Protoplasmic streaming in plant cells is directly visible in the cases of Chara corallina and Nittella flexilis, and this streaming is understood to play the role of transportation of biological materials. For this reason, related studies have focused on molecular transportation from a fluid mechanical viewpoint. However, the experimentally observed distribution of the velocity along the flow direction $x$, which exhibits two peaks at $V_x\!=\!0$ and at a finite $V_x(\not=\!0)$, remains to be studied. In this paper, we numerically study whether this behavior of the flow field can be simulated by a two-dimensional stochastic Navier-Stokes (NS) equation for Couette flow, in which random Brownian force is assumed. We present the first numerical evidence that these peaks are reproduced by the stochastic NS equation, which implies that the Brownian motion or the stochastic nature of the fluid particles plays an essential role in the emergence of the peaks in the velocity distribution. We also find that the position of the peak at $V_x(\not=\!0)$ moves with the variation in the strength $D$ of the random Brownian force, which also changes depending on physical parameters such as the kinematic viscosity, boundary velocity and diameter of plant cells.

中文翻译：

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原生质流中速度分布的随机流体动力学模拟

在 Chara corallina 和 Nittella flexilis 的情况下，植物细胞中的原生质流是直接可见的，这种流被理解为起着生物材料运输的作用。出于这个原因，相关研究从流体力学的角度关注分子传输。然而，实验观察到的速度沿流动方向 $x$ 的分布，在 $V_x\!=\!0$ 和有限的 $V_x(\not=\!0)$ 处表现出两个峰值，仍然是学习了。在本文中，我们数值研究了流场的这种行为是否可以通过二维随机 Navier-Stokes (NS) 方程来模拟，其中假设随机布朗力。我们提供了第一个数值证据，证明这些峰值是由随机 NS 方程再现的，这意味着布朗运动或流体粒子的随机性在速度分布峰值的出现中起着至关重要的作用。我们还发现 $V_x(\not=\!0)$ 处的峰值位置随着随机布朗力的强度 $D$ 的变化而移动，这也取决于运动粘度等物理参数，植物细胞的边界速度和直径。