Long-Distance/Time Surf-Zone Tracer Evolution Affected by Inner-Shelf Tracer Retention and Recirculation

The evolution of a surf-zone released tracer (approximate to 100 $\approx 100$ Liter over 4 hr) was observed for approximate to 30 $\approx 30$ h. Surf-zone tracer was transported alongshore (y) with relatively steady mean speed v(SZ) approximate to 0.18 m s(-1), consistent with obliquely incident wave forcing. Maximum in situ surf-zone tracer concentration decayed exponentially with 1.6 km alongshore e-folding length scale, that is, 2.5 hr advective time scale. Surf-zone tracer time-series evolved downstream of the release from a top-hat structure for y <= 1 km to increasingly skewed farther downstream. Within approximate to 1.5 $\approx 1.5$ km of the northward propagating tracer front, inner-shelf tracer was confined to onshore of approximate to 4LSZ $\approx 4{L}_{\mathrm{S}\mathrm{Z}}$ (surf-zone width L-SZ approximate to 100 m) and was alongshore patchy. A coupled surf-zone/inner-shelf tracer advection-diffusion-exchange box model reproduces the observed surf-zone downstream max concentration decay and temporal skewness, with surf-zone flushing time kSZ-1 approximate to 2.3 ${k}_{\mathrm{S}\mathrm{Z}}<^>{-1}\approx 2.3$ h. A weaker inner-shelf unidirectional-exchange rate k(IS) approximate to k(SZ)/2 indicates reduced horizontal mixing outside the surf-zone. Surf-zone temporal skewness is linked to inner-shelf tracer storage, differential surf-zone/inner-shelf advection, and recirculation, that is, non-asymptotic shear dispersion. On the inner-shelf (approximate to 3LSZ $\approx 3{L}_{\mathrm{S}\mathrm{Z}}$), tracer vertical structure differed in the morning versus afternoon suggesting internal tide and solar forced thermal modulation. Model parameters representing surf-zone processes are well constrained by existing observations and scales. However, the many overlapping inner-shelf processes make a single process based generalization of inner-shelf cross-shore exchange rate (i.e., k(IS)) and alongshore transport difficult.