A stagnant free-surface flow is an instantaneous flow field of pure acceleration with zero velocity and a deformed surface. There exists a potential-flow acceleration field. With zero velocity and the acceleration field given, there is a limiting free-surface position which possesses one peak at its point of highest elevation. By complex analysis, it can be shown that the surface peak has a right angle. We elaborate on an elementary model of two-dimensional stagnant free-surface flow with a peak. Our model may serve to describe a situation of maximal single-wave run-up with a given energy at a uniformly sloping beach. The highest possible run-up of an incoming solitary wave corresponds to zero kinetic energy. It encompasses an idealized situation where the kinetic wave energy is converted into potential energy in a water mass piling up along the slope to become stagnant at one single moment. Multipoles with singularities outside the fluid domain may give rise to a smooth and gradual deceleration needed for a non-breaking run-up process. A pair of dipoles with an orientation perpendicular to a given slope represents the stagnant acceleration fields with the highest surface peak spatially concentrated along the slope. Thereby, a one-parameter family of surface shapes is constituted, only dependent on the slope angle. The initial flow field, the initial free surface, the initial isobars and the geometric parameters are all calculated for different slope angles.

停滞的自由表面流是纯加速度的瞬时流场，速度为零，表面变形。存在势流加速场。在零速度和给定加速度场的情况下，存在一个有限的自由表面位置，该位置在其最高仰角处具有一个峰。通过复杂分析，可以表明表面峰具有直角。我们详细阐述了一个带有峰值的二维停滞自由表面流的基本模型。我们的模型可能有助于描述在均匀倾斜的海滩上具有给定能量的最大单波上升情况。入射孤波的最大可能上升对应于零动能。它涵盖了一种理想情况，其中在沿斜坡堆积的水团中，动波能量被转换为势能，并在一个瞬间停滞。在流体域外具有奇异点的多极子可能会导致不间断的启动过程所需的平稳且逐渐的减速。垂直于给定斜率的一对偶极子代表停滞的加速度场，其最高表面峰沿斜率在空间上集中。由此，仅依赖于倾斜角就构成了一个单参数的表面形状族。初始流场，初始自由表面，初始等压线和几何参数都针对不同的倾斜角进行了计算。在流体域外具有奇异点的多极子可能会导致不间断的启动过程所需的平稳且逐渐的减速。垂直于给定斜率的一对偶极子代表停滞的加速度场，其最高表面峰沿斜率在空间上集中。由此，仅依赖于倾斜角就构成了一个单参数的表面形状族。初始流场，初始自由表面，初始等压线和几何参数都针对不同的倾斜角进行了计算。在流体域外具有奇异点的多极子可能会导致不间断的启动过程所需的平稳且逐渐的减速。垂直于给定斜率的一对偶极子代表停滞的加速度场，其最高表面峰沿斜率在空间上集中。由此，仅依赖于倾斜角就构成了一个单参数的表面形状族。初始流场，初始自由表面，初始等压线和几何参数都针对不同的倾斜角进行了计算。由此，仅依赖于倾斜角就构成了一个单参数的表面形状族。初始流场，初始自由表面，初始等压线和几何参数都针对不同的倾斜角进行了计算。由此，仅依赖于倾斜角就构成了一个单参数的表面形状族。初始流场，初始自由表面，初始等压线和几何参数都针对不同的倾斜角进行了计算。