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

Second-order structure functions for directionally spread waves (⁠⁠) 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 (⁠equation ⁠).

However, there is not decisive evidence of an inverse energy cascade for moderate directional spreads (⁠equation ⁠). 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.