When a liquid stream is injected into a gaseous atmosphere, it destabilizes and continuously passes through different states characterized by different morphologies. Throughout this process, the flow dynamics may be different depending on the region of the flow and the scales of the involved liquid structures. Exploring this multi-scale, multi-dimensional phenomenon requires some new theoretical tools, some of which need yet to be elaborated. Here, a new analytical framework is proposed on the basis of two-point statistical equations of the liquid volume fraction. This tool, which originates from single phase turbulence, allows us notably to decompose the fluxes of liquid in flow–position space and scale space. Direct numerical simulations of liquid–gas turbulence decaying in a triply periodic domain are then used to characterize the time and scale evolution of the liquid volume fraction. It is emphasized that two-point statistics of the liquid volume fraction depend explicitly on the geometrical properties of the liquid–gas interface and in particular its surface density. The stretch rate of the liquid–gas interface is further shown to be the equivalent for the liquid volume fraction (a non-diffusive scalar) of the scalar dissipation rate. Finally, a decomposition of the transport of liquid in scale space highlights that non-local interactions between non-adjacent scales play a significant role.

中文翻译：

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尺度空间中的液体输运

当液体流被注入到气态环境中时，它会不稳定并不断通过具有不同形态特征的不同状态。在整个过程中，流动动力学可能因流动区域和所涉及液体结构的尺度而异。探索这种多尺度、多维度的现象需要一些新的理论工具，其中一些还需要详细阐述。在这里，基于液体体积分数的两点统计方程，提出了一种新的分析框架。这种源自单相湍流的工具使我们能够显着地分解流动位置空间和尺度空间中的液体通量。然后使用在三重周期域中衰减的液-气湍流的直接数值模拟来表征液体体积分数的时间和尺度演变。需要强调的是，液体体积分数的两点统计明确取决于液-气界面的几何特性，特别是其表面密度。液-气界面的拉伸率进一步显示为等效于标量耗散率的液体体积分数（非扩散标量）。最后，对尺度空间中液体传输的分解强调了非相邻尺度之间的非局部相互作用起着重要作用。需要强调的是，液体体积分数的两点统计明确取决于液-气界面的几何特性，特别是其表面密度。液-气界面的拉伸率进一步显示为等效于标量耗散率的液体体积分数（非扩散标量）。最后，对尺度空间中液体传输的分解强调了非相邻尺度之间的非局部相互作用起着重要作用。需要强调的是，液体体积分数的两点统计明确取决于液-气界面的几何特性，特别是其表面密度。液-气界面的拉伸率进一步显示为等效于标量耗散率的液体体积分数（非扩散标量）。最后，对尺度空间中液体传输的分解强调了非相邻尺度之间的非局部相互作用起着重要作用。