The quantification of turbulent mixing in nature is predicated by inherent randomness of causal events, and obtaining relevant turbulence statistics requires ensemble averaging of identical realizations that are unachievable in field observations or onerous in laboratory situations. Laboratory modeling is often used to study nonstationary natural processes, but jitters due to intrinsic variability of events as well as experimental uncertainties introduce additional (spurious) fluctuations that affect ensemble averaging of individual realizations. In this paper, the phase-aligned ensemble averaging technique (PAET), which aligns the events based on information on flow structures, is introduced in the context of environmental fluid mechanics studies. The accuracy and computational efficiency of PAET are investigated systematically for two cases: (1) synthetic density field alignment and (2) laboratory flows involving collision of counter flowing gravity currents. The latter is a frequent phenomenon in the stable atmospheric boundary layer in mountainous areas. In the synthetic density field case, the PAET aligns the complex structures precisely within the allowable range of measurement accuracy. For the experimental gravity current case, the precisely aligned result is unknown, and the results of PAET are compared with those obtained with the Monte Carlo method, a simulated annealing algorithm, and the gradient descent method; the PAET was found to be the most efficient. This study broaches the PAET as a versatile method for obtaining accurate turbulence statistics in laboratory experiments designed to mimic environmental flows where spatial and temporal inhomogeneities abound.

自然界中湍流混合的量化是由因果事件的固有随机性决定的，要获得相关的湍流统计数据，需要对相同的实现进行整体平均，这在现场观察中是无法实现的，或者在实验室情况下是繁重的。实验室建模通常用于研究非平稳自然过程，但是由于事件的固有可变性以及实验不确定性造成的抖动会引入其他（虚假）波动，从而影响单个实现的整体平均。本文在环境流体力学研究的背景下，引入了基于流结构信息对齐事件的相位对齐集成平均技术（PAET）。针对以下两种情况，系统地研究了PAET的准确性和计算效率：（1）合成密度场对准和（2）涉及逆流重力流碰撞的实验室流。后者是山区稳定大气边界层中的常见现象。在合成密度场的情况下，PAET在允许的测量精度范围内精确对准复杂的结构。对于实验重力流情况，精确对准的结果是未知的，并且将PAET的结果与通过Monte Carlo方法，模拟退火算法和梯度下降法获得的结果进行比较；发现PAET是最有效的。这项研究将PAET作为一种通用方法，用于在旨在模拟空间和时间不均匀性大量存在的环境流动的实验室实验中获得准确的湍流统计数据。