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Phenomenology of decaying turbulence beneath surface waves

Published online by Cambridge University Press:  08 October 2025

Gregory LeClaire Wagner Open the ORCID record for Gregory LeClaire Wagner [Opens in a new window]  and
Navid C. Constantinou Open the ORCID record for Navid C. Constantinou [Opens in a new window]
Gregory LeClaire Wagner*
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA, USA
Navid C. Constantinou
Affiliation:
University of Melbourne, Parkville, VIC, Australia Australian Research Council Centre of Excellence for the Weather of the 21st Century, Australia
*
Corresponding author: Gregory LeClaire Wagner, glwagner@mit.edu
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Abstract

This paper explores decaying turbulence beneath surface waves that is initially isotropic and shear free. We start by presenting phenomenology revealed by wave-averaged numerical simulations: an accumulation of angular momentum in coherent vortices perpendicular to the direction of wave propagation, suppression of kinetic energy dissipation and the development of depth-alternating jets. We interpret these features through an analogy with rotating turbulence (Holm 1996 Physica D. 98, 415–441), wherein the curl of the Stokes drift, ${\boldsymbol{\nabla}} \times {\boldsymbol{u^{S}}}$, takes on the role of the background vorticity (for example, $(f_0 + \beta y) {\boldsymbol{\hat{z}}}$ on the beta plane). We pursue this thread further by showing that a two-equation model proposed by Bardina et al. (1985 J. Fluid Mech. 154, 321–336) for rotating turbulence reproduces the simulated evolution of volume-integrated kinetic energy. This success of the two-equation model – which explicitly parametrises wave-driven suppression of kinetic energy dissipation – carries implications for modelling turbulent mixing in the ocean surface boundary layer. We conclude with a discussion about a wave-averaged analogue of the Rossby number appearing in the two-equation model, which we term the ‘pseudovorticity number’ after the pseudovorticity ${\boldsymbol{\nabla }} \times {\boldsymbol{u}}^S$. The pseudovorticity number is related to the Langmuir number in an integral sense.

JFM classification

Geophysical and Geological Flows: Ocean processes Waves/Free-surface Flows: Surface gravity waves Turbulent Flows: Rotating turbulence

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A51
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© The Author(s), 2025. Published by Cambridge University Press

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