these models.…”

“…Multi-layered non-hydrostatic wave-flow models (e.g., Zijlema and Stelling, 2008, Bradford, 2010, Ma et al, 2012 describe the free-surface as a single-valued free-surface (akin to 2DH phase-resolving models). Although this simplification allows them to capture the dissipation of breaking waves and 3D flows more efficiently, it also implies that they cannot resolve all details of the breaking process such as wave overturning, and breaking wave-generated turbulence (e.g., Derakhti et al, 2016b, Rijnsdorp et al, 2017.…”