Nonlinear sloshing in zero gravity
Nonlinear sloshing in zero gravity
复制标题
零重力下的非线性晃动
DOI：
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发表时间：
2002
影响因子：
3.7
通讯作者：
J. Billingham
中科院分区：
文献类型：
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作者：
J. Billingham
我们研究的效果的时间周期性的，横向加速度的二维流动的流体与自由表面的表面张力，限制在两个平面之间，平行的墙壁在零重力的条件下。我们假设，每个接触线的速度是一个规定的，单值函数的流体和固体之间的动态接触角的壁。我们开始通过获得小振幅驻波的解析解，当这个函数是线性的，流体是无粘性的，横向加速度足够小。这导致运动的阻尼，除非接触角是固定的或接触线是固定的。在这些情况下，我们包括对壁边界层流动的影响，这是阻尼的另一个主要来源。然后，我们考虑弱非线性解的无粘问题时，接触角几乎是常数和外部强迫接近共振。该解表明了对强迫频率变化的滞后响应的可能性。最后，我们研究的完全非线性，无粘问题的数值解，使用desingularized积分方程技术。我们发现，周期解，混沌解和解决方案的拓扑结构的流体变化，无论是通过自相交或夹断，都是可能的。
We study the effect of a time-periodic, lateral acceleration on the two-dimensional flow of a fluid with a free surface subject to surface tension, confined between two plane, parallel walls under conditions of zero gravity. We assume that the velocity of each contact line is a prescribed, single-valued function of the dynamic contact angle between fluid and solid at the wall. We begin by obtaining analytical solutions for the small-amplitude standing waves that evolve when this function is linear, the fluid is inviscid and the lateral acceleration is sufficiently small. This leads to damping of the motion, unless either the contact angles are fixed or the contact lines are pinned. In these cases, we include the effect on the flow of the wall boundary layers, which are the other major sources of damping. We then consider the weakly nonlinear solution of the inviscid problem when the contact angle is almost constant and the external forcing is close to resonance. This solution indicates the possibility of a hysteretic response to changes in the forcing frequency. Finally, we examine numerical solutions of the fully nonlinear, inviscid problem using a desingularized integral equation technique. We find that periodic solutions, chaotic solutions and solutions where the topology of the fluid changes, either through self-intersection or pinch off, are all possible.