Microorganisms self-propelling in a fluid create flow fields that impact the dynamics of other swimmers. Some organisms can be biased and have a preferred swimming direction, e.g., those displaying gyrotaxis, chemotaxis or phototaxis, and as a result often focus along thin lines. Here we use numerical computations and far-field theoretical calculations to show that the position of a collection of biased swimmers moving along a line is unstable to a zigzag mode when the swimmers act on the fluid as pusher dipoles. This instability takes the form of periodic transverse oscillations in the position of the swimmers. We predict theoretically that the most unstable wavelength is equal to twice the inter-swimmer distance and that the growth rate of the instability increases linearly with the magnitude of the stresslet, both of which are in quantitative agreement with our numerical simulations.

在流体中自我推进的微生物会产生影响其他游泳者动态的流场。一些生物可能有偏见并有偏好的游泳方向，例如，那些表现出回旋性、趋化性或趋光性，因此通常沿着细线聚焦。在这里，我们使用数值计算和远场理论计算来表明，当游泳者作为推动偶极子作用于流体时，沿线移动的一组有偏差的游泳者的位置对于锯齿形模式是不稳定的。这种不稳定性表现为游泳者位置的周期性横向振荡。我们从理论上预测，最不稳定的波长等于游泳者间距离的两倍，并且不稳定性的增长率随应力波的大小线性增加，这两者都与我们的数值模拟在定量上一致。