Time reversal of waves in hydraulics: experimental and theoretical proof with applications

Abstract

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.