论文标题
边界对理想流体力和开尔文的最小能量定理的影响
Boundary Effects on Ideal Fluid Forces and Kelvin's Minimum Energy Theorem
论文作者
论文摘要
中性导体上方的电荷上的静电力通常很有吸引力。令人惊讶的是，这种力在某些几何形状中变得排斥（Levin＆Johnson 2011），这是静电定理的结果。基于开尔文（1849）的类似最小能量定理，在理想流体的理论中有效，在存在边界的情况下，我们对稳定和不稳定的流体力显示了相应的影响。关于不稳定的力，提出了两个主要结果。首先，事实证明，在存在边界的情况下始终增加。其次，在接近边界的身体模型中，不稳定的力通常是排斥的（Lamb 1975，§137），我们提出了一种几何形状，该力可以吸引力。至于稳定的力，有一个主要结果：在伯努利吸力夹的模型中，稳定力通常具有吸引力，我们表明力在某些几何形状中变得排斥。当边界在开尔文定理预测的能量最小值时，当边界近似流线时，不稳定和稳定的力都会逆转符号。
The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson 2011), a result that follows from an energy theorem in electrostatics. Based on the analogous minimum energy theorem of Kelvin (1849), valid in the theory of ideal fluids, we show corresponding effects on steady and unsteady fluid forces in the presence of boundaries. Two main results are presented regarding the unsteady force. First, the added mass is proven to always increase in the presence of boundaries. Second, in a model of a body approaching a boundary, where the unsteady force is typically repulsive (Lamb 1975, §137), we present a geometry where the force can be attractive. As for the steady force, there is one main result: in a model of a Bernoulli suction gripper, for which the steady force is typically attractive, we show that force becomes repulsive in some geometries. Both the unsteady and steady forces are shown to reverse sign when boundaries approximate flow streamlines, at energy minima predicted by Kelvin's theorem.
