Dynamics and scaling of a small river discharging into the surf zone

We use an idealized numerical model to investigate the dynamics and fate of a small river discharging into the surf zone. Our study reveals that the plume reaches a steady state, at which point the combined advective and diffusive freshwater fluxes from the surf zone to the inner shelf balance the river discharge. At steady state, the surf zone is well-mixed vertically due to wave-enhanced vertical diffusion and has a strong cross-shore salinity gradient. The horizontal gradient leads to a cross-shore buoyancy-driven circulation, directed offshore at the surface and onshore near the bottom, which opposes the wave-driven circulation. Using a scaling analysis based on momentum and freshwater budgets, we determine that the steady state alongshore plume extent (𝐿𝑝) and the fraction of river water trapped in the surf zone depend on the ratio of the near-field plume length to the surf zone width (𝐿𝑛 𝑓 /𝐿𝑠𝑧) across a wide range of discharge and wave conditions. This scaling also allows us to predict the residence time and freshwater fraction (or dilution ratio) in the steady-state plume, which range from approximately 0.1 to 10 days and 0.1 to 0.3, respectively. Our findings establish the basic dynamics and scales of an idealized plume in the surf zone, as well as estimates of residence times and dilution rates that may provide guidance to coastal managers.

本研究采用理想化数值模型，探究汇入碎波带（surf zone）的小型河流径流的动力过程与归宿。研究结果表明，该羽流（plume）会达到稳态：此时从碎波带向陆架内缘输运的平流与扩散淡水通量之和，与河流径流量达到平衡。稳态下，受波浪强化的垂向扩散作用影响，碎波带内垂向混合充分，且存在显著的跨岸盐度梯度。该水平盐度梯度会驱动形成跨岸浮力环流：表层水流向海，近底水流向岸，与波浪驱动的环流方向相反。本研究基于动量收支与淡水收支开展尺度分析，结果表明：在广泛的径流与波浪条件范围内，稳态下的沿岸羽流范围（𝐿𝑝）以及滞留于碎波带的河流水体占比，取决于近场羽流长度与碎波带宽度的比值（𝐿ₙ𝑓/𝐿ₛ𝑧）。该尺度分析框架还可用于预测稳态羽流的驻留时间与淡水占比（或稀释比），二者的取值范围分别约为0.1至10天，以及0.1至0.3。本研究的结果明确了碎波带内理想化羽流的基本动力过程与尺度特征，同时给出了驻留时间与稀释率的估算值，可为海岸管理者提供参考依据。