Phenomenology of decaying turbulence beneath surface waves
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916997576523776 |
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| author | Wagner, Gregory L. Constantinou, Navid C. |
| author_facet | Wagner, Gregory L. Constantinou, Navid C. |
| contents | 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), wherein the curl of the Stokes drift, $\boldsymbol{\nabla}\times\boldsymbol{u}^S$, takes on the role of the background vorticity (for example, $(f_0 + βy) \hat{\boldsymbol{z}}$ on the beta plane). We pursue this thread further by showing that a two-equation model proposed by Bardina et al. (1985) for rotating turbulence reproduces the simulated evolution of volume-integrated kinetic energy. This success of the two-equation model -- which explicitly parametrizes wave-driven suppression of kinetic energy dissipation -- carries implications for modeling 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phenomenology of decaying turbulence beneath surface waves Wagner, Gregory L. Constantinou, Navid C. Fluid Dynamics Atmospheric and Oceanic Physics 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), wherein the curl of the Stokes drift, $\boldsymbol{\nabla}\times\boldsymbol{u}^S$, takes on the role of the background vorticity (for example, $(f_0 + βy) \hat{\boldsymbol{z}}$ on the beta plane). We pursue this thread further by showing that a two-equation model proposed by Bardina et al. (1985) for rotating turbulence reproduces the simulated evolution of volume-integrated kinetic energy. This success of the two-equation model -- which explicitly parametrizes wave-driven suppression of kinetic energy dissipation -- carries implications for modeling 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. |
| title | Phenomenology of decaying turbulence beneath surface waves |
| topic | Fluid Dynamics Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2503.03871 |