arXiv subjects

Saulo Mendes

Publications and source records attributed to Saulo Mendes.

11 recordsLinked to original sources

arXiv2026

Effect of directionality on extreme wave formation during nonlinear shoaling

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves. Nevertheless, research on depth-induced NED has been predominantly confined to unidirectional irregular waves, while the role of directionality remains largely unexplored. The scarce studies on multidirectional waves mainly rely on numerical simulations and have yielded conflicting results. In this work, we report on an experimental investigation of wave directionality on the depth-induced non-equilibrium wave statistics. High-order statistical moments, skewness and kurtosis, are used as proxies for the non-equilibrium wave response. Our results indicate that the directional spreading has a minor effect on decreasing the maximum values of these statistical moments. In contrast, the incidence direction plays a significant role in the non-equilibrium wave response, which is attributed to the effective bottom slope.

physics.flu-dyn↗

arXiv2025

Evolution of extreme nonlinear wave fields over strongly reflective plane beaches

The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the leading parameter controlling the reflection rates and types of breakers. Although little is known about the effect of reflection rates on the formation of extreme nonlinear waves, some debate has arisen regarding whether high reflection rates enhance the nonlinearity at the tail of the wave height distribution. In this work, we provide theoretical evidence that at very steep beaches of smooth composition, the reflection rate near unity will tend to stabilize the excess kurtosis otherwise generated by shoaling and controlled in magnitude by the bottom slope magnitude. We further verified this result through fully nonlinear numerical simulations, reaching a good agreement.

nlin.PS↗

arXiv2025

Shoaling of Finite-Amplitude Rogue Waves

Rogue wave formation and enhancement over coastal areas have been documented over the last decade. However, this recent knowledge is in apparent contradiction with the established observation of sub-Gaussian wave statistics near shallow water. Current theories and experiments describe the rogue wave amplification near shallow water regimes, but only for small-amplitude waves, and thus, not accounting for wave-breaking processes. To address this gap, we perform experiments to probe inhomogeneous wave fields nearing the wave-breaking regime. We also show that by increasing the significant wave height towards the breaking limit, the kinetic energy grows faster than the variance of the surface elevation due to nonlinearity, providing a physical explanation why the occurrence of rogue wave first increases in shallower waters and suddenly decreases further shorewards.

physics.flu-dyn↗

arXiv2024

Symmetric influence of forward and opposing tidal currents on rogue wave statistics

Rogue waves are associated with various ocean processes, both at the coast and in the open ocean. In either zone, inhomogeneities in the wave field caused by shoaling, crossing seas or current interactions disturb wave statistics, increasing rogue wave probability and magnitude. Such amplification of the frequency of rogue waves and their intensity, i.e. the maximum normalized height, have been attested in numerical simulations and laboratory studies, in particular for wave-current interactions. In this study, we investigate the effect of the current intensity and direction on rogue wave probability, by analyzing long-term observations from the southern North Sea. We observe that the amplification is similar for opposing and following currents. Despite the sea states being dominantly broad-banded and featuring a large directional spread, anomalous statistics are of the same order of magnitude as those observed in unidirectional laboratory experiments for stationary currents.

physics.ao-ph↗

arXiv2024

Direction Symmetry of Wave Field Modulation by Tidal Current

Theoretical studies on the modulation of unidimensional regular waves over a flat bottom due to a current typically assign an asymmetry between the effects of opposing/following streams on the evolution of major sea variables, such as significant wave height. The significant wave height is expected to monotonically increase with opposing streams and to decrease with following streams. To some extent, observations on data sets containing a few thousand of waves or over a continuous series of about a day confirm this prediction. Here, based on a multi-year dataset, we show that in very broad-banded seas with high directional spread, the asymptotic behavior of sea variables is highly non-trivial and does not follow the theoretical predictions, especially at high values of the ratio between tidal stream and group speed.

physics.flu-dyn↗

arXiv2023

Effect of shoaling length on rogue wave occurrence

The impact of shoaling on linear water waves is well-known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the "rapid'" nature of the shoaling process, i.e., shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through the development of a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the slope length and the slope gradient of a shoal and focus on the slope length to investigate the rapidness of the shoaling process on the evolution of key statistical and spectral sea-state parameters. Provided the shoal slope is 1/10 or steeper, our results indicate that the non-equilibrium dynamics is involved even for rather short shoaling lengths and becomes dominant in the regime of large lengths. When the non-equilibrium dynamics governs the wave evolution, further extending the slope length no longer influences the statistical and spectral measures. Thus, the shoaling effect on rogue waves is mainly driven by the slope magnitude rather than the slope length. Moreover, the simulations show that a higher cut-off frequency of the wave spectrum has a smaller impact on wave statistics than expected for a flat bottom in deep water and that insufficient attenuation of low-frequency waves at the downstream domain boundary has notable influence on wave statistics atop the shoal.

physics.flu-dyn↗

arXiv2023

A Continuous Non-ergodic Theory for the Wave Set-up

Inhomogeneities in the wave field due to wave groups, currents, and shoaling among other ocean processes can affect the mean water level. In this work, the classical and unsolved problem of continuously computing the set-down and the following set-up induced by wave breaking on a shoal of constant finite slope is tackled. This is possible by using available theoretical knowledge on how to approximate the distribution of wave random phases in finite depth. Then, the non-homogeneous spectral analysis of the wave field allows the computation of the ensemble average by means of the phase distribution and the inversion of the integral of the second moment for the special case of a shoaling process with uniform phase distribution. In doing so, I am able to obtain a direct effect of the slope magnitude on the phases distribution. Therefore, an analytical and slope-dependent mean water level with continuity over the entire range of water depth is provided.

physics.flu-dyn↗

arXiv2023

Nonlinear Wave Transformation over Steep Breakwaters

Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As the spatial evolution of the exceedance probability of irregular waves is affected by second-order effects in steepness, the nonlinear shoaling coefficient throughout a symmetrical and steep breakwater is investigated through a stochastic framework. By inverting the effect of slope on normalized wave height distribution, it is possible to obtain a closed-form slope dependence of the nonlinear shoaling coefficient compatible with experiments over steep breakwaters.

physics.flu-dyn↗

arXiv2023

Global assessment of university research comprehensiveness

The demand for global university league tables has been high over the past two decades. However, significant criticism of their methodologies is accumulating without being addressed. I revisit global university league tables by normalizing each field as to create a uniform distribution of value. Then, the overall performance of an institution is interpreted as the probability of having a high score in any given academic field. I focus on the similarity of institutions across ten criteria related to academic performance in eighty subjects of all fields of knowledge. The latter does not induce a zero-sum game, removing one of the most prominent negative features of established league tables. The present assessment shows that the main difference between hundreds of leading global research universities is whether their coverage of all areas of human knowledge is comprehensive or specialized, as their mean performance per subject is nearly indistinguishable. I compare the results with the main league tables and found excellent agreement, suggesting that regardless of their methodologies, research-intensive institutions perform well in rankings if they are comprehensive. This comprehensiveness is ultimately dependent on institutional age, privileged funding allocation and regional academic culture. Consequently, when the size of an institution is taken out of the picture, I found no correlation between comprehensiveness and quality, and no difference can be found in the mean quality of institutions regionally or globally. Furthermore, I find the reputation and prestige of several famous institutions to far exceed their performance within the present methodology, while numerous institutions with less reputation and visibility perform better than expected.

physics.soc-ph↗

arXiv2023

Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves

Bathymetric changes have been experimentally shown to affect the occurrence of rogue waves. We recently derived a non-homogeneous correction to the spectral analysis, allowing to describe the evolution of the rogue wave probability over a shoal. Here, we extend this work to the evolution of the excess kurtosis of the surface elevation, that plays a central role in estimating rare event probabilities. Furthermore, we provide an upper bound to the excess kurtosis. In intermediate and deep water regimes, a shoal does not affect wave steepness nor bandwidth significantly, so that the vertical asymmetry between crests and troughs, the excess kurtosis, and the exceedance probability of wave height stay rather constant. In contrast, in shallower water, a sharp increase in wave steepness increases the vertical asymmetry, resulting in a growth of both the tail of the exceedance probability and the excess kurtosis.

physics.flu-dyn↗

arXiv2022

Saturation of Rogue Wave Amplification over Steep Shoals

The shoaling of surface gravity waves has been acknowledged as a mechanism of rogue wave formation. This problem is generally reduced to water waves passing over a step, but non-equilibrium physics allows finite slopes to be considered. Using non-homogeneous spectral analysis of a spatially varying energy density ratio we describe the dependence of the amplification as a function of the slope steepness. Increasing the slope increases the amplification of rogue wave probability, until this amplification saturates at steep slopes. In contrast, the increase of the down slope of a subsequent de-shoal zone leads to a monotonic decrease in the rogue wave probability, thus featuring a strong asymmetry between shoaling and de-shoaling zones. Due to the saturation of the rogue wave amplification at steep slopes, our model is applicable beyond its range of validity up to a step, thus elucidating why previous models based on a step could describe the physics of steep finite slopes. We also explain why the rogue wave probability increases over a shoal while it is lower in shallower water.

physics.flu-dyn↗