Effect of submerged vegetation on water surface geometry and air-water momentum transfer

TL;DR

This study investigates how submerged vegetation affects water surface geometry and the transfer of momentum to the overlying air. Using fully resolved multiphase DNS with an immersed-boundary canopy and a deformable air–water interface, the authors compare vegetated and smooth-bed cases under identical forcing. They find that vegetation smooths interface deformations and regularizes spanwise wave fronts, yet the air-side momentum transfer, characterized by an unchanged equivalent roughness length ($y_s \approx 0.022 H$), remains essentially the same when expressed in appropriate log-law form; the interfacial slip velocity $U_{\text{int}}$ drops by ~40%, largely accounting for the observed similarity. The results imply that, in the fully rough regime, submerged vegetation can be neglected in atmospheric boundary-layer models regarding surface roughness, with the surface velocity at the interface as the key measurable parameter. This work provides quantitative guidance for nature-based coastal protections and improves understanding of air–sea coupling in vegetated environments.

Abstract

Understanding how submerged vegetation modifies the water surface is crucial for modeling momentum exchange between shallow waters and the atmosphere. In particular, quantifying its impact on the equivalent aerodynamic roughness of the water surface is essential for improved boundary-layer parameterization in oceanic and atmospheric models. In this Letter, we present fully resolved multiphase simulations of gravity-driven flow over a fully submerged vegetated bed, capturing the coupled dynamics of air, water, and individual plant stems, under quasi-realistic conditions (the air/water viscosity ratio is real, while the density ratio is reduced tenfold). Our results show that vegetation submerged for four times its height regularizes the water surface suppressing strong deformations and homogenizing streamwise-propagating wave fronts along the transversal direction. Despite these alterations, the equivalent roughness perceived by the overlying air flow remains unchanged. These findings clarify vegetation-surface interactions and provide quantitative insights for nature-based wave mitigation strategies and atmospheric boundary-layer modeling.

Figures (4)

• Figure 1: Simulation setup, showing the individually resolved stems of the submerged canopy and the turbulent air–water interface above. Relevant variables and parameters are sketched over an instantaneous realization of the system. Simulations capture the coupled dynamics of air and water, influenced by vegetation, to quantify how submerged canopies modify interface deformation.
• Figure 2: Visualizations of the turbulent structures (panels a,b) and interface deformation (panels c,d) above the smooth and vegetated bed in the left and right panels, respectively. In (a) and (b), red iso-surfaces denote regions of high streamwise velocity in the water, while in the air orange iso-surfaces correspond to fast fluid moving towards the interface and purple iso-surfaces to slow fluid rising upward. In (b) we also isolate Kelvin-Helmholts rollers in the water as brown iso-surfaces of the filtered pressure field (see main text for details). In (c) and (d) we color interface fluctuations from $-0.2H$ to $0.2H$ seen from the top with a linear colormap ranging from blue to green, with white at null values. The interface appears qualitatively more rippled in the smooth bed case, while in the vegetated bed case we appreciate the spanwise regularization of streamwise--propagating wave fronts over the underlying rollers.
• Figure 3: Characterization of the interface deformation. Panel (a) shows the probability density function of the interface elevation, while panel (b) refers to the different components of the surface normal $\hat{n}$, oriented upward. In panel (c) we present the joint probability density function of the normal components along the streamwise and spanwise directions, while in panel (d) we report the distribution of the Gaussian curvature $\mathcal{K}$. Vegetation preferentially alters interface deformation along the transverse direction, reducing intense fluctuations.
• Figure 4: Characterization of the surface roughness. In panel (a) we report the mean profiles of the streamwise velocity in the air: the collapse of the two curves highlights the negligible effect of submerged vegetation on the air flow. Results from the simulations of bernardini-etal-2014 over a flat rigid wall are reported as a dotted line, with the offset between those and our results quantifying the momentum deficit due to roughness. We report the fit with the log-law in equation \ref{['eq:genLogLaw']} as a gray dash-dotted line, and annotate the ratio between the equivalent roughness of the surface and the significant wave height above that. Our data are in good agreement with those of sullivan-etal-2000, reported in panel (a) as black squares. In panel (b) we show the integrated components of the shear stress balance (from equation \ref{['eq:shearBalance']} in the text).