River Flow Induced Nonlinear Modulation of M₄ Overtide in Large Estuaries

River discharge is known to enhance tidal damping and tidal wave deformation in estuaries. While the damping effect on astronomical tides has been well documented, river impact on tidal wave deformation and associated overtide generation (shallow water harmonics of one or more astronomical constituents, such as M₄) remains insufficiently understood. Overtides affect tidal asymmetry, extreme water levels, and subsequent sediment transport and flooding management, thus meriting in-depth examination. Being inspired by unusual overtide changes in the landward and seaward parts of the Changjiang Estuary under low and high river discharges, in this work, we use a schematized tidal estuary model to systematically explore overtide variations under different river discharges. Model results show enhanced overtide generation in the case with river discharge compared with that without river impact. The M₄ amplitude decreases in the landward parts of the estuary, but increases in the seaward parts under increasing river discharges. The potential energy of M₄ integrated throughout the estuary shows nonlinear variations and reaches a transitional maximum when the river discharge to tidal mean discharge (R2T) ratio at the mouth is close to unity. Similar nonlinear behaviors are observed for compound tides like MS₄ when more astronomical constituents are prescribed and triad tidal interactions are enabled. The space-dependent overtide variability is more profound in large estuaries with high river discharges like the Amazon and Changjiang estuaries. It is ascribed to the inherently nonlinear river-tide interactions, specifically the twofold effects of river discharge in enhancing bottom stress, which simultaneously enhances dissipation of astronomical constituents and reinforces the energy transfer to overtides. These findings highlight the profound nonlinear impact of river discharge on overtides, and inform the study of tidal asymmetry and compound flood risk in large estuaries and deltas.