Surf Zone States and Energy Dissipation Regimes — A Similarity Model

A similarity parameter is derived to describe surf zone dissipation using the classical energy dissipation model for surf zone bores. This parameter can also be interpreted as a relative beach slope parameter, βγ, and, for shallow water sinusoidal waves, is the ratio of the local beach slope and the local wave steepness (H/L). βγ = 1 defines the boundary between two different energy dissipation regimes. Conditions with βγ < 1 represent over-dissipative conditions, where the classical bore dissipation model provides more dissipation than that required for depth-limited waves (constant H/h) to be maintained. Conditions with βγ > 1 represent under-dissipative conditions, where the bore model provides insufficient dissipation for depth-limited conditions to occur. Conditions with βγ = 1 at the breakpoint lead to locally saturated but not depth-limited surf. Hence, the new similarity parameter distinguishes between saturated and unsaturated surf conditions. Based on this bore dissipation model, an analytical model for the wave height transformation of monochromatic waves on planar beaches is derived. The cross-shore variation in wave height obtained from this model show different functional forms; concave upward for over-dissipative conditions and convex upward for under-dissipative conditions. Further, the analytical model shows that depth-limited conditions within the inner surf zone are not possible with this bore dissipation model and the model assumptions. Additional work is required to determine if this parameter is a useful predictor of other surf zone characteristics. Highlights: We derive a similarity parameter to describe surf zone dissipation. The similarity parameter defines the boundary of two dissipation regimes. The parameter distinguishes between saturated and unsaturated surf conditions. The classical bore dissipation model cannot predict depth-limited wave heights on a plane beach.