Langmuir circulations (LCs) generated by the interaction between wind-driven currents and surface waves can engulf the whole water column in neutrally stratified shallow water and interact with the turbulence in the bottom boundary layer. In this study, we perform a mechanistic study using wall-resolved large-eddy simulations (LES) based on the Craik–Leibovich equations to investigate the effects of LCs on turbulence statistics in the bottom half of shallow water. The highest Reynolds number considered in this paper, $Re_{\unicode[STIX]{x1D70F}}=1000$, is larger than the values considered in wall-resolved LES studies of shallow-water Langmuir turbulence reported in literature. The logarithmic layer is diagnosed based on a plateau region in the profile of a diagnostic function. It is found that the logarithmic layer disrupted at $Re_{\unicode[STIX]{x1D70F}}=395$ reappears at $Re_{\unicode[STIX]{x1D70F}}=1000$, but the von Kármán constant is slightly different from the traditional value $0.41$. To study the effects of LCs on turbulence statistics, LCs are extracted using streamwise averaging. The velocity fluctuations $u_{i}^{\prime }$ are decomposed into a LC-coherent part $u_{i}^{L}$ and a residual turbulence part $u_{i}^{T}$. It is found that the profiles of LC-coherent Reynolds shear stress $-\langle u^{L}v^{L}\rangle$ obtained at various Reynolds numbers are close to each other in the water-column coordinate $y/h$, with $h$ being the half-water depth. As the Reynolds number (or, by definition, the ratio between the outer and inner length scales) increases, the influence of LCs on the near-bottom momentum transfer is reduced, which is responsible for the reappearance of the logarithmic layer. At all of the Reynolds numbers under investigation, the peaks of $\langle u^{L}u^{L}\rangle$ are collocated in the water-column coordinate $y/h$, while those of $\langle u^{T}u^{T}\rangle$ are collocated in the inner-scale coordinate $y/(\unicode[STIX]{x1D708}/u_{\unicode[STIX]{x1D70F}})$. Due to the increase in the distance between the peaks of $\langle u^{L}u^{L}\rangle$ and $\langle u^{T}u^{T}\rangle$ with the Reynolds number, the profile of $\langle u^{\prime }u^{\prime }\rangle$ forms a bimodal shape at $Re_{\unicode[STIX]{x1D70F}}=700$ and $1000$.

The effects of a water surface wave on the vorticity in the turbulence underneath are studied for Langmuir turbulence using wave-phase-resolved large-eddy simulation. The simulations are performed on a dynamically evolving wave-surface-fitted grid such that the phase-resolved wave motions and their effects on the turbulence are explicitly captured. This study focuses on the vorticity structures and dynamics in Langmuir turbulence driven by a steady and co-aligned progressive wave and surface shear stress. For the first time, the detailed vorticity dynamics of the wave–turbulence interaction in Langmuir turbulence in a wave-phase-resolved frame is revealed. The wave-phase-resolved simulation provides detailed descriptions of many characteristic features of Langmuir turbulence, such as elongated quasi-streamwise vortices. The simulation also reveals the variation of the strength and the inclination angles of the vortices with the wave phase. The variation is found to be caused by the periodic stretching and tilting of the wave orbital straining motions. The cumulative effect of the wave on the wave-phase-averaged vorticity is analysed using the Lagrangian average. It is discovered that, in addition to the tilting effect induced by the Lagrangian mean shear gradient of the wave, the phase correlation between the vorticity fluctuations and the wave orbital straining is also important to the cumulative vorticity evolution. Both the fluctuation correlation effect and the mean tilting effect are found to amplify the streamwise vorticity. On the other hand, for the vertical vorticity, the fluctuation correlation effect cancels the mean tilting effect, and the net change of the vertical vorticity by the wave straining is negligible. As a result, the wave straining enhances only the streamwise vorticity and cumulatively tilts vertical vortices towards the streamwise direction. The above processes are further quantified analytically. The role of the fluctuation correlation effect in the wave-phase-averaged vorticity dynamics provides a deeper understanding of the physical processes underlying the wave–turbulence interaction in Langmuir turbulence.

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