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Jin-Bao Song and Michael L. Banner

Abstract

Wave breaking in the open ocean and coastal zones remains an intriguing yet incompletely understood process, with a strong observed association with wave groups. Recent numerical study of the evolution of fully nonlinear, two-dimensional deep water wave groups identified a robust threshold of a diagnostic growth-rate parameter that separated nonlinear wave groups that evolved to breaking from those that evolved with recurrence. This paper investigates whether these deep water wave-breaking results apply more generally, particularly in finite- water-depth conditions. For unforced nonlinear wave groups in intermediate water depths over a flat bottom, it was found that the upper bound of the diagnostic growth-rate threshold parameter established for deep water wave groups is also applicable in intermediate water depths, given by k 0 h ≥ 2, where k 0 is the mean carrier wavenumber and h is the mean depth. For breaking onset over an idealized circular arc sandbar located on an otherwise flat, intermediate-depth (k 0 h ≥ 2) environment, the deep water breaking diagnostic growth rate was found to be applicable provided that the height of the sandbar is less than one-quarter of the ambient mean water depth. Thus, for this range of intermediate-depth conditions, these two classes of bottom topography modify only marginally the diagnostic growth rate found for deep water waves. However, when intermediate- depth wave groups (k 0 h ≥ 2) shoal over a sandbar whose height exceeds one-half of the ambient water depth, the waves can steepen significantly without breaking. In such cases, the breaking threshold level and the maximum of the diagnostic growth rate increase systematically with the height of the sandbar. Also, the dimensions and position of the sandbar influenced the evolution and breaking threshold of wave groups. For sufficiently high sandbars, the effects of bottom topography can induce additional nonlinearity into the wave field geometry and associated dynamics that modifies the otherwise robust deep water breaking-threshold results.

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Michael L. Banner and Jin-Bao Song

Abstract

Part I of this study describes the authors' findings on a robust threshold variable that determines the onset of breaking for unforced, irrotational deep water waves and proposes a means of predicting the strength of breaking if the breaking threshold is exceeded. Those results were based on a numerical study of the unforced evolution of fully nonlinear, two-dimensional inviscid wave trains and highlight the fundamental role played by the nonlinear wave group dynamics. In Part II the scope of these calculations is extended to investigate the additional influence of wind forcing and background shear on the evolution to breaking.

Using the methodology described in Part I, the present study focuses on the influence of wind forcing and vertical shear on long-term evolution toward breaking or recurrence of the maximum of the local energy density within a wave group. It investigates the behavior of a dimensionless local growth rate parameter that reflects the mean energy flux to the energy maximum in the wave group and provides a clearer physical interpretation of the evolution toward recurrence or breaking. Typically, the addition of the wind forcing and surface layer shear results in only small departures from the irrotational, unforced cases reported in Part I. This indicates that nonlinear hydrodynamic energy fluxes within wave groups still dominate the evolution to recurrence or breaking even in the presence of these other mechanisms. Further, the calculations confirm that the breaking threshold for this growth rate found for unforced irrotational wave groups in Part I is also applicable for cases with wind forcing and shear typical of open ocean conditions. Overall, this approach provides an earlier and more decisive indicator for the onset of breaking than previously proposed breaking thresholds and suggests a foundation for predicting the strength of breaking events.

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Jin-Bao Song and Michael L. Banner

Abstract

Finding a robust threshold variable that determines the onset of breaking for deep water waves has been an elusive problem for many decades. Recent numerical studies of the unforced evolution of two-dimensional nonlinear wave trains have highlighted the complex evolution to recurrence or breaking, together with the fundamental role played by nonlinear intrawave group dynamics. In Part I of this paper the scope of two-dimensional nonlinear wave group calculations is extended by using a wave-group-following approach applied to a wider class of initial wave group geometries, with the primary goal of identifying the differences between evolution to recurrence and to breaking onset. Part II examines the additional influences of wind forcing and background shear on these evolution processes.

The present investigation focuses on the long-term evolution of the maximum of the local energy density along wave groups. It contributes a more complete picture, both long-term and short-term, of the approach to breaking and identifies a dimensionless local average growth rate parameter that is associated with the mean convergence of wave-coherent energy at the wave group maximum. This diagnostic growth rate appears to have a common threshold for all routes to breaking in deep water that have been examined and provides an earlier and more decisive indicator for the onset of breaking than previously proposed breaking thresholds. The authors suggest that this growth rate may also provide an indicative measure of the strength of wave breaking events.

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Yao Xu, Hailun He, Jinbao Song, Yijun Hou, and Funing Li

Abstract

Buoy-based observations of surface waves during three typhoons in the South China Sea were used to obtain the wave characteristics. With the local wind speeds kept below 35 m s−1, the surface waves over an area with a radius 5 times that of the area in which the maximum sustained wind was found were mainly dominated by wind-wave components, and the wave energy distribution was consistent with fetch-limited waves. Swells dominated the surface waves at the front of and outside the central typhoon region. Next, the dynamics of the typhoon waves were studied numerically using a state-of-the-art third-generation wave model. Wind forcing errors made a negligible contribution to the surface wave results obtained using hindcasting. Near-realistic wind fields were constructed by correcting the idealized wind vortex using in situ observational data. If the different sets of source terms were further considered for the forcing stage of the typhoon, which was defined as the half inertial period before and after the typhoon arrival time, the best model performance had mean relative biases and root-mean-square errors of −0.7% and 0.76 m, respectively, for the significant wave height, and −3.4% and 1.115 s, respectively, for the peak wave period. Different sets of source terms for wind inputs and whitecapping breaking dissipation were also used and the results compared. Finally, twin numerical experiments were performed to investigate the importance of nonlinear wave–wave interactions on the spectrum formed. There was evidence that nonlinear wave–wave interactions efficiently transfer wave energy from high frequencies to low frequencies and prevent double-peak structures occurring in the frequency-based spectrum.

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An-Zhou Cao, Hui Chen, Wei Fan, Hai-Lun He, Jin-Bao Song, and Ji-Cai Zhang

Abstract

Previous studies have shown that strong tidal currents can cause intense turbulent mixing near the seafloor in continental shelf areas. To quantify the turbulent mixing, the eddy viscosity coefficient is generally used. In this study, an estimation scheme is proposed to evaluate the eddy viscosity profile (EVP) in the bottom Ekman boundary layer based on the adjoint method. The estimation scheme is composed of the bottom Ekman boundary layer model and its adjoint model, and a minimization algorithm. The feasibility and effectiveness of the proposed scheme are validated by a series of twin experiments, where the proposed scheme is compared with three other schemes in previous studies. When large measurement errors exist, the proposed scheme performs better than the three other schemes. When large Ekman balance errors exist, the proposed scheme is better than two of the other schemes. The selection of components of the steady current and tidal constituents also influences the performance of the proposed scheme. Successful estimation of the EVP requires the usage of intense components of the steady current and tidal constituents. With the usage of the intense components, increasing the number of tidal constituents cannot lead to a more accurate estimation of the EVP.

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Zhongshui Zou, Shuiqing Li, Jian Huang, Peiliang Li, Jinbao Song, Jun A. Zhang, and Zhanhong Wan

Abstract

Turbulence over the mobile ocean surface has distinct properties compared to turbulence over land. Thus, findings that are based on the turbulent kinetic energy (TKE) budget and Monin–Obukhov similarity theory (MOST) over land may not be applicable to conditions over ocean partly because of the existence of a wave boundary layer (the lower part of atmospheric boundary layer including effects of surface waves; we used the term “WBL” in this article for convenience), where the total stress can be separated into turbulent stress and wave coherent stress. Here the turbulent stress is defined as the stress generated by wind shear and buoyancy, while the wave coherent stress accounts for the momentum transfer between ocean waves and atmosphere. In this study, applicability of the turbulent kinetic energy (TKE) budget and the inertial dissipation method (IDM) in the context of the MOST within the WBL are examined. It was found that turbulent transport terms in the TKE budget should not be neglected when calculating the total stress under swell conditions. This was confirmed by observations made on a fixed platform. The results also suggested that turbulent stress, rather than total stress, should be used when applying the MOST within the WBL. By combining the TKE budget and MOST, our study showed that the stress computed by the traditional IDM corresponds to the turbulent stress rather than the total stress. The swell wave coherent stress should be considered when applying the IDM to calculate the stress in the WBL.

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Jia Sun, Hailun He, Xiaomin Hu, Dingqi Wang, Cen Gao, and Jinbao Song

Abstract

We used a mesoscale atmospheric model to simulate Typhoon Hagupit (2008) in the South China Sea (SCS). First, we chose optimized parameterization schemes based on a series of sensitivity tests. The results suggested that a combination of the Kain–Fritsch cumulus scheme and the Goddard microphysics scheme was the best choice for reproducing both the track and intensity of Typhoon Hagupit. Next, the simulated rainfall was compared with microwave remote sensing products. This comparison validated the model results for both the magnitude of rainfall and the location of heavy rain relative to the typhoon’s center. Furthermore, the potential vorticity and vertical wind speed displayed the asymmetric horizontal and tilted vertical structures of Typhoon Hagupit. Finally, we compared the simulation of air–sea turbulent fluxes with estimations from an in situ buoy. The time series of momentum fluxes were roughly consistent, while the model still overestimated heat fluxes, especially right before the typhoon’s arrival at the buoy.

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Jian Huang, Zhongshui Zou, Qingcun Zeng, Peiliang Li, Jinbao Song, Lin Wu, Jun A. Zhang, Shuiqing Li, and Pak-wai Chan

Abstract

The turbulent structure within the marine atmospheric boundary layer is investigated based on four levels of observations at a fixed marine platform. During and before a cold front, the ocean surface is dominated by wind sea and swell waves, respectively, affording the opportunity to test the theory recently proposed in laboratory experiments or for flat land surfaces. The results reveal that the velocity spectra follow a k −1 law within the intermediate wavenumber (k) range immediately below inertial subrange during the cold front. A logarithmic height dependence of the horizontal velocity variances is also observed above the height of 20 m, while the vertical velocity variances increase with increasing height following a power law of 2/3. These features confirm the attached eddy model and the “top-down model” of turbulence over the ocean surface. However, the behavior of velocity variances under swell conditions is much different from those during the cold front, although a remarkable k −1 law can be observed in the velocity spectra. The quadrant analysis of the momentum flux also shows a significantly different result for the two conditions.

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