Diagnosis of residual flow drivers in estuaries with the densimetric tidal Froude number

Abstract

Diagnosis of Residual Flow Drivers in Estuaries with the Densimetric Tidal Froude Number

Residual circulation in estuaries drives salt intrusion, material transport, and ecosystem functioning. Yet the ability to diagnose its dominant forcing mechanism remains a challenge. While previous studies suggest that the densimetric tidal Froude number (Frt) may distinguish tidal from baroclinic forcing, its reliability across varying estuarine conditions and spatial scales requires systematic evaluation. This study investigates whether Frt can reliably diagnose the dominant drivers of residual circulation in estuaries by using a suite of process-oriented numerical simulations in an idealized estuary–shelf system with Gaussian cross-channel bathymetry. The model configuration spans a wide parameter space, including variations in tidal amplitude, channel depth, lateral slope, and river discharge. Residual circulation regimes are diagnosed using the ratio between the barotropic and baroclinic terms of the tidally averaged, axial momentum equation obtained from the model outputs, together with the transverse structure of residual flows, allowing direct comparison with Frt predictions. This study demonstrates, for the first time, that Frt can reliably diagnose the dominant driver of residual circulation when the density length scale is defined over the shortest feasible axial distances. Crucially, the results show that the skill of Frt is highly sensitive to this spatial scale: its performance deteriorates when the density gradient is computed over lengths that extend into regions with heterogeneous forcing. Across all simulations, Frt functions as a robust bulk indicator of tide-dominated, density-dominated, and near-balanced regimes only when the density scale is restricted to zones where the axial salinity gradient is approximately constant. Such zones consistently occupy the seaward side of the peak salinity gradient. Within this region, Frt emerges as a reliable diagnostic tool and offers practical value for field applications that require identifying the prevailing residual-flow driver. Tidally driven circulation is characterized by relatively high Frt values (0.53 ± 0.31), density-driven circulation by low values (−0.23 ± 0.16), and near-balanced regimes occupy a narrow transitional interval (0.12 ± 0.14) in which neither process exerts clear dominance. Future research may evaluate how these thresholds vary with the estuarine configuration.