Motion of an inertial squirmer in a density stratified fluid
Motion of an inertial squirmer in a density stratified fluid
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DOI：
10.1017/jfm.2020.719
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发表时间：
2020-10
影响因子：
3.7
通讯作者：
R. More;A. Ardekani
中科院分区：
文献类型：
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作者：
R. More;A. Ardekani
摘要我们利用典型的蠕动模型研究了惯性游泳者在线性密度分层流体中的自航问题。我们通过直接数值求解Navier-Stokes方程来量化推手(从后方推进)和拉手(从前方推进)的游泳速度，使用有限体积法求解流体流动，并使用分布式拉格朗日乘子法对游泳者进行建模。模拟的雷诺数($Re$)在5到100之间，弗劳德数($Fr$)在1到10之间。我们发现，增加流体分层强度会降低推进器和拉出器在均匀流体中的游泳速度。当它们在较重的流体中移动时，由于较轻的流体在各自的再循环区被困在它们各自的再循环区，这些蠕动动物所经历的浮力增加是这种减少的原因之一。随着层积的增加，等水晶石的变形倾向于较小，这为它们周围的蠕动物体产生的流动提供了阻力。这种阻力随着层积的增加而增加，因此降低了蠕动的游泳速度。分层还可以稳定拉料器周围的流动，使其轴对称甚至保持在较高的$Re$，因此，当$Re$大于$O(10)$时，导致稳定，否则在均质流体中是不存在的。相反，强烈的层结会使推进器周围的流动变得非稳定和三维，从而导致推进器运动的不稳定，否则在均匀流体中是稳定的和轴对称的。推手比拉手更有效率，这是因为沿其表面和下游有有效的涡量对流。关于个体蠕动产生的混合效率的数据解释了观察到的由一群蠕动产生的混合的趋势。
Abstract We investigate the self-propulsion of an inertial swimmer in a linearly density stratified fluid using the archetypal squirmer model which self-propels by generating tangential surface waves. We quantify swimming speeds for pushers (propelled from the rear) and pullers (propelled from the front) by direct numerical solution of the Navier–Stokes equations using the finite volume method for solving the fluid flow and the distributed Lagrange multiplier method for modelling the swimmer. The simulations are performed for Reynolds numbers ($Re$) between 5 and 100 and Froude numbers ($Fr$) between 1 and 10. We find that increasing the fluid stratification strength reduces the swimming speeds of both pushers and pullers relative to their speeds in a homogeneous fluid. The increase in the buoyancy force experienced by these squirmers due to the trapping of lighter fluid in their respective recirculatory regions as they move in the heavier fluid is one of the reasons for this reduction. With increasing the stratification, the isopycnals tend to deform less, which offers resistance to the flow generated by the squirmers around them to propel themselves. This resistance increases with stratification, thus, reducing the squirmer swimming velocity. Stratification also stabilizes the flow around a puller keeping it axisymmetric even at high $Re$, thus, leading to stability which is otherwise absent in a homogeneous fluid for $Re$ greater than $O(10)$. On the contrary, a strong stratification leads to instability in the motion of pushers by making the flow around them unsteady and three-dimensional, which is otherwise steady and axisymmetric in a homogeneous fluid. A pusher is a more efficient swimmer than a puller owing to efficient convection of vorticity along its surface and downstream. Data for the mixing efficiency generated by individual squirmers explain the trends observed in the mixing produced by a swarm of squirmers.