When the Froude number F of a free-surface flow ranges between 0.3 and 3, the flow is unstable and frequently characterised by free surface undulations, with the undular hydraulic jump being a seminal flow in hydro-environmental mechanics. The presence of the free surface undulations significantly affects the flow field, with major velocity and pressure field redistributions between successive crests and troughs. All the current theoretical models to simulate undular hydraulic jumps are limited to two-dimensional flow conditions, ignoring all the relevant three-dimensional flow effects, namely shock-wave drag, turbulent breaking and turbulent stresses. These aspects are critically accounted for in this review article, where a depth-averaged Boussinesq model which approximately accounted for 3D flow effects was presented, constituting the first attempt in this line. The model predictions were compared with experimental results from different sources for F₁ < 1.5, with F₁ the inflow Froude unnumber, resulting a reasonable agreement with observations. The curvature distribution parameter was found to controlling the wave length, and an approximate value was obtained based on ideal fluid flow computations. The new depth-averaged model did not include the effect of flow concentration in the centerline, observed physically, but this 3D feature is analysed at the first wave crest based on an improved treatment of flow curvature, highlighting the impact of the ratio q_CL/q on the velocity profile features with q_CL the centerline discharge. The main limitation of the new model, presented in this critical review, originated from approximating a complex 3D flow by a depth-averaged model. However, the predictions with the new approximate treatment of 3D effects produced better results than those previously reported.

当自由表面流的弗劳德数 F 介于 0.3 和 3 之间时，流动是不稳定的，并且经常以自由表面起伏为特征，其中不规则水跃是水环境力学中的一种开创性流动。自由表面起伏的存在显着影响流场，在连续的波峰和波谷之间具有主要的速度和压力场重新分布。目前所有模拟波浪形水跃的理论模型都仅限于二维流动条件，忽略了所有相关的三维流动效应，即激波阻力、湍流破坏和湍流应力。这些方面在这篇评论文章中得到了严格的解释，其中提出了一个深度平均的 Boussinesq 模型，该模型大致解释了 3D 流动效应，构成这一行的第一次尝试。将模型预测与来自不同来源的 F 的实验结果进行比较₁  < 1.5，F ₁流入弗劳德无数，结果与观察结果合理一致。找到控制波长的曲率分布参数，并基于理想流体流动计算获得近似值。新的深度平均模型不包括物理观察到的中心线流动集中的影响，但基于改进的流动曲率处理在第一个波峰处分析了该 3D 特征，突出了比率q _CL / q与q _CL的速度剖面特征中心线放电。本次批判性评论中提出的新模型的主要限制源于通过深度平均模型逼近复杂的 3D 流。然而，对 3D 效果进行新的近似处理的预测产生了比以前报告的更好的结果。