AI 中文总结
研究通过实验室实验开发波浪诱导冰侵蚀模型，重构公式并引入无量纲系数α，用实验校准α，拟合剖面再现波谷下深度依赖性，虽有效水线系数接近怀特公布值，但不构成独立验证，揭示了表面附近未解决的影响。
AI 中文摘要
在一些运行中的冰山和海岸侵蚀模型中，垂直冰前沿的波浪诱导融化是通过怀特（1980年）的粗糙壁面参数化来表示的，其封闭链记录不完整，常用的紧凑表达式是在水线处给出的。我们重构了公式，使用约恩松的隐式关系及其朗伯 - W解指定了粗糙 - 湍流波摩擦封闭，并将模型扩展到线性波运动学下的深度分辨融化速率剖面。由于水平和垂直轨道速度分量是相关的，我们使用水平分量作为方便的代表性尺度，并引入无量纲系数α来处理剩余的封闭不确定性。重构得出水线系数，怀特合成速度定义下为3.0×10^ - 4，参考选择α = 1时为2.09×10^ - 4，均未直接重现怀特公布的1.46×10^ - 4。然后通过两个淡水冰的单色波槽实验从波谷以下的剖面校准α。校准中使用了完整的朗伯 - W摩擦系数。1.54秒和0.87秒周期的最佳拟合值分别为0.684和0.612，相对差异约为11%。它们相应的有效水线系数，1.43×10^ - 4和1.28×10^ - 4，接近怀特公布的值，但不构成独立验证。拟合剖面再现了波谷以下观测到的深度依赖性，而表面附近的偏差暴露了间歇性淹没、局部波浪冲击和不确定热强迫的未解决影响。
英文摘要
Wave-induced melting of vertical ice fronts is represented in several operational iceberg and coastal-erosion models by the rough-wall parameterization of White (1980), whose closure chain is incompletely documented and whose commonly used compact expression is stated at the waterline. We reconstruct the formulation, specify the rough-turbulent wave-friction closure using Jonsson's implicit relation and its Lambert-W solution, and extend the model to a depth-resolved melt-rate profile under linear wave kinematics. Because the horizontal and vertical orbital-velocity components are linked, we use the horizontal component as a convenient representative scale and introduce a dimensionless coefficient alpha for the remaining closure uncertainty. The reconstruction gives a waterline coefficient of 3.0 x 10^-4 with White's resultant-velocity definition and 2.09 x 10^-4 for the reference choice alpha = 1; neither reproduces White's published 1.46 x 10^-4 directly. Two monochromatic wave-flume experiments with freshwater ice are then used to calibrate alpha from profiles below the wave trough. The full Lambert-W friction coefficient is used in this calibration. Best-fit values are 0.684 and 0.612 for periods of 1.54 and 0.87 s, respectively, a relative difference of approximately 11%. Their corresponding effective waterline coefficients, 1.43 x 10^-4 and 1.28 x 10^-4, are close to White's published value but do not constitute an independent validation. The fitted profiles reproduce the observed depth dependence below the trough, while deviations near the surface expose unresolved effects of intermittent submergence, local wave impact, and uncertain thermal forcing.
Comments37 pages, 14 figures, 6 tables. Code and data: https://doi.org/10.5281/zenodo.21512504
