Direct numerical simulations of the nonbreaking surface-wave-induced turbulence

Abstract Direct numerical simulations of the turbulence induced by nonbreaking surface waves were conducted to clarify the turbulence generation mechanism and evaluate the turbulent mixing intensity with a sigma-coordinate free-surface nonhydrostatic model. One of the simulations was modeled after a previously reported laboratory experiment with a wave of 30 cm wavelength and 1 cm amplitude freely propagating on the initially stratified water under a windless condition. The simulation showed that organized vortex pairs like Langmuir circulations (LCs) grew, and the water was mixed vertically. The enstrophy budget analysis revealed that the vortex pairs were generated nonlocally through the interaction between surface waves and a surface shear flow, the same mechanism for the LCs, except that the flow is forced by not the wind but the virtual wave stress due to viscous wave attenuation. The analysis also revealed that the local turbulence generation mechanism by the wave orbital motions (as inferred by the previous laboratory study) did not work in our simulated turbulence. The simulated eddy diffusivity was $$\varvec{O}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> </mml:math> (10 $$^{\varvec{-5}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> m $$^{\varvec{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> s $$^{\varvec{-1}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> ) and its vertical profile and temporal changes were different from those of the parameterized diffusivity based on the local turbulence generation mechanism. The nonbreaking wave-induced mixing observed in our simulations under windless conditions is expected to occur in the real open ocean. These results suggest that to parameterize this mixing, parameterization of the nonlocal Langmuir turbulence, with wind stress replaced by virtual wave stress, could be an effective approach.