The Absence of Stokes Drift in Waves

TL;DR

This paper investigates why Stokes drift is rarely observed in experiments, attributing it to subtle boundary and gradient effects that cause energy losses and distortions, challenging classical assumptions about wave momentum transfer.

Contribution

The study reveals that boundary effects and microbreaking events explain the absence of Stokes drift in experiments, highlighting the nonuniversality of wave interactions and the importance of boundary considerations.

Findings

Boundary effects cause significant energy loss in wave packets.

Monochromatic sound waves distort asymmetrically to conserve momentum.

Wave interactions are highly system-dependent and boundary-sensitive.

Abstract

Stokes drift has been as central to the history of wave theory as it has been distressingly absent from experiment. Neither wave tanks nor experiments in open bodies detect this without nearly canceling "eulerian flows." Acoustic waves have an analogous problem that is particularly problematic in the vorticity production at the edges of beams. Here we demonstrate that the explanation for this arises from subtle end-of-packet and wavetrain gradient effects such as microbreaking events and wave-flow decomposition subtleties required to conserve mass and momentum and avoid fictitious external forces. These losses occur at both ends of packets and can produce a significant nonviscous energy loss for translating and spreading surface wave packets and wavetrains. In contrast, monochromatic sound wave packets will be shown to asymmetrically distort to conserve momentum. This provides an interesting analogy to how such internal forces arise for gradients of electromagnetic wavetrains in media. Such examples show that the interactions of waves in media are so system dependent as to be completely nonuniversal. These give further examples of how boundary effects must be carefully considered for conservation laws especially when harmonic functions are involved. The induced flows in establishing surface waves are shown to be time changing and dependent on wave history and suggest that some classical work based on mass flux and wave interactions may need to be reconsidered.