发表机构
Seoul National University（首尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广 Carrier--Greenspan 变换至移动底床，识别出保持不变量的底床运动族，给出波浪生成与爬高的闭式解，并通过实验验证预测。
AI 中文摘要
Carrier--Greenspan 全纯变换将恒定坡度海滩上的非线性浅水方程线性化。我们将该变换推广到移动底床，并识别出保持 Carrier--Greenspan 不变量的一族底床运动。底床梯度必须在空间上均匀，即 $h(x,t)=\rho(t)x+\mathcal{B}(t)$，而常数 $\rho$ 则回归经典坡度。对于这一族运动，水平加速参考系可消除强迫项。底床运动随后从全纯方程中消失，两个求积公式即可恢复物理变量。若梯度随时间变化，床面位移在离岸方向无界增长，远场无法保持静止。因此，计算域必须是有限的，尽管枢轴可置于任意位置。底床倾斜式造波机可实现这一族运动。对于铰链响应、所生成波浪的波峰到波谷陡度以及前导非线性修正，均可得到闭式解。该修正依赖于陡度所参考的点，因此前导波峰波与前导波谷波之间存在差异。由于铰链位于海滩趾部，这些闭式解提供了经典平面海滩解所需的入射波。因此，仅凭板运动即可预测爬高。陡度的预测无需拟合常数，且与参考计算结果一致。本文首次报道了水平底床上的 61 次实验，将测试推广至更深水域和更长的板运动。实测爬高遵循预测爬高，但存在无粘理论无法解释的偏移。
英文摘要
The Carrier--Greenspan hodograph transformation linearises the nonlinear shallow-water equations on a beach of constant slope. We extend the transformation to a moving bottom and identify the family of bottom motions that preserves the Carrier--Greenspan invariants. The bottom gradient must be uniform in space, that is, $h(x,t)=ρ(t)x+\mathcal{B}(t)$, and constant $ρ$ returns the classical slope. For this family a horizontally accelerating frame removes the forcing. The bottom motion then disappears from the hodograph equation, and two quadratures recover the physical variables. If the gradient varies in time, the bed displacement grows without bound offshore and the far field cannot remain at rest. The domain must therefore be finite, although the pivot may be placed anywhere. A bottom-tilting wave maker realises this family. Closed forms follow for the hinge response, for the crest-to-trough steepness of the generated wave, and for the leading nonlinear correction. The correction depends on the point to which the steepness is referred, and so differs between a leading-elevation and a leading-depression wave. Because the hinge is at the beach toe, these closed forms provide the incident wave required by the classical plane-beach solution. The run-up can therefore be predicted from the plate motion alone. The steepness is predicted without a fitted constant and agrees with the reference computations. Sixty-one runs over a level bed, reported here for the first time, carry the test to deeper water and longer plate motions. The measured run-up follows the predicted run-up, with an offset that the inviscid theory does not account for.
Comments20 pages, 6 figures. Under consideration for publication in Journal of Fluid Mechanics. Supplementary data (61 flat-bottom runs) included as ancillary files
