Abstract Two-dimensional (2D) local scour beneath two submarine pipelines in tandem under wave-plus-current conditions is investigated numerically. A fully-coupled hydrodynamic and morphologic model based on unsteady Reynolds-averaged Navier-Stokes (URANS) equations with the k − ω turbulence closure is applied. The model is validated against existing experimental measurements involving live-bed scour beneath a single pipeline and beneath two pipelines in tandem, respectively. The model is then employed to simulate scour beneath two tandem pipelines under wave-plus-current conditions for a variety of Keulegan-Carpenter ( K C ) numbers and relative current strengths. Horizontal gap ratios (the horizontal gap distance between two pipelines divided by the pipeline diameter) ranging from 1 to 4 are modelled. It is found that for conditions involving waves plus a low-strength current, the scour pattern beneath two pipelines behaves like that in the pure-wave condition. Conversely, when the current has equal strength to the wave-induced flow, the scour pattern beneath two pipelines resembles that in the pure-current condition. It is also observed that in the pure-wave condition the equilibrium scour depth beneath each pipeline is affected by both K C and the horizontal gap ratio, except for K C = 5.6 . For such a small K C , the horizontal gap ratio has insignificant influence on the equilibrium scour depth, since vortex shedding does not occur. When the current strength relative to the waves is low, the scour development beneath the upstream and the downstream pipelines are similar. However, when the current has equal strength to the waves, the scour development beneath the downstream pipeline has a different pattern to that upstream. Namely, smaller horizontal gap ratios result in delayed scour beneath the downstream pipeline.

中文翻译：

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两条海底管道串联下波加电流诱发冲刷的数值研究

摘要 数值研究了波浪加电流条件下串联的两条海底管道下方的二维（2D）局部冲刷。应用了基于非定常雷诺平均 Navier-Stokes (URANS) 方程的完全耦合的流体动力学和形态学模型，其中包含 k - ω 湍流闭合。该模型针对现有的实验测量进行了验证，这些实验测量分别涉及单个管道下方和两条串联管道下方的活床冲刷。然后，该模型用于模拟在波浪加电流条件下，针对各种 Keulegan-Carpenter (KC) 数和相对电流强度的两条串联管道下方的冲刷。水平间隙比（两条管道之间的水平间隙距离除以管道直径）建模为 1 到 4。研究发现，在波浪加低强度水流条件下，两条管道下方的冲刷模式表现得与纯波浪条件下的情况相似。相反，当电流强度与波浪感应流动的强度相等时，两条管道下方的冲刷模式类似于纯电流条件下的冲刷模式。还观察到，在纯波条件下，每条管道下方的平衡冲刷深度受 KC 和水平间隙比的影响，除了 KC = 5.6。对于如此小的 KC，水平间隙比对平衡冲刷深度的影响不显着，因为不会发生涡流脱落。当相对于波浪的电流强度较低时，上游和下游管道下方的冲刷发展相似。然而，当水流的强度与波浪相等时，下游管道下的冲刷发展模式与上游不同。即，较小的水平间隙比导致下游管道下方的延迟冲刷。