Comparing Ocean Surface Boundary Vertical Mixing Schemes Including Langmuir Turbulence

Six recent Langmuir turbulence parameterization schemes and five traditional schemes are implemented in a common single‐column modeling framework and consistently compared. These schemes are tested in scenarios versus matched large eddy simulations, across the globe with realistic forcing (JRA55‐do, WAVEWATCH‐III simulated waves) and initial conditions (Argo), and under realistic conditions as observed at ocean moorings. Traditional non‐Langmuir schemes systematically underpredict large eddy simulation vertical mixing under weak convective forcing, while Langmuir schemes vary in accuracy. Under global, realistic forcing Langmuir schemes produce 6% (−1% to 14% for 90% confidence) or 5.2 m (−0.2 m to 17.4 m for 90% confidence) deeper monthly mean mixed layer depths than their non‐Langmuir counterparts, with the greatest differences in extratropical regions, especially the Southern Ocean in austral summer. Discrepancies among Langmuir schemes are large (15% in mixed layer depth standard deviation over the mean): largest under wave‐driven turbulence with stabilizing buoyancy forcing, next largest under strongly wave‐driven conditions with weak buoyancy forcing, and agreeing during strong convective forcing. Non‐Langmuir schemes disagree with each other to a lesser extent, with a similar ordering. Langmuir discrepancies obscure a cross‐scheme estimate of the Langmuir effect magnitude under realistic forcing, highlighting limited understanding and numerical deficiencies. Maps of the regions and seasons where the greatest discrepancies occur are provided to guide further studies and observations

Wave Boundary Layer Turbulence over Surface Waves in a Strongly Forced Condition

Accurate predictions of the sea state–dependent air–sea momentum flux require a thorough understanding of the wave boundary layer turbulence over surface waves. A set of momentum and energy equations is derived to formulate and analyze wave boundary layer turbulence. The equations are written in wave-following coordinates, and all variables are decomposed into horizontal mean, wave fluctuation, and turbulent fluctuation. The formulation defines the wave-induced stress as a sum of the wave fluctuation stress (because of the fluctuating velocity components) and a pressure stress (pressure acting on a tilted surface). The formulations can be constructed with different choices of mapping. Next, a large-eddy simulation result for wind over a sinusoidal wave train under a strongly forced condition is analyzed using the proposed formulation. The result clarifies how surface waves increase the effective roughness length and the drag coefficient. Specifically, the enhanced wave-induced stress close to the water surface reduces the turbulent stress (satisfying the momentum budget). The reduced turbulent stress is correlated with the reduced viscous dissipation rate of the turbulent kinetic energy. The latter is balanced by the reduced mean wind shear (satisfying the energy budget), which causes the equivalent surface roughness to increase. Interestingly, there is a small region farther above where the turbulent stress, dissipation rate, and mean wind shear are all enhanced. The observed strong correlation between the turbulent stress and the dissipation rate suggests that existing turbulence closure models that parameterize the latter based on the former are reasonably accurate

Optical Measurements of Capillary-Gravity Wave Spectra Using a Scanning Laser Slope Gauge

A description of a new scanning laser slope gauge (SLSG) is given and the results obtained from both laboratory wind-wave tank and field measurements are presented. The device relies on the measurements of two components of surface slope to compute spatial and temporal lags that are used to estimate the full three-dimensional slope spectrum. The device is capable of resolving frequencies up to 34.7 Hz and wavelengths in the range between 7.9 × 10−3 and 3.08 × 10−1 m. The technique makes use of a two-dimensional laser scanner that samples the perimeter of a circle of 0.154-m diameter (an unfilled aperture). Both laboratory and field results indicate the device is well suited to measure the full three-dimensional spectra of capillary-gravity waves and is capable of providing ground-truthing measurements for the verification of remotely sensed ocean surface features

Sea State Dependence of the Wind Stress Over the Ocean Under Hurricane Winds

The impact of the surface wave field (sea state) on the wind stress over the ocean is investigated with fetch-dependent seas under uniform wind and with complex seas under idealized tropical cyclone winds. Two different approaches are employed to calculate the wind stress and the mean wind profile. The near-peak frequency range of the surface wave field is simulated using the WAVEWATCH III model. The high-frequency part of the surface wave field is empirically determined using a range of different tail levels. The results suggest that the drag coefficient magnitude is very sensitive to the spectral tail level but is not as sensitive to the drag coefficient calculation methods. The drag coefficients at 40 m/s vary from to depending on the saturation level. The misalignment angle between the wind stress vector and the wind vector is sensitive to the stress calculation method used. In particular, if the cross-wind swell is allowed to contribute to the wind stress, it tends to increase the misalignment angle. Our results predict enhanced sea state dependence of the drag coefficient for a fast moving tropical cyclone than for a slow moving storm or for simple fetch-dependent seas. This may be attributed to swell that is significantly misaligned with local wind

Turbulent Airflow at Young Sea States with Frequent Wave Breaking Events: Large-Eddy Simulation

A neutrally stratified turbulent airflow over a very young sea surface at a high-wind condition was investigated using large-eddy simulations. In such a state, the dominant drag at the sea surface occurs over breaking waves, and the relationship between the dominant drag and local instantaneous surface wind is highly stochastic and anisotropic. To model such a relationship, a bottom boundary stress parameterization was proposed for the very young sea surface resolving individual breakers. This parameterization was compared to the commonly used parameterization for isotropic surfaces. Over both the young sea and isotropic surfaces, the main near-surface turbulence structure was wall-attached, large-scale, quasi-streamwise vortices. Over the young sea surface, these vortices were more intense, and the near-surface mean velocity gradient was smaller. This is because the isotropic surface weakens the swirling motions of the vortices by spanwise drag. In contrast, the young sea surface exerts little spanwise drag and develops more intense vortices, resulting in greater turbulence and mixing. The vigorous turbulence decreases the mean velocity gradient in the roughness sublayer below the logarithmic layer. Thus, the enhancement of the air–sea momentum flux (drag coefficient) due to breaking waves is caused not only by the streamwise form drag over individual breakers but also by the enhanced vortices. Furthermore, contrary to an assumption used in existing wave boundary layer models, the wave effect may extend as high as 10–20 times the breaking wave height

Impact of Dominant Breaking Waves on Air–Sea Momentum Exchange and Boundary Layer Turbulence at High Winds

Large-eddy simulation (LES) is used to investigate how dominant breaking waves in the ocean under hurricane-force winds affect the drag and near-surface airflow turbulence. The LES explicitly resolves the wake turbulence produced by dominant-scale breakers. Effects of unresolved roughness such as short breakers, nonbreaking waves, and sea foam are modeled as the subgrid-scale drag. Compared to the laboratory conditions previously studied using the same method, dominant-scale breakers in open-ocean conditions are less frequent, and the subgrid-scale drag is more significant. Nevertheless, dominant-scale breakers are more fully exposed to high winds and produce more intense wakes individually. As a result, they support a large portion of the total drag and significantly influence the turbulence for many ocean conditions that are likely to occur. The intense wake turbulence is characterized by flow separation, upward bursts of wind, and upward flux of the turbulent kinetic energy (TKE), all of which may influence sea spray dispersion. Similarly to the findings in the laboratory conditions, high production of wake turbulence shortcuts the inertial energy cascade, causes high TKE dissipation, and contributes to the reduction of the drag coefficient. The results also indicate that if the drag coefficient decreases with increasing wind at very high winds, as some recent observations suggest, then the unresolved roughness must also decrease

Effect of Surface Waves on Air–Sea Momentum Exchange. Part I: Effect of Mature and Growing Seas

The effect of surface waves on air–sea momentum exchange over mature and growing seas is investigated by combining ocean wave models and a wave boundary layer model. The combined model estimates the wind stress by explicitly calculating the wave-induced stress. In the frequency range near the spectral peak, the NOAA/ NCEP surface wave model WAVEWATCH-III is used to estimate the spectra, while the spectra in the equilibrium range are determined by an analytical model. This approach allows for the estimation of the drag coefficient and the equivalent surface roughness for any surface wave fields. Numerical experiments are performed for constant winds from 10 to 45 m s−1 to investigate the effect of mature and growing seas on air–sea momentum exchange. For mature seas, the Charnock coefficient is estimated to be about 0.01 ∼ 0.02 and the drag coefficient increases as wind speed increases, both of which are within the range of previous observational data. With growing seas, results for winds less than 30 m s−1 show that the drag coefficient is larger for younger seas, which is consistent with earlier studies. For winds higher than 30 m s−1, however, results show a different trend; that is, very young waves yield less drag. This is because the wave-induced stress due to very young waves makes a small contribution to the total wind stress in very high wind conditions

Effect of surface waves on Charnock coefficient under tropical cyclones

The dependence of the air‐sea momentum flux on surface wave fields is investigated at very high winds under tropical cyclones. A coupled wave‐wind model is applied to estimate the momentum flux under ten hurricanes in the western Atlantic Ocean during 1998–2003. The model explicitly calculates the wave‐induced stress vector and the total wind stress vector from a given wind speed vector and a calculated wave spectrum. It is found that the neutral drag coefficient levels off at high wind speeds under tropical cyclones, being consistent with recent observations and previous modeling studies. The most important finding of this study is that the Charnock coefficient is mainly determined by two parameters: the input wave age (wave age determined by the peak frequency of wind energy input) and the wind speed, regardless of the complexity of the wave field under a real hurricane, and that the Charnock coefficient increases with the input wave age at very high winds

Impact of Breaking Wave Form Drag on Near-Surface Turbulence and Drag Coefficient over Young Seas at High Winds

The effects of breaking waves on near-surface wind turbulence and drag coefficient are investigated using large-eddy simulation. The impact of intermittent and transient wave breaking events (over a range of scales) is modeled as localized form drag, which generates airflow separation bubbles downstream. The simulations are performed for very young sea conditions under high winds, comparable to previous laboratory experiments in hurricane-strength winds. The results for the drag coefficient in high winds range between about 0.002 and 0.003. In such conditions more than 90% of the total air–sea momentum flux is due to the form drag of breakers; that is, the contributions of the nonbreaking wave form drag and the surface viscous stress are small. Detailed analysis shows that the breaker form drag impedes the shear production of the turbulent kinetic energy (TKE) near the surface and, instead, produces a large amount of small-scale wake turbulence by transferring energy from large-scale motions (such as mean wind and gusts). This process shortcuts the inertial energy cascade and results in large TKE dissipation (integrated over the surface layer) normalized by friction velocity cubed. Consequently, the large production of wake turbulence by breakers in high winds results in the small drag coefficient obtained in this study. The results also suggest that common parameterizations for the mean wind profile and the TKE dissipation inside the wave boundary layer, used in previous Reynolds-averaged Navier–Stokes models, may not be valid

Effect of Surface Waves on Air–Sea Momentum Exchange. Part II: Behavior of Drag Coefficient under Tropical Cyclones

Present parameterizations of air–sea momentum flux at high wind speed, including hurricane wind forcing, are based on extrapolation from field measurements in much weaker wind regimes. They predict monotonic increase of drag coefficient (Cd) with wind speed. Under hurricane wind forcing, the present numerical experiments using a coupled ocean wave and wave boundary layer model show that Cd at extreme wind speeds strongly depends on the wave field. Higher, longer, and more developed waves in the right-front quadrant of the storm produce higher sea drag; lower, shorter, and younger waves in the rear-left quadrant produce lower sea drag. Hurricane intensity, translation speed, as well as the asymmetry of wind forcing are major factors that determine the spatial distribution of Cd. At high winds above 30 m s−1, the present model predicts a significant reduction of Cd and an overall tendency to level off and even decrease with wind speed. This tendency is consistent with recent observational, experimental, and theoretical results at very high wind speeds