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Abstract The meroplanktonic larvae of many invertebrate and vertebrate species rely on physical transport to move them across the shelf to their adult habitats. One potential mechanism for cross‐shore larval transport is Stokes drift in internal waves. Here, we develop theory to quantify the Stokes velocities of neutrally buoyant and depth‐keeping organisms in linear internal waves in shallow water. We apply the analyses to theoretical and measured internal wave fields, and compare results with a numerical model. Near the surface and bottom boundaries, both neutrally buoyant and depth‐keeping organisms were transported in the direction of the wave's phase propagation. However, neutrally buoyant organisms were transported in the opposite direction of the wave's phase at mid depths, while depth‐keeping organisms had zero net transport there. Weakly depth‐keeping organisms had Stokes drifts between the perfectly depth‐keeping and neutrally buoyant organisms. For reasonable wave amplitudes and phase speeds, organisms would experience horizontal Stokes speeds of several centimeters per second—or a few kilometers per day in a constant wave field. With onshore‐polarized internal waves, Stokes drift in internal waves presents a predictable mechanism for onshore transport of meroplanktonic larvae and other organisms near the surface, and offshore transport at mid depths.
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This content will become publicly available on May 16, 2026
Stokes waves are unstable, even very small ones
WS: it is difficult to write about Thomas Kappeler in the past tense. He was a brilliant mathematician, but more importantly he was a wonderfully open, generous, and friendly person. I was fortunate that we had many opportunities to spend time together and discuss mathematics. I greatly miss him.A Stokes wave is a traveling free-surface periodic water wave that is constant in the direction transverse to the direction of propagation. Even Stokes waves of very small amplitude are unstable when subjected to various perturbations. We present a brief survey of this phenomenon with emphasis on transverse perturbations.
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- Award ID(s):
- 2205710
- PAR ID:
- 10617306
- Publisher / Repository:
- EMS Press
- Date Published:
- Journal Name:
- EMS Surveys in Mathematical Sciences
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2308-2151
- Page Range / eLocation ID:
- 71 to 78
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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