Time reversal of waves is an intriguing wave property that underpins a breadth of applications in physics and engineering. Waves contain information about their sources and the media through which they propagate. Thus, time reversal of measured wave signals has the potential of localizing and characterizing wave sources and of inferring the properties of the medium. Herein, we experimentally demonstrate the time reversibility of acoustic waves propagating in water-filled viscoelastic high-density polyethylene (HDPE) pipes. Evidently, the two mechanisms that restrict time reversal are the stability of wave paths to perturbations and damping. Perturbations, however, are found to grow slowly in time (∼t^1/2) and are not critical for the time reversal of waves. To evaluate the effect of damping, we perform an order of magnitude analysis on the non-reversible terms of the coupled waveguide momentum equations and derive a dimensionless time reversal parameter TR showing that damping develops linearly with time (i.e. TR ∼ t). Subsequently, we apply the TR parameter to our experiments and relevant experimental proofs from the literature to find that the time reversal of waves only holds for TR ∼ 1 or less; hence providing a criterion to estimate the range over which time reversal-based wave techniques and methodologies are valid. Finally, we discuss the various existing applications of time reversal in hydro-environmental research and engineering and anticipate that the presented work will stimulate further development.

波的时间反转是一种有趣的波特性，它支撑着物理学和工程学中的广泛应用。Waves 包含有关其来源和传播媒介的信息。因此，测量波信号的时间反转具有定位和表征波源以及推断介质特性的潜力。在这里，我们通过实验证明了声波在充水粘弹性高密度聚乙烯 (HDPE) 管道中传播的时间可逆性。显然，限制时间反转的两种机制是波路径对扰动和阻尼的稳定性。然而，我们发现扰动随时间缓慢增长（~ t ^1/2) 并且对于波浪的时间反转并不重要。为了评估阻尼的影响，我们对耦合波导动量方程的不可逆项进行了一个数量级的分析，并得出了一个无量纲时间反转参数TR，表明阻尼随时间线性发展（即TR ∼ t）。随后，我们将TR参数应用于我们的实验和文献中的相关实验证明，发现波的时间反转仅适用于TR∼ 1 或更少；因此提供了一个标准来估计基于时间反转的波浪技术和方法的有效范围。最后，我们讨论了时间逆转在水文环境研究和工程中的各种现有应用，并预计所提出的工作将刺激进一步的发展。