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Mutual Interaction between Surface Waves and Langmuir Circulations Observed in Wave-Resolving Numerical Simulations

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  • 1 Graduate School of Science, Kyoto University, Kyoto, and Research Fellow of Japan Society for the Promotion of Science, University of Tokyo, Tokyo, Japan
  • 2 Graduate School of Science, Kyoto University, Kyoto, Japan
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Abstract

Wave-resolving simulations of monochromatic surface waves and Langmuir circulations (LCs) under an idealized condition are performed to investigate the dynamics of wave–current mutual interaction. When the Froude number (the ratio of the friction velocity of wind stress imposed at the surface and wave phase speed) is large, waves become refracted by the downwind jet associated with LCs and become amplitude modulated in the crosswind direction. In such cases, the simulations using the Craik–Leibovich (CL) equation with a prescribed horizontally uniform Stokes drift profile are found to underestimate the intensity of LCs. Vorticity budget analysis reveals that horizontal shear of Stokes drift induced by the wave modulation tilts the wind-driven vorticity to the downwind direction, intensifying the LCs that caused the waves to be modulated. Such an effect is not reproduced in the CL equation unless the Stokes drift of the waves modulated by LCs is prescribed. This intensification mechanism is similar to the CL1 mechanism in that the horizontal shear of the Stokes drift plays a key role, but it is more likely to occur because the shear in this interaction is automatically generated by the LCs whereas the shear in the CL1 mechanism is retained only when a particular phase relation between two crossing waves is kept locked for many periods.

Current affiliation: Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba, Japan.

Corresponding author: Yasushi Fujiwara, yfujiwara@edu.k.u-tokyo.ac.jp

Abstract

Wave-resolving simulations of monochromatic surface waves and Langmuir circulations (LCs) under an idealized condition are performed to investigate the dynamics of wave–current mutual interaction. When the Froude number (the ratio of the friction velocity of wind stress imposed at the surface and wave phase speed) is large, waves become refracted by the downwind jet associated with LCs and become amplitude modulated in the crosswind direction. In such cases, the simulations using the Craik–Leibovich (CL) equation with a prescribed horizontally uniform Stokes drift profile are found to underestimate the intensity of LCs. Vorticity budget analysis reveals that horizontal shear of Stokes drift induced by the wave modulation tilts the wind-driven vorticity to the downwind direction, intensifying the LCs that caused the waves to be modulated. Such an effect is not reproduced in the CL equation unless the Stokes drift of the waves modulated by LCs is prescribed. This intensification mechanism is similar to the CL1 mechanism in that the horizontal shear of the Stokes drift plays a key role, but it is more likely to occur because the shear in this interaction is automatically generated by the LCs whereas the shear in the CL1 mechanism is retained only when a particular phase relation between two crossing waves is kept locked for many periods.

Current affiliation: Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba, Japan.

Corresponding author: Yasushi Fujiwara, yfujiwara@edu.k.u-tokyo.ac.jp
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