Two-dimensional inverse energy cascade in a laboratory surf zone for varying wave directional spread

Abstract

Surfzone eddies enhance the dispersion and transport of contaminants, bacteria, and larvae across the nearshore, altering coastal water quality and ecosystem health. During directionally spread wave conditions, vertical vortices (horizontal eddies) are injected near the ends of breaking crests. Energy associated with these eddies may be transferred to larger-scale, low-frequency rotational motions through an inverse energy cascade, consistent with two-dimensional turbulence. However, our understanding of the relationships between the wave conditions and the dynamics and energetics of low-frequency surfzone eddies are largely based on numerical modeling. Here, we test these relationships with remotely sensed and in situ observations from large-scale directional wave basin experiments with varying wave conditions over alongshore-uniform barred bathymetry. Surface velocities derived with particle image velocimetry were employed to assess the spatial scales of low-frequency surfzone eddies and compute structure functions with alongshore velocities. Second-order structure functions for directionally spread waves (σθ≥10°) are consistent with energy flux to larger or smaller length scales, while normally incident, unidirectional waves do not display this behavior. Third-order structure functions suggest that the surfzone flows exhibit a bidirectional energy cascade—a direct cascade to smaller and inverse cascade to larger length scales—during large directional spreads waves (σθ≥18°). However, there is not decisive evidence of an inverse energy cascade for moderate directional spreads (σθ=10°). Energy flux varies by cross-shore location and increases with increasing directional spread and wave height. Eddy decorrelation length scales weakly depend on wave directional spread. These findings advance our understanding of the dynamics linking wave breaking to large-scale rotational motions that enhance mixing and lead to rip currents, important conduits for cross-shore material exchange.