The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes–based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.

中文翻译：

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二维主动悬浮液中的冷凝物形成和多尺度动力学

主动悬浮液中微游泳器的集体作用导致主动湍流是中尺度的时空混沌动力学，其特征是涡旋和射流的存在规模远远大于单个活性成分的特征尺寸。为了描述这种动力学，已经提出了由小规模力驱动的基于Navier-Stokes的单流体模型。在这里，我们为二维（2D）密集悬浮液的情况提供了此类模型的理由。考虑到由经典湍流形成的从主动湍流到大尺度模式（称为凝结水）的过渡情况，我们随后对作为主动驱动函数的单流体模型的性质进行了深入的数值研究。牛顿二维湍流中的逆能量级联。最近显示了使用单流体模型[M. Linkmann等。，物理 启快报 122，214503（2019）]为二维主动悬架支持两个非平衡稳定状态，一个具有冷凝物和一个没有，这是由一个亚临界过渡分离。在这里，我们报告了有关这种过渡的更多细节，例如磁滞现象，并讨论了一个低维模型，该模型描述了通过小规模驱动和凝结水之间的非局部尺度耦合进行过渡的主要特征。