The temporal vortex-gas free shear layer is a Hamiltonian system of N-point vortices in a singly-periodic domain relevant to the (large-scale) development of plane (3D Navier–Stokes) turbulent shear layers. It has been shown (Suryanarayanan et al., 2014) that there are three distinct temporal regimes in its evolution, including an intermediate self-similar regime (RII) with a universal constant spreading rate, and a final state of relative equilibrium. Here, we study the evolution of vortex-gas free shear layers affected by viscosity as simulated by the addition of a random walk component to the motion of the vortices (Chorin, 1973). We show that while the momentum thickness of the layer, $\theta$, scales as $t^{1∕2}$ in the first and final regimes for the viscous system, it grows as $t^1$ in the intermediate Regime II (observed here for momentum thickness Reynolds numbers $R{e}_{\theta }$ from 50 to over 5000 across different simulations), with the same universal growth rate $d\theta ∕d\left(t\Delta U\right)=0.0166\pm 0.0002$ as in the inviscid case. This suggests that the non-equilibrium universality of Regime II is robust to small perturbations of the Hamiltonian, and that this result could have general consequences for systems with long-range interactions. We further find that, even under conditions where the viscous shear stress is not negligible, the Reynolds shear stress adjusts itself in such a way that their sum is a constant in Regime II and equal to the value of the latter in the inviscid case. The implications of this observation on the dynamics of turbulent shear flows are elaborated.

时空涡流无剪切层是单周期域中与平面（3D Navier–Stokes）湍流剪切层（大规模）发展有关的N点涡旋的哈密顿系统。研究表明（Suryanarayanan等，2014），其演化过程中存在三种截然不同的时间机制，包括具有普遍恒定扩展率的中间自相似机制（RII）和相对平衡的最终状态。在这里，我们研究了受粘度影响的无涡流自由剪切层的演变，这是通过向涡流的运动中添加随机游走分量来模拟的（Chorin，1973）。我们表明，尽管该层的动量厚度很大，$\theta$，缩放为 ${Ť}^{\mathrm{1个}∕2}$ 在粘性系统的第一个和最后一个状态中，它随着 ${Ť}^{\mathrm{1个}}$ 在中级政区II中（此处观察到动量厚度雷诺数 $\mathrm{[R}{Ë}_{\theta }$ 从50到5000跨越不同的模拟），具有相同的普遍增长率 $d\theta ∕d\left(Ť\Delta ü\right)=0。0166\pm 0。0002$如无形的情况。这表明制度II的非平衡普遍性对哈密顿量的小扰动具有鲁棒性，并且该结果可能会对具有长距离相互作用的系统产生一般性影响。我们进一步发现，即使在粘性剪切应力不可忽略的条件下，雷诺剪应力也会进行自我调整，以使它们的总和在Regime II中为常数，并且在无粘性情况下等于后者的值。阐述了这种观察对湍流剪切流动力学的影响。