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Abstract Spectral surface wave models predict the wave action evolution of multiple wave components. It is well understood that the group speed of the wave action of a particular wave component is modified if an Eulerian near-surface current exists. However, a typical ocean wave field also introduces a significant integrated Stokes drift, or Lagrangian mass transport, and its impact on the group speed of a particular wave component is not well known. In this study, the wave evolution equations are derived in the presence of two wave trains, and the impacts of one wave train on the phase and group speeds of the other wave train are investigated. The results are extended to estimate the impact of the entire wave spectrum on the propagation of a particular wave train. It is found that the group speed of the dominant waves can be significantly enhanced by the presence of other waves, by up to 0.3–0.4 m s⁻¹or 4%–5%, in strongly wind-forced conditions under tropical cyclones. This increase of the group speed is almost twice as large as the advection by a sheared current with the same profile as the Stokes drift integrated over the wave spectrum. Introducing this enhanced group speed in the wave models may make a noticeable impact on their surface wave predictions. It is also found that the increase of the phase speed of a particular wave component is much larger than the advection by a sheared current with the same profile as the integrated Stokes drift. 

Mathematica and Matlab codes used in the study 

Abstract Recent field observations suggest that the air‐sea momentum flux (or the drag coefficient) is significantly reduced when the dominant wind‐forced surface waves are misaligned from local wind. Such conditions may occur under rapidly changing strong winds (such as under tropical cyclones) or in coastal shallow waters where waves are refracted by bottom topography. A recent Large Eddy Simulation (LES) study also shows that the drag coefficient is reduced by a misaligned strongly forced wave train (with a small wave age of 1.37). In order to investigate more realistic field conditions, this study employs LES to examine the effect of a misaligned (up to 90°) surface wave train over a wide range of wave age up to 10.95. For all wave ages examined, the drag coefficient is reduced compared to the flat surface condition when the misalignment angle exceeds around 22.5°–45°. The drag reduction may occur even if the form drag of the wave train is positive. 

Abstract The drag coefficient under tropical cyclones and its dependence on sea states are investigated by combining upper-ocean current observations [using electromagnetic autonomous profiling explorer (EM-APEX) floats deployed under five tropical cyclones] and a coupled ocean–wave (Modular Ocean Model 6–WAVEWATCH III) model. The estimated drag coefficient averaged over all storms is around 2–3 × 10 −3 for wind speeds of 25–55 m s −1 . While the drag coefficient weakly depends on wind speed in this wind speed range, it shows stronger dependence on sea states. In particular, it is significantly reduced when the misalignment angle between the dominant wave direction and the wind direction exceeds about 45°, a feature that is underestimated by current models of sea state–dependent drag coefficient. Since the misaligned swell is more common in the far front and in the left-front quadrant of the storm (in the Northern Hemisphere), the drag coefficient also tends to be lower in these areas and shows a distinct spatial distribution. Our results therefore support ongoing efforts to develop and implement sea state–dependent parameterizations of the drag coefficient in tropical cyclone conditions. 

This study utilizes a large-eddy simulation (LES) approach to systematically assess the directional variability of wave-driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik–Leibovich vortex force, is obtained through spectral wave simulations. LT’s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of a TC’s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth-averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near-surface layer with predominant production of turbulent kinetic energy by Stokes drift shear, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind-driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind–wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind-forced waves.