We uncover a new type of turbulence – activity-induced homogeneous and isotropic turbulence – in a model that has been employed to investigate motility-induced phase separation (MIPS) in a system of microswimmers. The active Cahn–Hilliard–Navier–Stokes (CHNS) equations, also called active model H, provide a natural theoretical framework for our study. In this CHNS model, a single scalar order parameter ϕ, positive (negative) in regions of high (low) microswimmer density, is coupled with the velocity field u. The activity of the microswimmers is governed by an activity parameter ζ that is positive for extensile swimmers and negative for contractile swimmers. With extensile swimmers, this system undergoes complete phase separation, which is similar to that in binary-fluid mixtures. By carrying out pseudospectral direct numerical simulations (DNSs), we show, for the first time, that (a) this model develops an emergent nonequilibrium, but statistically steady, state (NESS) of active turbulence, for the case of contractile swimmers, if ζ is sufficiently large and negative, and (b) this turbulence arrests the phase separation. We quantify this suppression by showing how the coarsening-arrest length scale does not grow indefinitely, with time t, but saturates at a finite value at large times. We characterise the statistical properties of this active-scalar turbulence by employing energy spectra and fluxes and the spectrum of ϕ. For sufficiently high Reynolds numbers, the energy spectrum (k) displays an inertial range, with a power-law dependence on the wavenumber k. We demonstrate that, in this range, the flux Π(k) assumes a nearly constant, negative value, which indicates that the system shows an inverse cascade of energy, even though energy injection occurs over a wide range of wavenumbers in our active-CHNS model.

中文翻译：

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主动标量流体中的新型湍流和粗化抑制

我们在一个模型中发现了一种新型湍流——活动引起的均匀和各向同性湍流，该模型已用于研究微型游泳器系统中运动引起的相分离（MIPS）。主动 Cahn-Hilliard-Navier-Stokes (CHNS) 方程，也称为主动模型 H，为我们的研究提供了一个自然的理论框架。在此 CHNS 模型中，单个标量阶次参数phi （在高（低）微型游泳者密度区域为正（负））与速度场u耦合。微型游泳者的活动由活动参数z控制，该参数对于伸展游泳者为正，对于收缩游泳者为负。对于可伸展的游泳者，该系统经历完全的相分离，这类似于二元流体混合物中的相分离。通过进行伪谱直接数值模拟（DNS），我们首次表明，（a）对于收缩游泳者的情况，该模型产生了一种紧急的非平衡但统计上稳定的主动湍流状态（NESS），如果ζ足够大且为负值，并且 (b) 这种湍流阻止了相分离。我们通过展示粗化捕获长度尺度如何不会随着时间t无限增长，而是在长时间内饱和在有限值来量化这种抑制。我们通过使用能谱和通量以及ψ谱来表征这种主动标量湍流的统计特性。对于足够高的雷诺数，能谱( k ) 显示惯性范围，且幂律依赖于波数k。我们证明，在这个范围内，通量Π ( k ) 呈现几乎恒定的负值，这表明系统显示出能量的逆级联，即使能量注入发生在我们的主动 CHNS 中的大范围波数上模型。