Wave Slope Research Articles

PYCNOCLINE THICKNESS EFFECT ON INTERNAL WAVE BREAKING OVER A UNIFORM SLOPE

Internal waves play a significant role in the resuspension and transport of fine sediment adjacent to the sea bottom in the coastal region. Inall (2009) found the horizontal current and diffusion of mass due to the breaking of internal waves in the Fjord by using a fluorescent tracer. Internal waves have been shown to cause crucial mass transport and affect the ecological system. In particular, an internal solitary wave that progresses without changing the profile contributes to mass transport on a sloping bottom. Therefore, it is essential to clarify how an internal solitary wave breaks over a slope and transports mass. When pycnocline thickness is negligible in a twolayer fluid, an internal solitary wave breaking over a slope can be categorized into four breaker types by applying the latest classification based on wave slope, bottom slope gradient and an internal Reynolds number. Aghsaee et al. (2010) demonstrated that an internal solitary wave breaking over a slope can be categorized into four breaker types: surging, collapsing, plunging, and fission breakers using three-dimensional numerical simulations. They used wave slope and bottom slope gradient. However, some plunging and collapsing breakers were not appropriately categorized. Nakayama et al. (2019) solved the classification problem by introducing an internal Reynolds number based on the Korteweg–De Vries equation. However, it remains unsolved if this classification can categorize the breaking of an internal solitary wave under thick pycnocline conditions. This study uses numerical simulations to investigate the applicability of the classification under changing pycnocline thickness (Nakayama et al., 2021).

WAVE OVERTOPPING MITIGATION BY A VERTICAL WALL OR A WAVE RETURN WALL AT THE END OF A PITCHED ROCK SLOPE

This extended abstract contains two topics: stability of a pitched rock slope (in contrast to randomly placed rock) and mitigation of excessive wave overtopping at an existing rock slope. The stability of a single pitched rock layer could reasonably well be predicted by the Van der Meer formula. The criteria for start of damage and failure, however, become much stricter for a single armour layer. The commonly used EurOtop-equations for wave overtopping were used to fit influence factors for a vertical wall, with and without bullnose, and for a wave return wall. A vertical wall will increase the crest level, where the wave return wall replaces a part of the crest of the rock structure and has the same crest level as the original structure. Test conditions were focused on steep waves (high wave steepness) only, as this is the actual design situation for Singapore structures facing the sea directly.

Saturation of Ocean Surface Wave Slopes Observed During Hurricanes

AbstractDrifting buoy observations of ocean surface waves in hurricanes are combined with modeled surface wind speeds. The observations include targeted aerial deployments into Hurricane Ian (2022) and opportunistic measurements from the Sofar Ocean Spotter global network in Hurricane Fiona (2022). Analysis focuses on the slope of the waves, as quantified by the spectral mean square slope. At low‐to‐moderate wind speeds (<15 m s−1), slopes increase linearly with wind speed. At higher winds (>15 m s−1), slopes continue to increase, but at a reduced rate. At extreme winds (>30 m s−1), slopes asymptote. The mean square slopes are directly related to the wave spectral shapes, which over the resolved frequency range (0.03–0.5 Hz) are characterized by an equilibrium tail () at moderate winds and a saturation tail () at higher winds. The asymptotic behavior of wave slope as a function of wind speed could contribute to the reduction of surface drag at high wind speeds.

Hydraulic performance analysis for homogeneous mound breakwaters: Application of dimensional analysis and a new experimental technique

The main objective of this study is to apply the methodology proposed by Díaz-Carrasco et al. (2020), based on the dimensional analysis and a new experimental technique, to estimate and study the wave energy transformation on homogeneous mound breakwaters. The dimensional analysis includes the main variables of wave train, porous media and slope geometry that influence the hydraulic performance on mound breakwaters. For that, laboratory tests were performed in a wave flume for a homogeneous and permeable mound breakwater. A new experimental technique derived from the methodology of Díaz-Carrasco et al. (2020) is also applied for designing wave conditions in laboratory based on the interplay that the relative water depth, h/L, and the wave steepness, H/L, has on the hydraulic performance of the structure, called the sample space. An analysis was conducted to study the influence that each dimensionless variable has on wave energy transformation. The experimental results shows that there is a relationship between the reflected, KR2, transmitted, KT2, and dissipated energy, D∗, and the product of the relative water depth, h/L, and the incident wave steepness, HI/L. The selection of wave conditions from the new experimental technique of sample space allows quantifying regions of wave energy transformation and wave breaker types on the breakwater and it seems to be a useful technique for designing laboratory conditions.

The Study of the Bistatic Cross-Correlation Function of Two Signals Separated in Frequency Reflected by the Water Surface

The purpose of this study is to analyze the applicability conditions for the significant wave height (SWH) measurement approach based on measuring the cross-correlation function of two signals with similar frequencies reflected by the sea surface in the bistatic problem statement (the transmitting antenna and the receiving antenna are separated in space). When implementing this approach, the modulus of the normalized cross-correlation function for several pairs of signals with different frequency bases will be measured in the experiment. The advantage of this approach over the traditional method for radar altimetry, based on the analysis of the shape of the reflected pulse, is the high accuracy in measuring the SWH for weak waves. In the bistatic formulation of the problem, an important advantage of the approach under study is the possibility of obtaining analytical formulas for solving the direct problem. This paper presents the derivation of a formula for the modulus of the normalized cross-correlation function of reflected signals, which expresses an explicit relationship with the parameters of sea waves and the measurement geometry in the bistatic formulation of the problem. This paper considers the influence on the modulus of the normalized cross-correlation function of the antenna patterns of the transmitting and receiving antennas, the distances to the sea surface, the wave slope variances, the SWH and the frequency base of the transmitted signals. The optimal variants of the measurement scheme are discussed. The results and conclusions obtained can be easily expanded to underwater acoustic sounding.

Comparison of quantifiable electrocardiographic changes associated with severe hyperkalemia

BackgroundHyperkalemia (HK) is a life-threatening condition that is frequently evaluated by electrocardiogram (ECG). ECG changes in severe HK (≥ 6.3 mEq/L) are not well-characterized. This study sought to compare and correlate ECG metrics in severe HK to baseline normokalemic ECGs and serum potassium. MethodsA retrospective analysis of 340 severe HK encounters with corresponding normokalemic ECGs was performed. ResultsVarious ECG metrics were analyzed. P wave amplitude in lead II, QRS duration, T wave slope, ratio of T wave amplitude: duration, and ratios of T wave: QRS amplitudes were significantly different between normokalemic and HK ECGs. P wave amplitude attenuation in lead II correlated better with serum potassium than in V1. T wave metrics that incorporated both T wave and QRS amplitudes correlated better than metrics utilizing T wave metrics alone. ConclusionMultiple statistically significant and quantifiable differences among ECG metrics were observed between normokalemic and HK ECGs and correlated with increasing degrees of serum potassium and along the continuum of serum potassium. When incorporated into a logistic regression model, the ability to distinguish HK versus normokalemia on ECG improved significantly. These findings could be integrated into an ECG acquisition system that can more accurately identify severe HK.

Automated analysis of a large-scale paediatric dataset illustrates the interdependent relationship between epilepsy and sleep

Slow waves are an electrophysiological characteristic of non-rapid eye movement sleep and a marker of the restorative function of sleep. In certain pathological conditions, such as different types of epilepsy, slow-wave sleep is affected by epileptiform discharges forming so-called “spike-waves”. Previous evidence shows that the overnight change in slope of slow waves during sleep is impaired under these conditions. However, these past studies were performed in a small number of patients, considering only short segments of the recording night. Here, we screened a clinical data set of 39′179 pediatric EEG recordings acquired in the past 25 years (1994–2019) at the University Children’s Hospital Zurich and identified 413 recordings of interest. We applied an automated approach based on machine learning to investigate the relationship between sleep and epileptic spikes in this large-scale data set. Our findings show that the overnight change in the slope of slow waves was correlated with the spike-wave index, indicating that the impairment of the net reduction in synaptic strength during sleep is spike dependent.

Clinical applications of shear wave dispersion imaging for breast lesions: a pictorial essay.

Shear wave dispersion (SWD) imaging is a newly developed ultrasound technology designed to evaluate the dispersion slope of shear waves, which is related to tissue viscosity. This advanced imaging technique holds potential for distinguishing malignant lesions from benign lesions and normal breast tissue. The SWD slope, as determined by shear wave elastography (SWE), could offer crucial insights into the characterization of breast lesions. This article presents SWE and SWD images of both malignant and benign breast lesions, in addition to normal breast tissue.

Cardiac shear wave elastography can detect myocardial remodelling in LBBB patients undergoing CRT

Abstract Funding Acknowledgements Type of funding sources: None. Background Cardiac shear wave elastography (SWE) allows for the non-invasive assessment of myocardial stiffness via the detection of shear waves travelling through the heart after e.g. mitral valve closure (MVC). The propagation speed of these waves is directly related to myocardial stiffness. Myocardial stiffness depends on the intrinsic properties of the myocardium. Therefore, processes that alter these intrinsic properties, such as cardiac remodelling, could influence shear wave speed. In this way, SWE could be an interesting tool to directly and non-invasively monitor cardiac remodelling over time. Purpose To evaluate the effect of reverse remodelling on myocardial stiffness in left bundle branch block (LBBB) patients undergoing cardiac resynchronization therapy (CRT). Methods Fourteen non-ischemic patients with LBBB undergoing CRT were included. SWE was performed 1 day after CRT implantation and repeated after 6 and 12 months. Eleven age-matched healthy volunteers served as controls. Volumetric response was defined as ≥15% decrease in end-systolic volume after 1 year of CRT. Echocardiographic images were taken during biventricular (BiV) pacing ON (resynchronized) and BiV pacing OFF (native LBBB conduction), both with a conventional ultrasound machine and an experimental high frame rate ultrasound scanner (999 ± 134 frames/s). For SWE, LV parasternal long-axis views were acquired. Shear waves were visualized in M-modes of the septum, colour coded for tissue acceleration. The slope of the shear waves in the M-mode represents their propagation speed (Figure 1A). Results All included patients were volumetric responders. LV ejection fraction and global longitudinal strain improved significantly over time. LV volumes decreased significantly in all patients during one year of CRT (Table 1), reflecting reverse remodelling. Shear wave speed was significantly higher immediately after implantation compared to healthy controls during BiV ON (5.9±1.5 vs 4.6±1.1 m/s; p = 0.02; Figure 1B), but not at 6 months (5.3±1.5 vs 4.6±1.1 m/s; p = 0.19) and 12 months (5.1±1.1 vs 4.6±1.1 m/s; p = 0.39) after implantation (Figure 1B), indicating that myocardial stiffness normalized over time due to reverse remodelling. Moreover, shear wave speed was significantly higher during BiV OFF compared to BiV ON immediately after implantation (5.9±1.5 vs 6.7±1.4 m/s; p = 0.022) and at 6 months (5.3±1.5 vs 6.1±1.4 m/s; p = 0.048), indicating that the reintroduction of dyssynchrony increases shear wave speed after MVC (Figure 1B). One year after implantation shear wave speed was not significantly different between BiV ON and OFF (5.1±1.1 vs 5.2±0.4 m/s; p = 0.78; Figure 1B). This could imply that dyssynchrony decreases over time as a result of reverse remodelling. Conclusion SWE can non-invasively detect changes in myocardial properties during reverse remodelling under CRT. Myocardial stiffness gradually decreases towards the range of age-matched healthy hearts after CRT.

Steady-state waves at class II Bragg resonance

This paper examines class II Bragg resonance in the interaction between surface gravity waves and bottom ripples and derives the corresponding steady-state wave system based on the homotopy analysis method. Specifically, we study the resonance between a nonlinear oblique incident wave and a doubly periodic cosinusoidal bottom. The bottom extends infinitely in the horizontal direction, and its two bottom-wave components are collinear. We analyze the influence of the relative water depth, slope of the incident wave, slope of the bottom topography, and amplitude ratio of the two bottom-wave components on the energy distribution of the wave system. The energy distribution can be classified into two types. In type 1, the incident and resonant wave components have the same energy. In type 2, the energy of each component is different. There are two situations in both type 1 and type 2. The incident and resonant wave components account for most of the energy of the wave system, whereas the energy of other wave components cannot be ignored in the other system. These two situations were not identified in our previous study [Xu et al., “Equilibrium states with finite amplitudes at exactly and nearly class-I Bragg resonances,” J. Math. 2021, 9986114]. We then investigate the effects of different physical parameters (including the incident wave slope and bottom undulations) on the energy distribution, wave slope, and angular frequencies of the wave system. The results of this study deepen our understanding of class II Bragg resonance and suggest several directions for future research.

Asymmetry of sleep electrophysiological markers in patients with focal epilepsy.

Sleep can modulate epileptic activities, but our knowledge of sleep perturbation by epilepsy remains sparse. Interestingly, epilepsy and sleep both present with defining electrophysiological features in the form of specific graphoelements on EEG. This raises the possibility to identify, within ongoing EEG activity, how epilepsy impacts and disrupts sleep. Here, we asked whether the presence of a lateralized epileptic focus interferes with the expression of the dominant electrophysiological hallmarks of sleep: slow oscillations, slow waves and spindles. To this aim, we conducted a cross-sectional study and analysed sleep recordings with surface EEG from 69 patients with focal epilepsy (age range at EEG: 17-61 years, 29 females, 34 left focal epilepsy). Comparing patients with left and right focal epilepsy, we assessed inter-hemispheric asymmetry of sleep slow oscillations power (delta range, 0.5-4 Hz); sleep slow wave density; amplitude, duration and slope; and spindle density, amplitude, duration as well as locking to slow oscillations. We found significantly different asymmetries in slow oscillation power (P < 0.01); slow wave amplitude (P < 0.05) and slope (P < 0.01); and spindle density (P < 0.0001) and amplitude (P < 0.05). To confirm that these population-based differences reflect actual patient-by-patient differences, we then tested whether asymmetry of sleep features can classify laterality of the epileptic focus using a decision tree and a 5-fold cross-validation. We show that classification accuracy is above chance level (accuracy of 65%, standard deviation: 5%) and significantly outperforms a classification based on a randomization of epileptic lateralization (randomization data accuracy: 50%, standard deviation 7%, unpaired t-test, P < 0.0001). Importantly, we show that classification of epileptic lateralization by the canonical epileptic biomarker, i.e. interictal epileptiform discharges, improves slightly but significantly when combined with electrophysiological hallmarks of physiological sleep (from 75% to 77%, P < 0.0001, one-way ANOVA + Sidak's multiple comparisons test). Together, we establish that epilepsy is associated with inter-hemispheric perturbation of sleep-related activities and provide an in-depth multi-dimensional profile of the main sleep electrophysiological signatures in a large cohort of patients with focal epilepsy. We provide converging evidence that the underlying epileptic process interacts with the expression of sleep markers, in addition to triggering well-known pathological activities, such as interictal epileptiform discharges.

The timing of transcranial magnetic stimulation relative to the phase of prefrontal alpha EEG modulates downstream target engagement

BackgroundThe communication through coherence model posits that brain rhythms are synchronized across different frequency bands and that effective connectivity strength between interacting regions depends on their phase relation. Evidence to support the model comes mostly from electrophysiological recordings in animals while evidence from human data is limited. MethodsHere, an fMRI-EEG-TMS (fET) instrument capable of acquiring simultaneous fMRI and EEG during noninvasive single pulse TMS applied to dorsolateral prefrontal cortex (DLPFC) was used to test whether prefrontal EEG alpha phase moderates TMS-evoked top-down influences on subgenual, rostral and dorsal anterior cingulate cortex (ACC). Six runs (276 total trials) were acquired in each participant. Phase at each TMS pulse was determined post-hoc using single-trial sorting. Results were examined in two independent datasets: healthy volunteers (HV) (n = 11) and patients with major depressive disorder (MDD) (n = 17) collected as part of an ongoing clinical trial. ResultsIn both groups, TMS-evoked functional connectivity between DLPFC and subgenual ACC (sgACC) depended on the EEG alpha phase. TMS-evoked DLPFC to sgACC fMRI-derived effective connectivity (EC) was modulated by EEG alpha phase in healthy volunteers, but not in the MDD patients. Top-down EC was inhibitory for TMS pulses during the upward slope of the alpha wave relative to TMS timed to the downward slope of the alpha wave. Prefrontal EEG alpha phase dependent effects on TMS-evoked fMRI BOLD activation of the rostral anterior cingulate cortex were detected in the MDD patient group, but not in the healthy volunteer group. DiscussionResults demonstrate that TMS-evoked top-down influences vary as a function of the prefrontal alpha rhythm, and suggest potential clinical applications whereby TMS is synchronized to the brain's internal rhythms in order to more efficiently engage deep therapeutic targets.

Influence of Topographic and Geological Features on the Seismic Response of the Reef Site in the South China Sea

Insufficient comprehension of the seismic impact of the reef terrain, geology, and material properties of the reefs in the South China Sea still presents considerable impediments in studying the seismic response of reef engineering sites and assessing their seismic safety. To surmount this challenge, a seismic response analysis model of the reef-seawater system is established. This model takes into account the fluid-solid interaction effect, the wave radiation effect of the infinite seawater layer and the semi-infinite seabed, as well as the seismic wave input process of the reef-seawater system. Through targeted parameter analyses, the impact of various factors, including the shear wave velocity, thickness, and slope of distinct reef layers, the width of the reef flat, and the dynamic coupling effect of seawater on the seismic response of reef sites, is thoroughly examined. It has been determined that the seismic response of the reef site is markedly amplified as the shear wave velocity decreases and the thickness of the uppermost reef layer increases. While the effects of the slope gradient of the topmost reef layer and the width of the reef flat on the seismic response of the reef site are chiefly observed in the edge area and the central area, respectively. The layer of seawater plays a crucial role in radiation damping, serving as a medium for the dissipation of seismic energy and thereby weakening the overall seismic response of the reef site.

Numerical and Experimental Investigations on Non-Linear Wave Action on Offshore Wind Turbine Monopile Foundation

Monopiles are commonly utilized in offshore wind farms but are prone to non-linear wave loads and run-ups, significantly affecting their engineering design. Therefore, it is crucial to pursue a complete understanding of the non-linear wave action on monopile foundations. Both numerical and experimental investigations on the non-linear wave loads and run-ups on an offshore wind turbine monopile foundation are performed in this paper. The experiment is carried out at a scale of 1/30 in a wave flume at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, in which the wave loads and run-ups along the monopile are measured. Based on the second-order potential flow model and time-domain higher-order boundary element method (HOBEM), the related numerical tests are conducted to study the non-linear effects further. It is found that the present non-linear potential theory is sufficient for the simulation of wave force and run-ups on the monopile in the range of wave slope kA &lt; 0.15 before wave breaking. “W” type distribution of wave run-up along the monopile is found, in which the peak value occurs at the frontward side (i.e., θ =180°) and is the maximum due to full reflection; the two symmetrical minimum amplitudes lie in the zones of (45° ≤ θ ≤ 90°) and (270° ≤ θ ≤ 315°), whose positions shift downward with the increase of wave non-linearity. Energy transfer among the fundamental wave component and higher-order components is also found, which is most apparent on the backward side. Besides, the transverse resonance occurs in the wave flume due to the wavelength being near the flume width, which induces the wave run-up at the backward position larger than that at the frontward position.

Response of sleep slow oscillations to acoustic stimulation is evidenced by distinctive synchronization processes.

Closed-loop acoustic stimulation (CLAS) during sleep has shown to boost slow wave (SW) amplitude and spindle power. Moreover, sleep SW have been classified based on different processes of neuronal synchronization. Thus, different types of SW events may have distinct functional roles and be differentially affected by external stimuli. However, the SW synchronization processes affected by CLAS are not well understood. Here, we studied the effect of CLAS on the dissociation of SW events based on two features of neuronal synchronization in the electroencephalogram (topological spread and wave slope). We evaluated and classified individual SW events of 14 healthy subjects during a CLAS stimulated (STM) and a control night (CNT). Three main categories of SW events were found denoting (C1) steep slope SW with global spread, (C2) flat-slope waves with localized spread and homeostatic decline, and (C3) multipeaked flat-slope events with global spread. Comparing between conditions, we found a consistent increase of event proportion and trough amplitudes for C1 events during the time of stimulation. Furthermore, we found similar increases in post-stimulus spectral power in θ, β, and σ frequencies for CNT vs STIM condition independently of sleep stage or SW categories. However, topological analysis showed differentiated spatial dynamics in N2 and N3 for SW categories and the co-occurrence with spindle events. Our findings support the existence of multiple types of SW with differential response to external stimuli and possible distinct neuronal mechanisms.

Improving the standard protocol for above-water reflectance measurements: 1. Estimating effective wind speed from angular variation of sunglint.

The standard above-water protocol for measurement of water reflectance uses a measurement of wind speed to estimate the air-water interface reflectance factor and, thus, remove reflected skylight from upwelling radiance. This aerodynamic wind speed measurement may be a poor proxy for the local wave slope distribution in cases such as fetch-limited coastal and inland waters and/or where there are spatial or temporal differences between the wind speed measurement and the location of reflectance measurements. Here, an improved method is proposed, with a focus on sensors mounted on autonomous pan-tilt units and deployed on fixed platforms, replacing the aerodynamic wind speed measurement by optical measurements of angular variation of upwelling radiance. Using radiative transfer simulations, it is shown that the difference between two upwelling (i.e.,water plus air-water interface) reflectances acquired at least 10° apart from each other in the solar principal plane is strongly and monotonically related to effective wind speed. The approach shows good performance in twin experiments using radiative transfer simulations. Limitations of the approach are identified, including difficulties for a very high Sun zenith angle (>60∘), very low wind speed (<2m s -1), and, potentially, cases in which nadir-pointing angles are limited by optical perturbations from the viewing platform.

Parameter sensitivity of the excessive acceleration failure mode in second-generation intact stability

In this study, the parameter sensitivity of the level 1 and 2 assessments of the excessive acceleration failure mode in the International Maritime Organization second-generation intact stability was analyzed. Monte-Carlo simulations were conducted using the input parameter space, which was generated using a Gaussian distribution, and a variance-based sensitivity analysis was performed using the Monte-Carlo simulation results. The longitudinal and vertical positions of the check point, natural roll period, and roll decay coefficient were selected as input parameters for the level 1 assessment, whereas the roll damping coefficient and effective wave slope coefficient replaced the roll decay coefficient for the level 2 assessment. The results revealed that the highest total sensitivity index for the level 1 assessment was the natural roll period, which was 0.8, and the effective wave slope had a total sensitivity index of 0.5 for the level 2 assessment. This indicated that the uncertainty of the natural roll period was dominantly propagated to the resultant value of the level 1 assessment, while the effective wave slope coefficient was the most sensitive parameter in the level 2 assessment. The uncertainty in the input variable was found to cause the opposite decision if the resultant value was close to the criterion value under a given loading condition.

Improving Wave‐Based Air‐Sea Momentum Flux Parameterization in Mixed Seas

AbstractIn winter, the Northwest Tropical Atlantic Ocean can be characterized by various wave age‐based interactions among ocean current, surface wind and surface waves, which are critical for accurately describing surface wind stress. In this work, coupled wave‐ocean‐atmosphere model simulations are conducted using two different wave roughness parameterizations within COARE3.5, including one that relies solely on wind speed and another that uses wave age and wave slope as inputs. Comparisons with the directly measured momentum fluxes during the ATOMIC/EUREC4A experiments in winter 2020 show that, for sea states dominated by short wind waves under moderate to strong winds, the wave‐based formulation (WBF) increases the surface roughness length in average by 25% compared to the wind‐speed‐based approach. For sea states dominated by remotely generated swells under moderate to strong wind intensity, the WBF predicts significantly lower roughness length and surface stress (≈15%), resulting in increased near‐surface wind speed above the constant flux layer (≈5%). Further investigation of the mixed sea states in the model and data indicates that the impact of swell on wind stress is over‐emphasized in the COARE3.5 WBF, especially under moderate wind regimes. Various approaches are explored to alleviate this deficiency by either introducing directional alignment between wind and waves or using the mean wave period instead of the wave period corresponding to the spectral peak to compute the wave age. The findings of this study are likely to be site‐dependent, and mostly concern specific regimes of wind and waves where the original parameterization was deficient.

Wind–Wave Interaction for Strong Winds

Abstract In this paper, we revisit the problem of wind–wave interaction with emphasis on strong winds. For these events, it is assumed that nonlinearity is so large that the slope of the wind waves has reached a limiting steepness. Recent observations suggest that the drag decreases with wind in the strong wind speed regime. In this paper, we try to explain this. In the first step, we introduce a model for surface gravity waves and calculate explicitly the background roughness length from the original approach of Janssen. It is found that for young, steep wind sea, the background roughness length almost vanishes, giving a reduced drag. In addition, it is shown that for steep waves, the slowing down of the wind by waves is a nonlinear process; hence, the growth rate of the waves by wind depends in a nonlinear fashion on the wave spectrum. For strong winds, it is found that, as waves are typically steep, this nonlinear effect gives a further reduction of the wind input. As a consequence, in these extreme circumstances, the drag coefficient decreases with wind.

Revisiting the Cox and Munk wave-slope statistics using IASI observations of the sea surface

We use radiances collected from space by the Infrared Atmospheric Sounder Interferometer (IASI) when looking down at ocean surfaces during the day to remotely determine the probability distribution of wave slopes. This is achieved by using about 300 channels between 3.6 and 4.0μm and a physically-based approach which properly takes the contribution of the reflected solar radiation into account. Based on about 150 millions observations, the same number of wave-slope probabilities are retrieved for wind speeds (at 10 m) up to 15 m/s. We revisit and discuss the methodology proposed by Cox and Munk (CM) to derive their celebrated wave-slope probability distribution function (pdf) from photographs of the sun glitter. We propose an original and robust approach for accurate retrievals of the 7 parameters appearing in the Gram–Charlier representation of the pdf. Our results for the mean square slopes (MSSs) are fully compatible with those of CM, and with the more recent results by Bréon and Henriot, but our lower uncertainties enable to point out departures from the linear wind-speed dependencies and a slight overestimation of the upwind MSS described by the linear fit of CM at moderate wind speed. Our skewness and kurtosis coefficients show clear influences of the wind speed, with a steady decrease of the former and the alongwind kurtosis coefficient being maximal at moderate wind speeds, features that CM could not point out due to the limitations of their measurements. We revisit the renormalization procedure employed by CM to obtain the complete variances from truncated pdfs and show that it imposes stringent conditions on the kurtosis coefficients that allow to determine them accurately, with wind-dependent values specific to the local sea state. We also provide measurements of the shifted position of the most probable slope as well as a demonstration of a qualitative change of regime in the updown wind asymmetry of the wave-slope probability when the wind speed increases.