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.