Manifestation of spurious currents and interface regularization in wind turbulence over fast-propagating waves

TL;DR

The study addresses spurious currents and interface-regularization in wind–wave simulations by comparing geometric isoAdvector and algebraic MULES VOF approaches. It demonstrates that curvature errors in isoPhi create sizable spurious currents, while RDF-based curvature estimation (plicRDF) markedly reduces these artifacts, though interface-regularization (as in gradPhi) introduces artificial mass flux. Through static and moving drops, solitary waves, and monochromatic wave tests, the work links numerical artifacts to phase-averaged wind–wave stress fields and validates against Buckley et al. data, showing improved fidelity with RDF but highlighting persistent turbulence underprediction and the need for higher resolution or alternative models in turbulent regions. The findings inform best practices for high wave-age simulations, underscoring accurate curvature handling and careful management of interface regularization to enhance predictive capability for environmental and engineering applications.

Abstract

Accurate simulation of wind turbulence over fast-propagating waves requires interface-capturing methods that suppress numerical artifacts while accurately resolving momentum transfer across the interface. In high wave-age regimes, numerical errors at the air-water interface can reach magnitudes comparable to the physical flow, directly affecting predicted turbulence statistics. This study examines widely used interface-capturing techniques to evaluate how spurious currents and interface regularization influence wind-wave simulations through curvature estimation and flux discretization. A systematic assessment is performed using static and translating droplet benchmarks, together with solitary and monochromatic wave cases, to identify and quantify the dominant numerical error mechanisms. In addition, comparison with experimental measurements reveals how these primary error sources manifest in coupled wind-wave simulations. These findings clarify the numerical origin of the observed discrepancies and underscore the importance of accurate curvature and flux treatment in high wave-age regimes.

Figures (20)

• Figure 1: A schematic of $\phi_p\text{-isoface}$.
• Figure 2: (a) Illustration of the wave-following coordinate system $(\xi,\zeta)$, with $\xi$ and $\zeta$ represented by red and black solid lines, respectively. The wave surface is indicated by the thicker black solid line. (b) Corresponding wave phase $\Phi$ (Eq. \ref{['eq:phase identification']}) of the signal shown in (a).
• Figure 3: Schematic of the triple decomposition. The phase-averaged field $\langle \mathbf{u} \rangle (\xi,\zeta)$ is obtained from $N_{\text{samples}}$ snapshots, and the velocity field is decomposed into the wave-independent component $\mathbf{\overline{u}}(\zeta)$ (Eq. \ref{['eq:wave independent component']}), the wave-coherent component $\mathbf{\widetilde{u}}(\xi,\zeta)$ (Eq. \ref{['eq:wave coherent component']}), and the turbulent component $\mathbf{u'}(x,y,z,t)$ (Eq. \ref{['eq:definition of pure turbulence']})
• Figure 4: Snapshots of static drop simulations using (a) isoPhi, (b) plicRDF, and (c) gradPhi at $t = 10.21t_\sigma$. Colormaps indicate the velocity magnitude, and black arrows represent the velocity vector field. The drop interface, defined by the $\phi = 0.5$ contour, is shown with red solid lines.
• Figure 5: Curvature (pink triangle lines) and pressure jump (black hexagram lines) extracted at $t = 10.21t_\sigma$ along the horizontal line $y = 0~\textnormal{m}$ (dotted lines) and the diagonal line $y = x$ (solid lines) for (a) isoPhi, (b) plicRDF, and (c) gradPhi. The phase indicator $\phi$ is shown in yellow circles. Vertical gray solid lines denote the expected interface location ($\phi = 0.5$), and horizontal gray-dashed lines indicate reference values for curvature and pressure jump.