论文标题
粒子引起的对流不稳定性中的优先浓度
Preferential concentration in the particle-induced convective instability
论文作者
论文摘要
湍流中的重颗粒已显示在高应变速率或低涡度的区域中积累，这一过程被称为优先浓度。这可以在地球物理流中观察到，并在天体物理环境中推断出来，通常会导致颗粒的快速生长，这对于诸如雨或行星形成等物理过程至关重要。在这里，我们研究了在粒子驱动的对流不稳定性的背景下，在双向耦合系统中优先浓度的影响。为此，我们使用直接的数值模拟并采用两流体近似。我们专注于后者有效的粒径范围，即当stokes数字为$ \ lyssim o（0.1）$时。对于高于$ \ sim 0.01 $的Stokes数字，我们发现，使用RMS流体速度$ u _ {\ rm {rms {rms}} $的最大粒子浓度增强，粒子停止时间$τ_p$，粒子的差异性$κ__p$，$κ__p$ κ_P$。我们表明，可以从主导平衡的简单参数中理解这种缩放。我们还表明，平均尺度上典型的粒子浓度增强为$（u _ {\ rm {rms}}}^2τ_p/κ_p）^{1/2} $。最终，我们发现粒子浓度增强的概率分布函数在平均值上具有指数尾部的尾巴，其斜率比例为$（u _ {\ rm {rms}}^2τ_p /κ_p /κ_p）^{ - 1/2} $。我们将模型应用于地球物理和天体物理实例，并讨论其局限性。
Heavy particles in turbulent flows have been shown to accumulate in regions of high strain rate or low vorticity, a process otherwise known as preferential concentration. This can be observed in geophysical flows, and is inferred to occur in astrophysical environments, often resulting in rapid particle growth which is critical to physical processes such as rain or planet formation. Here we study the effects of preferential concentration in a two-way coupled system in the context of the particle-driven convective instability. To do so, we use Direct Numerical Simulations and adopt the two-fluid approximation. We focus on a particle size range for which the latter is valid, namely when the Stokes number is $\lesssim O(0.1)$. For Stokes number above $\sim 0.01$, we find that the maximum particle concentration enhancement over the mean scales with the rms fluid velocity $u_{\rm{rms}}$, the particle stopping time $τ_p$, and the particle diffusivity $κ_p$, as $u_{\rm{rms}}^2 τ_p / κ_p$. We show that this scaling can be understood from simple arguments of dominant balance. We also show that the typical particle concentration enhancement over the mean scales as $(u_{\rm{rms}}^2 τ_p/ κ_p)^{1/2}$. We finally find that the probability distribution function of the particle concentration enhancement over the mean has an exponential tail whose slope scales as $(u_{\rm{rms}}^2 τ_p / κ_p)^{-1/2}$. We apply our model to geophysical and astrophysical examples, and discuss its limitations.
