Displays

Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schrödinger equation (NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability (MI) of the NLSE was analyzed in this paper, and the region of MI for gravity waves (the necessary condition for the existence of freak waves) was identified. In this paper, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive (negative) vorticity on MI can be balanced out by that of uniform down- (up-)flow. Furthermore, the Peregrine breather (PB) solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of free surface elevation, whereas negative vorticity decreases it.

Showing the record strengths and growth-rates, a number of recent hurricanes have highlighted needs for improving forecasts of tropical cyclone intensities most sensitive to models of the air-sea coupling. Especially challenging is the nature and effect of the very small-scale phenomena, the sea-spray and foam, supposed to strongly affecting the momentum- and heat- air-sea fluxes at strong winds. This talk will focus on our progress in understanding and describing these "micro-scale" processes, their physical properties, the spray and foam mediated air-sea fluxes and the impact on the development of marine storms.

The starting points for this study were two laboratory experiments. The first one was designed for investigation of the spray generation mechanisms at high winds. We found out 3 dominant spray generating mechanisms: stretching liquid ligaments, bursting bubbles, splashing of the falling droplets and "bag-breakup". We investigated the efficiency spray-production mechanisms and developed the empirical statistics of the numbers of the spray generating events of each type. Basing on the "white-cap method" we found out the dependence of the spray-generating events on the wind fetch. The main attention was paid to the "bag-breakup" mechanism. Here we studied in detail the statistics of spray produced from one "bag-breakup" event. Basing on these developments, we estimated heat and momentum fluxes from the spray-generating events of different types and found out the dominant role of the "bag-breakup" mechanism.

To estimate the direct heat and momentum fluxes from the ocean surface to the atmosphere, we studied in the special experiment the foam impact on the short-wave part of the surface waves and the heat momentum exchange in the atmospheric boundary layer at high winds. Based on these results, we suggest a simple model for the aerodynamic and temperature roughness and the eddy viscosity in the turbulent boundary layer over a fractionally foam-covered water surface.

The synergetic effect of foam at the water surface and spray in the marine atmospheric boundary layer on ocean surface resistance at high winds is estimated so as to be able to explain the observed peculiarities of the air-sea fluxes at stormy conditions. Calculations within the nonhydrostatic axisymmetric model show, that the "microphysics" of the air-sea coupling significantly accelerate development of the ocean storm.

This work was supported by RFBR grant 19-05-00249 and RSF grant 19-17-00209.

Rapid intensification of tropical cyclones is a challenge for forecasters. In 2017, Hurricane Maria intensified to a Category 5 storm within 24 hours and devastated Puerto Rico. The official forecast and all computer models were unable to predict it. Hurricane Dorian had been predicted as a tropical storm; unexpectedly, it intensified into a Category 5 storm and destroyed the Bahamas. Soloviev et al. (2017) suggested that under the assumption of constant enthalpy exchange coefficient, rapid cyclone intensification and decay can be related to the drag coefficient dependence on wind speed including an “aerodynamic drag well” around 60 m/s. This concept is in general terms consistent with Emanuel’s (1988) theory of maximum potential intensity of a tropical cyclone and its extension by Lee et al. (2019). The influence of sea spray is still a significant uncertainty. In order to study the effect of spray on dynamics of tropical cyclones, we have implemented a Volume of Fluid to Discrete-Phase Model (VOF to DPM). This model re-meshes the areas with increased gradients or curvature, which are suspicious for the interface instability. The generated water particles that satisfy the condition of asphericity are converted into Lagrangian particles. The size distribution of spray measured in air-sea interaction facilities is used for the model verification. Due to dynamic remeshing, VOF to DPM resolves spray particle radius from ten micrometers to a few millimeters, which correspond to spume. Results of the numerical simulation show a dramatic increase of spume generation under major tropical cyclones. Though sub-micrometer and micrometer scale spray particles are not resolved in this simulation, they are likely less significant in the momentum exchange at the air-sea interface than spume. These results are expected to contribute to the parameterization and proper treatment of spray in forecasting models, including cases of rapid intensification and rapid decline of tropical cyclones.
References:
Emanuel, K. A. (1988). The maximum intensity of hurricanes. JAS 45, 1143–1155.
Soloviev, A. V., Lukas, R., Donelan, M.A., Haus, B. K., Ginis, I. (2017). Is the state of the air-sea interface a factor in rapid intensification and rapid decline of tropical cyclones? JGR - Oceans 122, 10174-10183.
Lee, W., Kim, S.‐H., Chu, P.‐S., Moon,I.‐J., and Soloviev, A. V. (2019). An index to better estimate tropical cyclone intensity change in the western North Pacific. GRL 46, 8960-8968.

The study is based on a simple parametric model, which is an extension of the self-similarity theory for surface waves generated by a wind field. According to the original similarity concept, the development of wind waves can be fully described using the scale of the fetch length (or time) and wind velocity. The aim of the work is to develop a parametric model to describe the wave generation in arbitrary spatio-temporal wind field. We assume that in this case similarity laws are also fulfilled, i.e., the rate of spectral the peak frequency and wave energy change is completely determined by the wave age. The source function is written in a form providing the stationary solution that corresponds to the well-known fetch law, confirmed in numerous experiments.

In order to extend the equations to the two-dimensional case, when the wind change occurs in both directions, it is assumed that the relations stay valid if the wind speed is replaced by its component in spectral peak direction. In this case, the system of equations should be supplemented by an expression for the evolution of spectral peak direction, describing its adaptating to the direction of non-uniform wind.

The algorithm for solving the complete system of equations describing the evolution of wave height, spectral peak frequency, its propagation direction and focusing/defocusing of wave energy, is based on the method of characteristics. To simulate the evolution of waves in a hurricane, we use the calculation in a non-stationary reference system associated with the hurricane. Coordinates, wave peak frequency, energy and direction are calculated along ray trajectory at every discrete time moment. To increase the stability of the numerical scheme, an implicit 4th-order Runge-Kutta method is used.

Test calculations were carried out for the case of the wave development from the coast with a uniform wind and then for an inhomogeneous cyclonic wind field for different hurricane speeds. The calculations reproduce the anisotropy of the energy distribution inside the hurricane and the effect of wave trapping by a moving cyclone. A comparison of the results with available field measurements of wave parameters in tropical cyclones showed their good agreement. The proposed algorithm can be used in wave forecast models and can serve for deeper understanding the wave field formation in extreme conditions.

The work was supported by Russian Science Foundation via grant 17-77-30019 and the Ministry of Education and Science of the Russian Federation under the State Assignment No. 0827-2018-0003.

The thermodynamic and emissive properties of the ocean thermal skin layer are crucial contributors to air-sea heat flux. In order to properly observe ocean surface temperature without disturbing any delicate fluid mechanical processes, thermal infrared imaging is often used. However, wind impacting the ocean surface complicates the extraction of meaningful information from thermal imagery; this is especially true for transient forcing phenomena such as wind gusts. Here, we describe wind gust-water surface interaction through its impact on skin layer thermal and emissive properties. Two key physical processes are identified: (1) the growth of centimeter-scale wind waves, which increases interfacial emissivity and (2) microscale wave breaking and shear, which mix the cool skin layer with warmer millimeter-depth water and increase the skin temperature. As more observations are made of air-sea interaction under transient forcing, the full consideration of these processes becomes increasingly important.

Numerous observations show that in spite of relative motions of floes caused by wave propagation in marginal ice zone (MIZ) direct contacts between them don’t occur. Nevertheless, relative motions of floes may influence formation of oscillating water currents between them which take and dissipate the energy of incoming waves. Full-scale and laboratory experiments were performed to investigate characteristics of water currents between interacting floes. The experiments included the investigation of vertical and horizontal oscillating motions of floes in ice environment. During the experiments we recorded floe accelerations, water pressure and water velocity. Main goal of the experiments was to estimate effective viscosity of water in gapes between interacting floes, describe floe-floe forces caused by the floe accelerations, and estimate the influence of slush formation on the effective viscosity of water. The floe motion was initiated by mechanical pooling, towing with a rope and by original pendulum rig. The experiments were performed in the Van-Mijen Fjord of Spitsbergen in winter seasons of 2018 and 2019, and in the wave flume at UNIS. A lubrication theory was used to describe the dependence of water pressure between interacting floes from their relative speed and the distance between approaching surfaces. Comparison of numerical simulations with experimental records showed that the action of water pressure and the formation of flow jets can prevent direct collision of approaching floes. Obtained analytical formulas are used for the formulation of rheological equations describing the behavior of broken ice in MIZ.                  

The reduction of arctic summer ice coverage has prompted a renewed interest in the physics of wave-ice interactions. Progress has been made on the observational, theoretical and modeling aspects of waves in the presence of ice.

This presentation will address our recent observational studies of spectral wave properties in the marginal ice zone, and in ice covered seas. Waves propagating through ice are attenuated and scattered, resulting in a pronounced change of the shape of the wave spectrum. In particular, the strong attenuation of the high frequency components affects wave steepness and the spectral bandwidth, and thus wave groupiness and the crest height distribution.

We present data for various ice conditions, obtained from drifting SWIFT buoys, a moored ADCP and moored inverted echosounders. All observations show well developed group structures of the waves. However, for different datasets we obtain opposite dependencies between wave groupiness and wave spectral characteristics. This suggests that depending on ice condition, both, the linear mechanism of wave superposition, or wave nonlinarites can be responsible for the wave group enhancement in ice. These mechanisms will be discussed.

The global analyses and medium range forecasts from the European Centre for Medium range Weather Forecasts rely on a state-of-the-art Numerical Weather Prediction (NWP) system. To best represent the air-sea exchanges, it is tightly coupled to an ocean wave model.  As part of ECMWF approach to Earth System Model, it is also coupled to a global ocean model for all its forecasting systems from the medium range up to the seasonal time scale.

Because the feedback from and to the ocean can be significant, it is only in the fully coupled system that parameterisation for air-sea processes should be revisited. For instance, it is now accepted that the drag coefficient should generally attained maximum values for storm winds but should level or even decrease for very strong winds, namely in tropical cyclones or intense mid-latitude wind storms.

A modification of the wind input source was tested, whereby the Charnock coefficient estimated by the wave model and therefore the drag coefficient sharply reduce for large winds (> 30 m/s). As a consequence, ECMWF tendency to under predict strong tropical cyclones was sharply alleviated, in better agreement with observational evidence. This change is now planned for operational implementation with the next model cycle (CY47R1, June 2020).

Experimental evidences also point to a sea state/wind dependency of the heat and moisture fluxes.  Following an extension of the wind wave generation theory, a sea state dependent parameterisation for the roughness length scales for heat and humidity has been tested. Again, a proper assessment of the different parameterisations warrants the fully coupled system. Experimentations so far indicate the benefit of such change. Ongoing work aims at future operational implementation.

Small-scale turbulent dynamics within the coupled atmospheric and oceanic wave boundary layers control air-sea fluxes of momentum and scalars. However measuring and understanding small-scale dynamics very close to the rapidly moving ocean surface remains technically challenging.

We present novel in situ measurements of small-scale motions in the airflow above, and in the water below the wavy air-water interface. A high resolution, large field of view PIV system (Particle Image Velocimetry) was developed for in situ air-water measurements within the first millimeters to meters above and below the wavy surface. The system was recently deployed on a single pile platform in the Szczecin lagoon (Baltic Sea coast, Germany). We will show first results and we will discuss the influence of waves on the partitioning of momentum flux within the coupled air-water wave boundary layers.

CFOSAT is the joint space mission of the French (CNES) and Chinese (CNSA) space agencies dedicated to the observation of ocean surface wind and waves. Two main on-board payloads, the Ku-band near-nadir wave scatterometer SWIM and dual-polarization Ku-band wind scatterometer SCAT for the first time provide regular synchronized surface wind vector and sea state observations on a global scale. 
 
After the first year of the mission, SWIM innovative wave scatterometer conception proved to be suitable for space-born directional wave spectra measurements. The overall performance of the instrument and the quality of inverted data are close to the planned specifications. Moreover, in particular cases, precise wave parameters can be estimated even in limited coastal seas with varying wave and wind conditions.
 
In this work, we will show examples of high-resolution directional wave spectrum fetch evolution as observed by CFOSAT mission. The present analysis was performed for areas with fetch-determined conditions, during periods when waves were generated by strong coastal winds. The dataset includes spectra starting from young wind waves (~20 km fetch distance) to mature almost developed sea state (>450 km fetch). The unique multi-beam configuration of SWIM provides multiple estimates of wave spectral parameters all over the sensor footprint along the satellite track. This allows the capturing of the very fine details of spectral variability with distance from the coast. It will be shown, the observed deviation of direction and wavelength of the measured spectral peak from a wave growth fetch law can be attributed to time-varying or topography-induced coastal wind field inhomogeneities. In some cases, this can be explained by local surface current configuration. The obtained results can be directly compared with third party remote sensing observations, numerical model outputs, classical wave fetch-growth laws, and existing empirical parametrizations. 

Accurate knowledge and understanding of the sea state and its variability is crucial to numerous oceanic and coastal engineering applications, but also to climate change and related impacts including coastal inundation from extreme weather and ice-shelf break-up. The increasing duration of the satellite altimeter record for sea state motivates a range of global analyses, including the examination of changes in ocean climate. For ocean surface waves in particular, the recent development and release of new products providing observations of altimeter-derived significant wave height make long term analyses fairly straightforward.

In this study, significant wave height climatologies and trends over 1992-2017 are intercompared in four recent high-quality global datasets using a consistent methodology. In particular, we make use of products presented by Ribal et al. (2019), and the recently released product developed through the European Space Agency Climate Change Initiative (CCI) for Sea State (Dodet et al. 2020, ESSD, in review). Regional differences in mean climatology are identified and linked to low and high sea states, while temporal trends from the altimetry products, and two reanalysis and hindcast datasets, show general similarity in spatial variation and magnitude but with major differences in equatorial regions and the Indian Ocean. Discrepancies between altimetry products likely arise from differences in calibration and quality control. However, multidecadal observations at buoy stations also highlight issues with wave buoy data, raising questions about their unqualified use, and more fundamentally about uncertainty in all sea state products. We discuss these results in the context of both the current state of knowledge of the changing wave climate, and the on-going development of CCI Sea State altimetry products.

Although the Southern Ocean is often viewed as a very remote area, it plays a critical role in global climate. Waves generated in intense Southern Ocean storms propagate across the Indian, Pacific and Atlantic Oceans and define the wave climate for many areas of these oceans. In addition, the wind and wave climate of the Southern Ocean plays an important role in determining the rate of decay of Antarctic glaciers which are an important element in global sea level change. Despite this important role, little is known about the wind and wave climate of this vast region. This paper will bring together a series of unique datasets to provide a comprehensive view of this wind and wave climate. These datasets include: the long duration model reanalysis dataset ERA-I, a 33-year calibrated and validated altimeter dataset and buoy data from four deployments. These buoys have been located at: Macquarie Island (540S), Campbell Island (520S), a site west of South America (550S) and the Southern Ocean Flux Buoy south of Tasmania (460S). Data from these buoy deployments spans a total of approximately 7 years and provides directional spectra in unique long fetch environments. In addition to providing valuable data for model validation, engineering design and Naval Architecture, these combined datasets provide new insights into air-sea interaction under extremely long fetch conditions. The paper will also use the satellite datasets to investigate changes in wave conditions in recent decades and the role that climate variability plays in such changes. This analysis will examine: long-term trends, annual variability and multi-year oscillations.

Ocean surface (wind-driven) waves continuously shape the coastal environment and play a relevant role in ocean-atmosphere interaction processes. They are also important in operational aspects of ports and have significant energy potential. This research is focused on the interannual variability of the wind waves in the Southeast Pacific, particularly its relationship with the Southern Annular Mode (SAM) and El Niño Southern Oscillation (ENSO). We used a 38-year wave simulation (1979-2016) performed using the Wavewatch III model forced with surface winds and ice concentration from the ERA-Interim reanalysis. Additionally, a cyclone tracking software was used to analyze the trajectories of the extratropical storms which generate the wind waves that reach the coast of western South America. Time series statistics, such as correlation and composites analysis, have been applied to both wave parameters (such as significant wave height and mean period) and directional spectra. Results show a significant and positive correlation between the SAM and the significant wave height and the mean period of the wind waves. However, local storms in central Chile, which are the most damaging extreme wave events for coastal infrastructure, are less frequent during the positive phase of the SAM. Furthermore, a trend analysis shows an increase of the significant wave height during the last decades, which is consistent with the trend toward the positive phase experienced by the SAM. On the other hand, the wave energy of remote origin that travels from the North Pacific toward the Southeast Pacific, which is maximum during the austral summer, shows a significant relationship with the extreme El Niño events. These energetic swells events that reach the coast of western South America during the austral summer are more intense and frequent during the warm phase of ENSO.

Extreme ocean waves shape world coastlines and significantly impact offshore operations. Climate change may further exacerbate these effects increasing losses in human lives and economic activities. Studies generally agree on the trends in the mean values, yet there is no consensus on the extreme events, and whether their magnitude and/or frequency are changing. The present work applies an innovative extreme value analysis approach to a multi-model ensemble wind-wave climate dataset, derived from seven global climate models, to evaluate projected extreme wave height changes towards the end of the 21st century. Under two greenhouse gas emission scenarios, we find that at the end of the 21st century, the one in 100-year wave height event increases across the scenarios by 5 to 15 % over the Southern Ocean. The North Atlantic shows a decrease at low to mid-latitudes (5 to 15 %) and an increase at the high latitudes (10 %). The extreme wave heights in the North Pacific increase at the high latitudes by 5 to 10 %. The present work suggests that pooling an ensemble of future projected ocean storms from different GCMs might significantly improve uncertainty estimates connected to future coastal and offshore wave extremes, thereby improving climate adaptation strategies.

The research we perform has important engineering applications since a lot of marine activities and offshore engineering activities are in shallow water areas where phenomena like bottom and white-capping dissipation and wind growth take place. The physical parametrization of such forcing/dissipation has become an important issue in the improvement of the performance of models in order to provide accurate sea-state information. In this regard, we perform a sensitivity analysis of dissipation parameterizations in the third-generation spectral wave model WAVEWATCH III using the ST6 source term packages, proposed by Zieger-Babanin 2015, to describe wind generation and dissipation due to white-capping and bottom friction.

A system of nested grids is used to model long distance swells generated in the North Atlantic Ocean and propagating all the way to the west coast of Ireland. We used a 30-minute coarse resolution for the North Atlantic grid, a 6-minute intermediate resolution for the North-East Atlantic, and a 3-minute fine resolution in coastal areas closer to Ireland.

The sensitivity analysis in the parameterization is based on the effect of the model performance by varying the adjustable parameters in the wind input source, swell dissipation in terms of the interaction of waves with oceanic turbulence and the drag coefficient to potentially eliminate a bias in the wind field. The results of the model for the coast of Ireland are discussed in terms of various parametrization schemes.

For more than 30 years, many studies have been carried out to improve the understanding of the air-sea interaction and its impact on the predictions of atmospheric and the oceanic processes. It is well understood that the accuracy in predictions of the wind-driven waves is highly dependent on the source input and dissipation terms. The Wave Boundary Layer (WBL) approach for the estimation of surface stress has previously been used to improve the wind and wave simulations under extreme conditions. However, until recently the WBL was only used to determine the roughness length (z₀) and drag coefficient (C_d), but not to alter the wind input source function in wave models. In this study, the wave boundary layer model (WBLM) was implemented in the OpenIFS coupled model as source functions as suggested by Du et al. (2017, 2019). The new wind input and dissipation terms are then tested using numerical model simulations, with a particular focus on the contribution of the high frequency tail in the source input function.  The comparison of the results of this study with published results hints at better performance of the model on the estimation of the roughness length and drag coefficient. This should improve predictions of the significant wave height and wind speeds, especially under extreme conditions.

Corresponding Author: Nefeli Makrygianni (makrygiannin@cardiff.ac.uk)

By using an Acoustic Doppler Velocimeter (ADV) mounted on the seabed of the continental shelf of the northern South China Sea, high frequency velocity fluctuations were measured for 4.5 days. The turbulent kinetic energy dissipation rate was estimated. During the observation, the strong ocean response to Typhoon Rammasun was recorded to compare the turbulent characteristics before and during the typhoon. The results show that the turbulence near the seabed is mainly generated by the tidal current shear and exhibits a quarter diurnal variation during the period before the typhoon. During the typhoon period, the dissipation rate dramatically increased from 1×10^-6 m² s^-3 to 1×10^-2 m² s^-3 within a short time, and the significant wave height and the surface wave orbital velocity showed the same tendency. This finding suggests that the turbulence is dominantly generated by the surface waves near the seabed.

Atmosphere and ocean are two important factors that affect the earth's climate system, and their interaction is an important topic in the study. In view of the lack of turbulence scale analysis in the traditional large-scale air-sea coupling model, this paper uses the Parallelized Large-Eddy Simulation Model (PALM) to explore the effect of Langmuir circulation on air-sea flux and turbulent kinetic energy budget at a small scale, and conducts air-sea coupled simulation for atmospheric boundary layer (ABL) and ocean mixed layer (OML). The results show that the distribution of air-sea flux near the surface is greatly influenced by the Langmuir circulation, thus strengthening the ocean mixing. The pressure term in the turbulent kinetic energy budget of the ocean is greatly affected by the Langmuir circulation near the sea surface and weakens rapidly as the depth deepens. This study shows the application of the small-scale air-sea coupling model in the study of air-sea flux, which has certain significance for the study of small-scale air-sea interaction.

Accurate cloud cover and radiative effect simulation remains a long-standing challenge for global climate models (GCMs). The Southern Ocean (SO) cloud cover is substantially underestimated by most GCMs. Therefore, too much shortwave radiation is absorbed by oceans, which causes an overly warm sea surface temperature (SST) bias over the SO. For the first time, sea spray effects on latent and sensible heat fluxes are considered in a climate model. The most notable sea spray impacts on heat fluxes occur over the SO, with anomalous latent heat fluxes up to -7.74 W m^-2. Enhanced latent heat release lead to SST cooling. In addition, more clouds are formed over the SO to reflect excessive downward shortwave radiation, especially low-level clouds at 1.51% increments. Our results provide a feasible solution to mitigate the lack of low-level clouds and overly warm SST biases over the SO in GCMs.

For the Arctic surface waves, one of the most uncontroversial viewpoints is that their escalation in the past few years is mainly caused by the ice extent reduction. Ice retreat enlarges the open water area, i.e., the effective fetch, and thus allows more wind input energy and available distance for wave evolution. This knowledge has been supported by a few previous studies on the Arctic waves which analyzed the correlation between time-series variations in wave height and ice coverage. However, from the perspective of space, the detailed relationship between retreating ice cover and increasing surface waves is not well studied. Hence, we performed such a study for the whole Arctic and its subregions, which will be helpful for a better understanding of the wave climate and for forecasting waves in the Arctic Ocean.

Wave data are produced by twelve-year (2007-2018) hindcasts of summer melt seasons (May-Sept.) and numerical tests with WAVEWATCH III. When a viscoelastic wave-ice model and a spherical multiple-cell grid are applied, simulated wave heights agree with available buoy data and previous research. After the validations, simulated significant wave heights over twelve-year summer melt seasons are used to demonstrate the detailed relationship between the escalation of wave height and reduction of ice extent for the whole Arctic and seven subregions. Through least square regression, we find that the mean wave height in the Arctic Ocean will increase by 0.071m (10⁶km²)^-1 when the ice extent is smaller than 9.4×10⁶km², and roughly 51% is contributed by the enlarged fetch. By analyzing the nondimensional wave energy and comparing the simulated wave height with Wilson IV, we prove the swell is widespread during the summertime in the current Arctic Ocean. Furthermore, we also display the variations in probabilities of occurrence of large waves as ice-edge retreats in seven subregions. Assuming that an ice free period occurs in the Arctic in September, the model results show that the simulated mean wave height is approximately 1.6m and the large waves occur much more frequently, which mean that the growth rate of wave height will be higher if the minimum ice extent keeps reducing in the future.

Data measured by ultrasonic anemometer moored at a fixed platform located in South China Sea has been used to analyze turbulence within wave boundary layer. Compared to wind seas, it can be found a dominant area in power spectra, cospectra and Ogive curves under swell conditions from the measurements at 8 m height above sea surface, which is consistent with earlier studies. Our result also shows that the cospectra have both negative and positive regions, which represent the upward and downward momentum induced by swell waves. The wave coherent stress derived from the cospectra shows that it is more larger than the traditional method, implying earlier studies have greatly underestimated the stress of swell. Our study also found that the change of sign of swell coherent stress was related to the wave age, i.e. for c_p/u_* ≥ 60, swell induced the upward momentum, for c_p/u_* < 60, vice versa.  

The Stokes drift in the marginal ice zones (MIZ) of the Arctic Ocean is modelled by WAVEWATCH III. Applying two viscoelastic and one empirical frequency-dependent wave-ice models, the modelled wave parameters and spectrum are compared with field observations in the Beaufort-Chukchi Sea. Three wave-ice parameterizations show similar abilities to produce the surface Stokes drift estimated from buoy measurements. By using five-year (2015-2019) hindcasted directional spectra of the autumn Arctic, we present and discuss the monthly mean surface Stokes drift (1-10 cm/s), e-folding depth (1-14 m) and vertically integrated transport (0.1-0.4 m2/s) in the marginal ice zones, which are stronger in October than in September. When bulk wave parameters are adopted to estimate the Stokes drift fields, the surface Stokes drift will be underestimated by about 44-59% with mean ice concentration smaller than 60%, and the Stokes e-folding depth will be overestimated by about 1.4 to 5.0 times increasing from the interior to the edge of the ice cover. Since the Stokes drift may be an important component of the total surface current, we compare the modelled surface Stokes drift with the Eulerian current from reanalysis data, which shows that the mean surface Stokes drift is typically about 30% of the Eulerian current over large parts of the MIZ in Arctic Ocean, and is of the same order or even larger in some sea areas of the Chukchi, E. Siberian and Laptev Seas. It indicates that the Stokes drift is necessary to be considered to better model the dynamic processes of the sea ice, especially for the drift of ice floes.

Over the past decade, reanalysis data products have found widespread application in many areas of research and have often been used for the assessment of the past and present climate. They produce reliable atmospheric fields at high temporal resolution, albeit at low-to-mid spatial resolution. On the other hand, climatological analyses, quite often down-scaled to represent conditions also in enclosed basins, lack the historical sequence of stormy events and are often provided at poor temporal resolution.

In this context, we investigated the possibility of using the ERA5 reanalysis 10-m wind (25-km and 1-hour resolution data) to assess the Mediterranean Sea wind climate (past and scenario). We propose a statistical strategy to relate ERA5 wind speeds over the sea to the past and future wind speeds produced by the COSMO-CLM (8-km and 6-hour resolution data) climatological model. In particular, the probability density function of the ERA5 wind speed at each grid point is adjusted to match that of COSMO-CLM. In this way, past ERA5 winds are corrected to account for the COSMO-CLM energy, while ERA5 scaled wind sequence can be projected in the future with COSMO-CLM scenario energy. Comparison with past observations confirms the validity of the adopted method.

In the Venezia2021 project, we have applied this strategy for the assessment of the changing wind and, after WAVEWATCH III model runs, also the wave climate in the Northern Adriatic Sea, especially in front of Venice and the MOSE barriers, under two IPCC (RCP 4.5 and 8.5) scenarios.

In general, this strategy may be applied to produce a scaled wind dataset in enclosed basins and improve past wave modeling applications based on any reanalysis wind data.

Forty years (1979-2019) of global wave hindcasts are developed with the third generation spectral wave model WAVEWATCH III® using the state-of-the-art observation-based source term parameterizations (i.e., ST6) and the advanced irregular-regular-irregular (IRI) 1/4 grid system. The wave model has been forced with two distinct wind databases sourced from the latest NCEP Climate Forecast System (CFS) and the fifth generation of the ECMWF climate reanalyses (ERA5), together with the ice concentration available from the EUMETSAT OSI SAF (version 2). The hindcasts not only include traditional integral wave parameters (e.g., wave height, period) but also provide various novel parameters such as the dominant wave breaking probability, wave-induced mixed layer depth and whitecap coverage that are derived from wave spectrum based on previous theoretical and empirical studies. Wave parameters are extensively validated against observations from in-situ buoys and satellite altimeters on a global scale. Possible applications of these hindcasts in the fields of freak waves, sea spray and air-sea gas transfer will also be discussed.

To construct a reanalyzed global ocean wave data set with improved accuracy, which is important for the better understanding and simulation of various near-surface ocean dynamics, a data assimilation method has been embedded to the global spectral wave model based on WW3. The major factors controlling the wave simulation accuracy are the wind condition and the parameterization on the wave energy development, dissipation and nonlinear processes between wave components. However, the atmospheric prediction accuracy is still not sufficient, and the parameterization cannot be generalized due to the local geographic conditions.

In detail, the data assimilation using the optimal interpolation method has been applied, verification through the comparison with satellite altimeters and buoy observations has been made with examination of the data assimilation effects. The significant wave heights computed by the integration of wave energy spectra are showed to be quite similar with observed results. However, the wave periods and directions related to the shape of wave energy spectra are not sufficiently comparable. Generally there have been difficulties in predicting the propagation of long period waves such as swells.

The wave energy spectra on wave number and direction domains was multiplied by optimal interpolation method with the ratio of observed significant wave heights on first guessed simulated results. The energy spectra was thereafter shifted by the difference between simulated and observed peak wave periods and directions. From then examination of the reanalysis simulation during 1 year, it could be seen that the accuracy of the model with the data assimilation shows better results than that without data assimilation.

Direct measurements have been conducted from a spar buoys deployed in the Gulf of Mexico, and in the vicinity of Todos Santos Island, offshore Ensenada BC, Mexico, in order to better understand ocean surface wave modulated processes under a variety of oceanographic and meteorological conditions. Full ocean surface wave directional spectrum is estimated from sea surface elevation data acquired with an array of capacitance wires, to represent directional spectrum as a function of frequency and direction, as well as a function of the wave number components Kx and Ky. Momentum transfer between ocean and the atmosphere is calculated directly through the eddy correlation method applied to wind velocity components acquired with a sonic anemometer. Momentum transfer variability is analysed to study its dependance on the surface wave conditions, with special emphasis on mixed sea states. Comparison between single peak spectra results with those cases where bi-modal spectra were present are performed in order to detect wind stress variability effects. Ocean-atmosphere transfer of momentum is studied and explained in terms of the shape and evolution of the surface wave spectrum. This research is funded by SENER-CONACYT 249795 and 201441 projects.

The sea surface wind stress is relevant in processes of different scales of space and time such as the exchange of gases and heat, the surface currents, the depth of the mixed layer, the turbulence injection into the ocean. The wind waves are the key component in the coupling of the lower layer of the the atmosphere and the surface layer of the ocean, and various studies have shown the direct and indirect effects on the surface wind stress. In the present study, we present the measurements of the momentum flux and the results meteorological variables at the interface between the ocean and the atmosphere, by using and Oceanographic and Marine Meteorology Buoy (BOMM1) between November 2017 and February 2018. The analysis of the results during moderate wind conditions (U_10N > 8 ms^-1) in which mixed sea state conditions occur (swell that interacts with locally generated wind waves) we found a decrease of the roughness length (z₀), related to developing waves with higher steepness (ak), the data suggest that the presence of swell alters the wind sea part of the spectrum, which leads a reduction of the energy level of the wind-generated waves, hence reducing the wind sea associated roughness. For well developed waves conditions, the roughness length is greater than the parametrization proposed by Drennan al., (2003) for pure wind sea conditions, the data suggest that this is due direct interaction of the wind airflow and swell with higher steepness.  The data of this work suggests that during these conditions (U_10N > 8 ms^-1) , the mechanism of reduction of the drag of the wind sea due to the presence of swell, and the increase of the wind stress by direct interaction of swell with the airflow causes the net effect of wave field to behave as expected under pure wind sea conditions, and there seems to be no swell effect.

The impact of ocean surface waves on wind stress at the air–sea interface under low to moderate wind
conditions was systematically investigated based on a simple constant flux model and flux measurements
obtained from two coastal towers in the East China Sea and South China Sea. It is first revealed that the
swell-induced perturbations can reach a height of nearly 30m above the mean sea surface, and these perturbations
disturb the overlying airflow under low wind and strong swell conditions. The wind profiles severely
depart from the classical logarithmic profiles, and the deviations increase with the peak wave phase speeds. At
wind speeds of less than 4 m/s, an upward momentumtransfer from the wave to the atmosphere is predicted,
which is consistent with previous studies. A comparison between the observations and model indicates that
the wind stress calculated by the model is largely consistent with the observational wind stress when considering
the effects of surface waves, which provides a solution for accurately calculating wind stress in ocean
and climate models. Furthermore, the surface waves at the air–sea interface invalidate the traditional
Monin–Obukhov similarity theory (MOST), and this invalidity decreases as observational height increases.

Numerical models have been widely utilized to simulate the ocean and climate system. Parameterizations of some important processes, however, including the vertical mixing induced by surface waves, are still missing in many ocean models. In this work we incorporate the vertical mixing induced by non-breaking surface waves derived from a wave model into the multi-resolution Finite Element Sea ice-Ocean Model (FESOM), and compare its effect with that of shortwave penetration, another key process to vertically redistribute the heat in the upper ocean. Numerical experiments reveal that both processes ameliorate the simulation of upper-ocean temperature in mid and low latitudes mainly on the summer hemisphere. The regions where nonbreaking wave generates stronger improvement are where large temperature bias exists. The non-breaking surface waves plays a more significant role in decreasing the mean cold biases at 50 m (by 1.0 °C, in comparison to 0.5 °C achieved by applying shortwave penetration). We conclude that the incorporation of mixing induced by non-breaking surface waves into FESOM is practically very helpful, and suggest that it needs to be considered in other ocean climate models as well.

Hydrodynamic processes at air-sea interface play a significant role on air-sea CO₂ gas exchange, which further affects global carbon cycle and climate change. CO₂ gas transfer velocity (K_CO2) is generally parameterized with wind speed but ocean surface waves have direct impact on the gas exchange. Thus, the relationship between wave breaking and CO₂ gas exchange was studied through laboratory experiments and by utilizing field campaign data. The results from laboratory show that wave breaking plays a significant role in CO₂ gas exchange in all experiments while wind forcing can also influence K_CO2. A non-dimensional empirical formula is established in which K_CO2 is expressed as the product of wave breaking probability, transformed Reynolds number and an enhancement factor of wind speed. The parameterization is then improved by considering the bubble-mediated gas transfer based on both laboratory and ship campaign data sets. In the end, the formula is employed in the estimation of global CO₂ uptake by ocean and the result is found consistent with reported values.

High-quality wave prediction with a numerical wave model is of societal value. To initialize the wave model, wave data assimilation (WDA) is necessary to combine the model and observations. Due to inaccurate wind forcing, imperfect numerical schemes, and approximated physical processes, a wave model is always biased in relation to the real world. In this study, two assimilation systems are first developed using two nearly independent wave models; then, “perfect” and “biased” assimilation frameworks based on the two assimilation systems are designed to reveal the uncertainties of WDA. A series of “biased” assimilation experiments is conducted to systematically examine the adverse impact of initial condition, boundary forcing, and model bias on WDA, then model bias play a strongest role among them . A statistical approach based on the results from multiple assimilation systems is explored to carry out bias correction, by which the final wave analysis is significantly improved with the merits of individual assimilation systems. The framework with multiple assimilation systems provides an effective platform to improve wave analyses and predictions and help identify model deficits, thereby improving the model.

Langmuir turbulence (LT) can have a significant impact on the ocean mixing in the ocean surface boundary layer. In this study, using the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COWAST) modeling system, a 3D wave-current coupled regional model of the South China Sea (SCS) was developed. And the second-moment closure model developed recently by Harcourt, which includes the effects of LT, was introduced into the circulation model to investigate its influence on the coupled models’ performance. Comparisons between the model results with and without LT effects and between the model results and the observations are analyzed. Overall, with the LT effects, the simulated results are more consistent with the observations. When the LT effects are not considered, the mean annual deviation between the model simulated sea surface temperature (SST) and the observed data in the SCS is 1.09℃, as the LT effects introduced, the mean annual SST deviation decrease to -0.06℃ and the deviation almost disappear. Compared with the huge improvement in SST simulation, the introduction of LT has less influence on the simulation of the upper mixing layer depth (MLD). Nevertheless, the model results have also been improved to some extent, with the model performance is improved by 12.7%. Moreover, the eastern and southern parts of the SCS show a more pronounced amelioration than other regions. From the intercomparisons among the experiments, it is also found that the LT exerts more significant impacts on both SST and MLD during spring and summer.

Turbulence over the mobile ocean surface has distinct properties compared to turbulence over land. This raises the issue of whether functions such as the turbulent kinetic energy (TKE) budget and Monin-Obukhov similarity theory (MOST) determined over land are directly applicable to ocean surfaces 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, and wave coherent stress accounts for the momentum transfer between ocean waves and atmosphere. In this study, applications of the turbulent kinetic energy (TKE) budget and the inertial dissipation method (IDM) in the context of the Monin-Obukhov similarity theory (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 combing the TKE budget and MOST, our study showed that the stress computed by the traditional IDM corresponds to turbulent stress rather than total stress. The swell wave coherent stress should be considered when applying the IDM to calculate the stress in the WBL.

This work aims to develop a new framework for the interaction of a subsurface flow and surface gravity water waves, based on a perturbation and multiple-scales expansion.  Surface waves are assumed of a narrow band δ (δ ), indicating they can be expressed as a carrier wave whose amplitude varies slowly in space and time relative to its phase. Using the Direct Integration Method proposed in Li & Ellingsen (2019), the effects of the vertical gradient of a subsurface flow are taken into account on the linear wave properties in an implicit fashion. At the second order in wave steepness ϵ, the forcing of the sub-harmonic bound waves is considered that plays a role in the primary equations for a subsurface flow.

The novel framework derives the continuity and momentum equations for a subsurface flow in two different formats, including both the depth integrated as well as the depth resolved version. The former compares with Smith (2006) to examine the roles of the rotationality of wave motions in the subsurface flow equations. The latter employs the sigma coordinate system proposed in Mellor (2003, 2008, 2015) and extends the framework therein to allow for quasi-monochromatic surface waves and the effects of the shear of a current on linear surface waves. Compared to Mellor (2003, 2008, 2015), the vertical flux/vertical radiation stress term in the proposed framework is approximated to one order of magnitude higher, i.e. O(ϵ²δ²).

References

Li, Y., Ellingsen, S. Å. A framework for modeling linear surface waves on shear currents in slowly varying waters. J. Geophys. Res. C: Oceans, (2019) 124(4), 2527-2545.

Mellor, G. L. The three-dimensional current and surface wave equations. J. Phys. Oceanogr., (2003) 33, 1978–1989.

Mellor, G. L. The depth-dependent current and wave interaction equations: a revision. J. Phys. Oceanogr., (2008) 38(11), 2587-2596.

Smith, J. A. Wave–current interactions in finite depth. Journal of Physical Oceanography, (2006) 36(7), 1403-1419.