Falkovich Gregory, Shlomo Doron
Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):067304. doi: 10.1103/PhysRevE.71.067304. Epub 2005 Jun 30.
We consider a passive pollutant advected by the flow due to linear random waves with finite attenuation. We derive the equation that governs the evolution of the pair correlation function of pollutant concentration and show that it coincides with the equation for the case of a short-correlated velocity. Due to a finite wave attenuation, nontrivial evolution (particularly, the growth of inhomogeneities) appears already in the second order in wave amplitudes. We show that random potential waves lead to the growth of concentration inhomogeneities. We identify two stationary solutions for the spectral density of concentration, equipartition, and flux state. Which one is established depends on the relation between mean square velocity gradients due to potential and solenoidal parts of the flow, respectively. We also analyze transient regimes and show how periodic component in the concentration distribution appears and disappears.
我们考虑一种被动污染物，它由于具有有限衰减的线性随机波而随流平流输送。我们推导了支配污染物浓度对关联函数演化的方程，并表明它与短关联速度情况下的方程一致。由于有限的波衰减，在波幅的二阶项中就已经出现了非平凡的演化（特别是不均匀性的增长）。我们表明随机势波会导致浓度不均匀性的增长。我们确定了浓度谱密度的两个定态解，即均分态和通量态。具体建立哪种状态取决于流的势部分和螺线管部分所导致的均方速度梯度之间的关系。我们还分析了瞬态过程，并展示了浓度分布中的周期性成分是如何出现和消失的。
