Charnock dynamics: a model for the velocity structure in the wave boundary layer of the air–sea interface

We present a unified model of the air–sea boundary layer, which takes account of the air–sea momentum exchange across the sea surface. The recognition of the importance of the velocity shears in the water (which comprise a frictional shear and the Stokes shear due to the wave motion) in determining the sea surface roughness is a distinctive feature of the analysis, which leads to a prediction of the Charnock constant (α) in terms of two independent parameters, namely the wave age and the ratio of the Stokes shear to the Eulerian shear in the water. This expression is used to interpret the large observational variability of the Charnock constant. The 10-m drag coefficient can also be expressed using similar reasoning, and the introduction of a relation in which the ratio of the frictional shear in the water to the frictional shear in the air decreases with the friction velocity yields predictive relations for the variation of the 10-m drag coefficient at very high wind speeds both in the open ocean and in wind–wave tanks. The physical interpretation of this relation is that the production of spray essentially returns momentum from the ocean to the atmosphere, and this process becomes progressively more important as the wind speed increases.     

On the variability of the Charnock constant and the functional dependence of the drag coefficient on wind speed: Part II-Observations

An analytical expression for the 10 m drag law in terms of the 10 m wind speed at the maximum in the 10 m drag coefficient, and the Charnock constant is presented, which is based on the results obtained from a model of the air-sea interface derived in Bye et al. (2010). This drag law is almost independent of wave age and over the mid-range of wind speeds (5?17 ms^?1) is very similar to the drag law based on observed data presented in Foreman and Emeis (2010). The linear fit of the observed data which incorporates a constant into the traditional definition of the drag coefficient is shown to arise to first-order as a consequence of the momentum exchange across the air-sea boundary layer brought about by wave generation and spray production which are explicitly represented in the theoretical model.     

Correlation equation for the marine drag coefficient and wave steepness

This work questions, starting from dimensional considerations, the generality of the belief that the marine drag coefficient levels off with increasing wind speed. Dimensional analysis shows that the drag coefficient scales with the wave steepness as opposed to a wave-age scaling. A correlation equation is employed here that uses wave steepness scaling at low aspect ratios (inverse wave steepnesses) and a constant drag coefficient at high aspect ratios. Invoked in support of the correlation are measurements sourced from the literature and at the FINO1 platform in the North Sea. The correlation equation is then applied to measurements recorded from buoys during the passage of hurricanes Rita, Katrina (2005) and Ike (2008). Results show that the correlation equation anticipates the expected levelling off in deeper water, but a drag coefficient more consistent with a Charnock type relation is also possible in more shallower water. Some suggestions are made for proceeding with a higher-order analysis than that conducted here.     

Prediction of the drag law for air–sea momentum exchange

In this paper, we use the inertial coupling relation as a similarity model for the air–sea boundary layer, to predict the 10-m drag coefficient. Excellent agreement with the commonly used statistical relationship of Garratt (1992) is found for a fully developed growing wind wave sea with a constant inertial drag coefficient, K_I = 1.5 × 10^–3. This suggests that the inertial coupling model can be used to realistically predict the 10 m drag coefficient under more general wind wave conditions.Acknowledgements The paper was completed while JATB was a Fellow at the Hanse-Wissenschaftskolleg in Delmenhorst, Germany, in July and August 2004. The comments of two anonymous reviewers are gratefully acknowledged.     

Estimation of orographically induced wave drag in the stable boundary layer during the CASES-99 experimental campaign

This paper addresses the quantification of gravity wave drag due to small hills in the stable boundary layer. A single column atmospheric model is used to forecast wind and temperature profiles in the boundary layer. Next, these profiles are used to calculate vertical profiles of gravity wave drag. Climatology of wave drag magnitude and “wave drag events” is presented for the CASES-99 experimental campaign. It is found that gravity wave drag events occur for several relatively calm nights, and that the wave drag is then of equivalent magnitude as the turbulent drag. We also illustrate that wave drag events modify the wind speed sufficiently to substantially change the surface sensible heat flux.     

Extreme storm surge modelling in the North Sea

This study shows that storm surge model performance in the North Sea is mostly unaffected by the application of temporal variations of surface drag due to changes in sea state provided the choice of a suitable constant Charnock parameter in the sea-state-independent case. Including essential meteorological features on smaller scales and minimising interpolation errors by increasing forcing data resolution are shown to be more important for the improvement of model performance particularly at the high tail of the probability distribution. This is found in a modelling study using WAQUA/DCSMv5 by evaluating the influence of a realistic air-sea momentum transfer parameterization and comparing it to the influence of changes in the spatial and temporal resolution of the applied forcing fields in an effort to support the improvement of impact and climate analysis studies. Particular attention is given to the representation of extreme water levels over the past decades based on the example of the Netherlands. For this, WAQUA/DCSMv5 is forced with ERA-Interim reanalysis data. Model results are obtained from a set of different forcing fields, which either (i) include a wave-state-dependent Charnock parameter or (ii) apply a constant Charnock parameter (α _{C h} =?0.032) tuned for young sea states in the North Sea, but differ in their spatial and/or temporal resolution. Increasing forcing field resolution from roughly 79 to 12 km through dynamically downscaling can reduce the modelled low bias, depending on coastal station, by up to 0.25 m for the modelled extreme water levels with a 1-year return period and between 0.1 m and 0.5 m for extreme surge heights.     

Observation and simulation of a floe drift near the North Pole

The drift trajectory of a floe near the North Pole (87° N, 175° W) was observed during 8–19 August, 2010 based on the fourth Chinese National Arctic Research Expedition. The trajectory of the floe showed circular motions superimposed on straight drift. Each cycle had a period of about 12?h. The circular motion is inertial oscillation. The largest amplitude of inertial oscillation speed can reach 20?cm/s. After removing the inertial oscillation, the floe drift direction is about 40° on average to the right of the observed 10-m wind which is much larger than previous reports on the angle between sea-ice velocity and the geostrophic wind, and floe drift moves with a speed of about 1.4?% of the observed 10-m wind speed throughout the whole observation period. A simple dynamic sea ice-ocean coupled model and a three-dimensional sea ice-ocean coupled model are employed to simulate the floe drift. Both numerical models are with the widely used quadratic water-drag formulation, i.e., the stress is proportional to the square of the ice velocity relative to the ocean surface current. The inertial oscillation of the floe is successfully simulated by the simple passive drag model, while the floe drift amplitudes simulated from the three-dimensional model are relatively small.     

Momentum transfer at the ocean–atmosphere interface: the wave basis for the inertial coupling approach

 The inertial coupling approach for the momentum transfer at the ocean–atmosphere interface, which is based on the assumption of a similarity hypothesis in which the ratio between the water and air reference velocities is equal to the square root of the ratio between the air and water densities, is reviewed using a wave model. In this model, the air and water reference velocities are identified, respectively, with the spectrally weighted phase velocity of the gravity waves and the Stokes velocity at the water roughness length, which are evaluated in terms of the dimensionless frequency limits in Toba's equilibrium spectrum. It is shown that the similarity hypothesis is approximately satisfied by the wave model over the range of wave ages encountered in typical sea states, and that the predicted values of the dimensionless surface drift velocity, the dimensionless water reference velocity, and the Charnock constant are in reasonable agreement with observational evidence. The application of the bulk relationship for the surface shear stress, derived from the inertial coupling hypothesis in general circulation modeling, is also discussed. Received: 6 January 2001 / Accepted: 28 June 2001     

The statistics of wave height and crest elevation during the December 2012 storm in the North Sea

This paper concerns new field measurements of wave height and crest elevation probability distributions as measured in the North Sea during a storm in December 2012. The water surface elevation was recorded by Saab WaveRadar REX instruments mounted on eight fixed-jacket platforms in addition to a Datawell Directional Waverider buoy. The storm generated an easterly sea state which peaked well in excess of the 100-year wave height for that direction in the region. Furthermore, 19 freak waves occurred during the storm according to the definition as reported by Haver (2000). The present study demonstrates that the significant steepness and spectral bandwidth during the storm remain almost constant. Consequently, there is little change in the commonly applied design wave height and crest elevation probability distributions throughout the storm. Whilst the bulk of the recorded data was in good agreement with the theoretical distributions, it was demonstrated that when the wind speed was larger than 25 m/s, the measured crest elevation lies above the second-order Forristall distribution.     

夜间稳定边界层中小尺度地形激发的形式阻力和波动阻力

通过求解含有摩擦耗散的线性化大气动力学方程组,得到了在夜间稳定大气边界层中小尺度地形产生的波动阻力和形式阻力的解析解.结果表明边界层中的稳定度、风速和湍流状态、边界层厚度、上部残余层中的稳定度和风速以及地形高度和坡度,都会影响波动阻力和形式阻力的大小,应在数值模式的参数化方案中给予考虑.分析还表明,当地形坡度减到一定程度时,形式阻力可以忽略不计.     

Amplification of the storm surges in shallow waters of the Pertuis Charentais (Bay of Biscay,France)

The Pertuis Charentais are shallow coastal embayments formed by the islands of Oleron and Re in the north-eastern Bay of Biscay. The low-lying coasts of the Pertuis Charentais are susceptible to extensive flooding caused by the storm surges generated in the North Atlantic. Numerical modelling of the 24 October 1999 surge event is performed in the present study in order to elucidate the impact of the wind-wave-tide-surge interactions on the surge propagation in the Pertuis Charentais. A 2D numerical model is constructed to simulate the wave and tide-surge propagation on a high-resolution finite-element grid by using the TELEMAC and TOMAWAC software. The effect of the wave-induced enhancement on the sea surface drag and on the bottom friction is evaluated by using the models of Janssen (1991) and Christoffersen and Jonsson (1985), respectively. The radiation stress is estimated by employing the approach of Longuet-Higgins and Stewart (1964). It is demonstrated that the peak surge in the night on 23–24 October has been amplified inside the Pertuis Charentais by about 20 cm due to the wind-wave interactions with the tide-surge currents. These interactions are strongest at the entrance to the Pertuis Charentais where the sea surface drag coefficient is significantly increased by the wind-wave coupling. The effect of the wave-tide-surge interactions is large enough to be included in the flood forecasting systems of this region.     

Moreton wave, “EIT wave”, and type II radio burst as manifestations of a single wave front

We show that a Moreton wave, an “EIT wave,” and a type II radio burst observed during a solar flare of July 13, 2004, might have been a manifestation of a single front of a decelerating shock wave, which appeared in an active region (AR) during a filament eruption. We propose describing a quasi-spheroidal wave propagating upward and along the solar surface by using relations known from a theory of a point-like explosion in a gas whose density changes along the radius according to a power law. By applying this law to fit the drop in density of the coronal plasma enveloping the solar active region, we first managed to bring the measured positions and velocities of surface Moreton wave and “EIT wave” into correspondence with the observed frequency drift rate of the meter type II radio burst. The exponent of the vertical coronal density falloff is selected by fitting the power law to the Newkirk and Saito empirical distributions in the height range of interest. Formal use of such a dependence in the horizontal direction with a different exponent appears to be reasonable up to distances of less than 200 Mm around the eruption center. It is possible to assume that the near-surface shock wave weakens when leaving this radius and finally the active region, entering the region of the quiet Sun where the coronal plasma density and the fast-mode speed are almost constant along the horizontal.     

Storm observations by remote sensing and influences of gustiness on ocean waves and on generation of rogue waves

The impact of the gustiness on surface waves under storm conditions is investigated with focus on the appearance of wave groups with extreme high amplitude and wavelength in the North Sea. During many storms characterized by extremely high individual waves measured near the German coast, especially in cold air outbreaks, the moving atmospheric open cells are observed by optical and radar satellites. According to measurements, the footprint of the cell produces a local increase in the wind field at sea surface, moving as a consistent system with a propagation speed near to swell wave-traveling speed. The optical and microwave satellite data are used to connect mesoscale atmospheric turbulences and the extreme waves measured. The parameters of open cells observed are used for numerical spectral wave modeling. The North Sea with horizontal resolution of 2.5?km and with focus on the German Bight was simulated. The wind field “storm in storm,” including moving organized mesoscale eddies with increased wind speed, was generated. To take into account the rapid moving gust structure, the input wind field was updated each 5?min. The test cases idealized with one, two, and four open individual cells and, respectively, with groups of open cells, with and without preexisting sea state, as well the real storm conditions, are simulated. The model results confirm that an individual-moving open cell can cause the local significant wave height increase in order of meters within the cell area and especially in a narrow area of 1–2?km at the footprint center of a cell (the cell's diameter is 40–90?km). In a case of a traveling individual open cell with 15?m·s^?1 over a sea surface with a preexisting wind sea of and swell, a local significant wave height increase of 3.5?m is produced. A group of cells for a real storm condition produces a local increase of significant wave height of more than 6?m during a short time window of 10–20?min (cell passing). The sea surface simulation from modeled wave spectra points out the appearance of wave groups including extreme individual waves with a period of about 25?s and a wavelength of more than 350?m under the cell's footprint. This corresponds well with measurement of a rogue wave group with length of about 400?m and a period of near 25?s. This has been registered at FiNO-1 research platform in the North Sea during Britta storm on November 1, 2006 at 04:00 UTC. The results can explain the appearance of rogue waves in the German Bight and can be used for ship safety and coastal protection. Presently, the considered mesoscale gustiness cannot be incorporated in present operational wave forecasting systems, since it needs an update of the wind field at spatial and temporal scales, which is still not available for such applications. However, the scenario simulations for cell structures with appropriate travel speed, observed by optical and radar satellites, can be done and applied for warning messages.     

Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope

The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.     

Recent Advances in Air–Sea Interaction Studies Applied to Overwater Air Quality Modeling: A Review

— Air quality modeling in the marine environment requires a better understanding of air–sea interaction. The behavior of the sea is different from that of the land, particularly with respect to the aerodynamic roughness parameter which changes temporally and spatially as a function of wind-generated wave characteristics. Recent improved understanding in air–sea interaction as applied to topics in air quality modeling are discussed. They include stability characteristics, variation of the wind speed with height, mixing height, standard deviation of crosswind and vertical wind, and the eddy diffusion. These topics are synthesized for scientists and engineers who need to improve the air quality modeling for overwater applications.     

On the wave field generated by a variable wind

Abstract

By using an empirical expression relating the rate of increase in wave energy to the local wind speed, an equation for the phase speed at the peak of the wave spectrum is derived. The solution of the equation is determined for some simple wind fields. In particular, the wave field caused by a localised storm moving steadily over an unbounded ocean is considered. It is also shown that only a small fraction of the momentum transferred from the wind into the water propagates away from a local storm area in the form of wave momentum.     

Derivation of a wave-state-dependent sea spray generation function and its application in estimating sea spray heat flux

A sea spray generation function(SSGF)for bubble-derived droplets that takes into account the impact of wave state on whitecap coverage was presented in this study.By combining the new SSGF with a previous wave-state-dependent SSGF for spume droplets,an SSGF applicable to both bubble-derived and spume droplets that includes the impacts of wave state was obtained.The produced SSGF varies with surface wind as well as with wave development.As sea surface wind increases,more sea spray droplets are produced,resulting in larger SSGFs and volume fluxes.Meanwhile,under the same wind conditions,the SSGF is mediated by wave state,with larger SSGFs corresponding to older waves and larger windsea Reynolds numbers.The impact of wave state on sea spray heat flux was then estimated by applying this SSGF while considering the thermodynamic feedback process.Under given atmospheric and oceanic conditions,the estimated sea spray heat flux increases with wind speed,wave age,and windsea Reynolds number.     

Developing configuration of WRF model for long-term high-resolution wind wave hindcast over the North Atlantic with WAVEWATCH III

The spatial resolution of wind forcing fields is critical for modeling ocean surface waves. We analyze here the performance of the non-hydrostatic numerical weather prediction system WRF-ARW (Weather Research and Forecasting) run with a 14-km resolution for hindcasting wind waves in the North Atlantic. The regional atmospheric model was run in the domain from 20° N to 70° N in the North Atlantic and was forced with ERA-Interim reanalysis as initial and boundary conditions in a spectral nudging mode. Here, we present the analysis of the impact of spectral nudging formulation (cutoff wavelengths and depth through which full weighting from reanalysis data is applied) onto the performance of the modeled 10-m wind speed and wind wave fields for 1 year (2010). For modeling waves, we use the third-generation spectral wave model WAVEWATCH III. The sensitivity of the atmospheric and wave models to the spectral nudging formulation is investigated via the comparison with reanalysis and observational data. The results reveal strong and persistent agreement with reanalysis data during all seasons within the year with well-simulated annual cycle and regional patterns independently of the nudging parameters that were tested. Thus, the proposed formulation of the nudging provides a reliable framework for future long-term experiments aiming at hindcasting climate variability in the North Atlantic wave field. At the same time, dynamical downscaling allows for simulation of higher waves in coastal regions, specifically near the Greenland east coast likely due to a better representation of the mesoscale atmospheric dynamics in this area.     

Development of waves under explosive cyclones in the Northwestern Pacific

The development of ocean waves under explosive cyclones (ECs) is investigated in the Northwestern Pacific Ocean using a hindcast wave simulation around Japan during the period 1994 through 2014. A composite analysis of the ocean wave fields under ECs is used to investigate how the spatial patterns of the spectral wave parameters develop over time. Using dual criteria of a drop in sea level pressure below 980 hPa at the center of a cyclone and a decrease of at least 12 hPa over a 12-h period, ECs are identified in atmospheric reanalysis data. Two areas under an EC were identified with narrow directional spectra: the cold side of a warm front and the right-hand side of an EC (relative to the propagating direction). Because ECs are associated with atmospheric fronts, ocean waves develop very differently under ECs than they do under tropical cyclones. Moreover, ECs evolve very rapidly such that the development of the ocean wave field lags behind the peak wind speed by hours. In a case study of an EC that occurred in January 2013, the wave spectrum indicates that a warm front played a critical role in generating distinct ocean wave systems in the warm and cold zones along the warm front. Both the warm and cold zones have narrow directional and frequency spectra. In contrast, the ocean wave field in the third quadrant (rear left area relative to the propagation direction) of the EC is composed of swell and wind sea systems propagating in different directions.