On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

Extreme value statistics in Raman fiber lasers

We present the numerical study of the statistical properties of the partially coherent quasi-CW high-Q cavity Raman fiber laser. The statistical properties are different for the radiation generated at the spectrum center or spectral wings. It is found that rare extreme events are generated at the far spectral wings at one pass only. The mechanism of the extreme events generation is a turbulent-like four-wave mixing of numerous longitudinal generation modes. The similar mechanism of extreme waves appearance during the laser generation could be important in other types of fiber lasers. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

INVESTIGATIONS INTO MECHANISMS UNDERLYING EXTREME WAVE FORMATIONS AND COMPUTATIONALLY INTENSIVE SIMULATIONS

Various mechanisms have been proposed to explain extreme waves or rogue waves in an oceanic environment including directional focusing, dispersive focusing, wave-current interaction, and nonlinear modulational instability. The Benjamin-Feir instability (nonlinear modulational instability), however, is considered to be one of the primary mechanisms for rogue-wave occurrence. The nonlinear Schrodinger equation is a well-established approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory. Solutions of the nonlinear Schrodinger equation, including new rogue-wave type solutions are presented in the author's dissertation work. The solutions are obtained by using a predictive eigenvalue map based predictor-corrector procedure developed by the author. Features of the predictive map are explored and the influences of certain parameter variations are investigated. The solutions are rescaled to match the length scales of waves generated in a wave tank. Based on the information provided by the map and the details of physical scaling, a framework is developed that can serve as a basis for experimental investigations into a variety of extreme waves as well localizations in wave fields. To derive further fundamental insights into the complexity of extreme wave conditions, Smoothed Particle Hydrodynamics (SPH) simulations are carried out on an advanced Graphic Processing Unit (GPU) based parallel computational platform. Free surface gravity wave simulations have successfully characterized water-wave dispersion in the SPH model while demonstrating extreme energy focusing and wave growth in both linear and nonlinear regimes. A virtual wave tank is simulated wherein wave motions can be excited from either side. Focusing of several wave trains and isolated waves has been simulated. With properly chosen parameters, dispersion effects are observed causing a chirped wave train to focus and exhibit growth. By using the insights derived from the study of the nonlinear Schrodinger equation, modulational instability or self-focusing has been induced in a numerical wave tank and studied through several numerical simulations. Due to the inherent dissipative nature of SPH models, simulating persistent progressive waves can be problematic. This issue has been addressed and an observation-based solution has been provided. The efficacy of SPH in modeling wave focusing can be critical to further our understanding and predicting extreme wave phenomena through simulations. A deeper understanding of the mechanisms underlying extreme energy localization phenomena can help facilitate energy harnessing and serve as a basis to predict and mitigate the impact of energy focusing.

Boulder deposition during major tsunami events

A remarkable accumulation of marine boulders located above the present spring tide level has occurred in two coastal lowlands of the Algarve (Portugal). The size-interval of the particles studied here is seldom reported in the literature in association with extreme events of coastal inundation, thus making this study of relevance to many other coasts worldwide. The spreads of boulders extend several hundred meters inland and well beyond the present landward limit of storm activity. The marine origin of the boulders is demonstrated by well-developed macro-bioerosion sculpturing and in situ skeletal remains of endolithic shallow marine bivalves. The good state preservation of the fossils within the boulders indicates that abrasion duringtransport and redeposition was not significant. We envisage boulder deposition as having taken place during the Lisbon tsunami of ad 1755 through the simultaneous landward entrainment of coarse particles from nearshore followed by rapid shoreward suspended-dominated transport and non-graded redeposition that excluded significant sorting by weight or boulder dimensions. We use numerical hydrodynamic modeling of tsunami (and storm) waves to test the observational data on boulder dimensions (density, size, distribution) on the most likely processes of sediment deposition. This work demonstrates the effectiveness of the study of boulder deposits in tsunami reconstruction. Copyright (C) 2011 John Wiley & Sons, Ltd.

Improvement of theoretical storm characterization for different climate conditions

The different theoretical models related with storm wave characterization focus on determining the significant wave height of the peak storm, the mean period and, usually assuming a triangle storm shape, their duration. In some cases, the main direction is also considered. Nevertheless, definition of the whole storm history, including the variation of the main random variables during the storm cycle is not taken into consideration. The representativeness of the proposed storm models, analysed in a recent study using an empirical maximum energy flux time dependent function shows that the behaviour of the different storm models is extremely dependent on the climatic characteristics of the project area. Moreover, there are no theoretical models able to adequately reproduce storm history evolution of the sea states characterized by important swell components. To overcome this shortcoming, several theoretical storm shapes are investigated taking into consideration the bases of the three best theoretical storm models, the Equivalent Magnitude Storm (EMS), the Equivalent Number of Waves Storm (ENWS) and the Equivalent Duration Storm (EDS) models. To analyse the representativeness of the new storm shape, the aforementioned maximum energy flux formulation and a wave overtopping discharge structure function are used. With the empirical energy flux formulation, correctness of the different approaches is focussed on the progressive hydraulic stability loss of the main armour layer caused by real and theoretical storms. For the overtopping structure equation, the total volume of discharge is considered. In all cases, the results obtained highlight the greater representativeness of the triangular EMS model for sea waves and the trapezoidal (nonparallel sides) EMS model for waves with a higher degree of wave development. Taking into account the increase in offshore and shallow water wind turbines, maritime transport and deep vertical breakwaters, the maximum wave height of the whole storm history and that corresponding to each sea state belonging to its cycle's evolution is also considered. The procedure considers the information usually available for extreme waves' characterization. Extrapolations of the maximum wave height of the selected storms have also been considered. The 4th order statistics of the sea state belonging to the real and theoretical storm have been estimated to complete the statistical analysis of individual wave height

Performance improvements of mooring systems for wave energy converters

In the development of wave energy converters, the mooring system is a key component for a safe station-keeping and an important factor in the cost of the wave energy production. Generally, when designing a mooring system for a wave energy converter, two important conditions must be considered: (i) that the mooring system must be strong enough to limit the drifting motions, even in extreme waves, tidal and wind conditions and (ii) it must be compliant enough so that the impact on wave energy production can be minimised. It is frequently found that these two conditions are contradictory. The existing solutions mainly include the use of heavy chains, which create a catenary shaped mooring configuration, allowing limited flexibility within the mooring system, and hence very large forces may still be present on mooring lines and thus on anchors. This solution is normally quite expensive if the costs of the materials and installation are included. This paper presents a new solution to the mooring system for wave energy converters within the FP7 project, ‘GeoWAVE’, which is a project aiming to develop a new generation of the moorings system for minimising the loads on mooring lines and anchors, the impact on the device motions for power conversion, and the footprint if it is applicable, and meanwhile the new types of anchors are also addressed within the project. However this paper will focus on the new mooring system by presenting the wave tank test results of the Pelamis wave energy converter model and the new developed mooring system. It can be seen that the new generation of mooring system can significantly reduce the loads on mooring lines and anchors, and reduce the device excursions as a result of the new mooring system when compare to the conventional catenary mooring.

Energy conversion: a comparison of fix- and self-referenced wave energy converters

The paper presents an investigation of fix-referenced and self-referenced wave energy converters and a comparison of their corresponding wave energy conversion capacities from real seas. For conducting the comparisons, two popular wave energy converters, point absorber and oscillating water column, and their power conversion capacities in the fixed-referenced and self-referenced forms have been numerically studied and compared. In the numerical models, the deviceâ s power extractions from seas are maximized using the correspondingly optimized power take-offs in different sea states, thus their power conversion capacities can be calculated and compared. From the comparisons and analyses, it is shown that the energy conversion capacities of the self-referenced devices can be significantly increased if the motions of the device itself can be utilized for wave energy conversion; and the self-referenced devices can be possibly designed to be compliant in long waves, which could be a very beneficial factor for device survivability in the extreme wave conditions (normally long waves). In this regards, the self-referenced WECs (wave energy converters) may be better options in terms of wave energy conversion from the targeted waves in seas (frequently the most occurred), and in terms of the device survivability, especially in the extreme waves when compared to the fix-referenced counterparts.

Low-frequency absorption cross section of the electromagnetic waves for extreme Reissner-Nordstrom black holes in higher dimensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The social impacts of heat waves

The effects of the 2003 European heat wave have highlighted the need for society to prepare itself for and cope more effectively with heat waves. This is particularly important in the context of predicted climate change and the likelihood of more frequent extreme climate events; to date, heat as a natural hazard has been largely ignored. In order to develop better coping strategies, this report explores the factors that shape the social impacts of heat waves, and sets out a programme of research to address the considerable knowledge gaps in this area. Heat waves, or periods of anomalous warmth, do not affect everyone; it is the vulnerable individuals or sectors of society who will most experience their effects. The main factors of vulnerability are being elderly, living alone, having a pre-existing disease, being immobile or suffering from mental illness and being economically disadvantaged. The synergistic effects of such factors may prove fatal for some. Heat waves have discernible impacts on society including a rise in mortality, an increased strain on infrastructure (power, water and transport) and a possible rise in social disturbance. Wider impacts may include effects on the retail industry, ecosystem services and tourism. Adapting to more frequent heat waves should include soft engineering options and, where possible, avoid the widespread use of air conditioning which could prove unsustainable in energy terms. Strategies for coping with heat include changing the way in which urban areas are developed or re-developed, and setting up heat watch warning systems based around weather and seasonal climate forecasting and intervention strategies. Although heat waves have discernible effects on society, much remains unknown about their wider social impacts, diffuse health issues and how to manage them.

Improving the health forecasting alert system for cold weather and heat-waves in England: a proof-of-concept using temperature-mortality relationships

Objectives In this study a prototype of a new health forecasting alert system is developed, which is aligned to the approach used in the Met Office’s (MO) National Severe Weather Warning Service (NSWWS). This is in order to improve information available to responders in the health and social care system by linking temperatures more directly to risks of mortality, and developing a system more coherent with other weather alerts. The prototype is compared to the current system in the Cold Weather and Heatwave plans via a case-study approach to verify its potential advantages and shortcomings. Method The prototype health forecasting alert system introduces an “impact vs likelihood matrix” for the health impacts of hot and cold temperatures which is similar to those used operationally for other weather hazards as part of the NSWWS. The impact axis of this matrix is based on existing epidemiological evidence, which shows an increasing relative risk of death at extremes of outdoor temperature beyond a threshold which can be identified epidemiologically. The likelihood axis is based on a probability measure associated with the temperature forecast. The new method is tested for two case studies (one during summer 2013, one during winter 2013), and compared to the performance of the current alert system. Conclusions The prototype shows some clear improvements over the current alert system. It allows for a much greater degree of flexibility, provides more detailed regional information about the health risks associated with periods of extreme temperatures, and is more coherent with other weather alerts which may make it easier for front line responders to use. It will require validation and engagement with stakeholders before it can be considered for use.

Wolf-Rayet optically thick winds with Alfven waves

The Wolf-Rayet (WR) stars are hot luminous objects which are suffering an extreme mass loss via a continuous stellar wind. The high values of mass loss rates and high terminal velocities of the WR stellar winds constitute a challenge to the theories of radiation driven winds. Several authors incorporated magnetic forces to the line driven mechanism in order to explain these characteristics of the wind. Observations indicate that the WR stellar winds may reach, at the photosphere, velocities of the order of the terminal values, which means that an important part of the wind acceleration occurs at the optically thick region. The aim of this study is to analyze a model in which the wind in a WR star begins to be accelerated in the optically thick part of the wind. We used as initial conditions stellar parameters taken from the literature and solved the energy, mass and momentum equations. We demonstrate that the acceleration only by radiative forces is prevented by the general behavior of the opacities. Combining radiative forces plus a flux of Alfven waves, we found in the simulations a fast drop in the wind density profile which strongly reduces the extension of the optically thick region and the wind becomes optically thin too close its base. The understanding how the WR wind initiate is still an open issue. (C) 2010 COSPAR. Published by Elsevier Ltd. All rights reserved.

Extreme climatic events: impacts of drought and high temperature on physiological processes in agronomically important plants

Climate models predict more frequent and more severe extreme events (e.g., heat waves, extended drought periods, flooding) in many regions for the next decades. The impact of adverse environmental conditions on crop plants is ecologically and economically relevant. This review is focused on drought and heat effects on physiological status and productivity of agronomically important plants. Stomatal opening represents an important regulatory mechanism during drought and heat stress since it influences simultaneously water loss via transpiration and CO2 diffusion into the leaf apoplast which further is utilized in photosynthesis. Along with the reversible short-term control of stomatal opening, stomata and leaf epidermis may produce waxy deposits and irreversibly down-regulate the stomatal conductance and non-stomatal transpiration. As a consequence photosynthesis will be negatively affected. Rubisco activase—a key enzyme in keeping the Calvin cycle functional—is heat-sensitive and may become a limiting factor at elevated temperature. The accumulated reactive oxygen species (ROS) during stress represent an additional challenge under unfavorable conditions. Drought and heat cause accumulation of free amino acids which are partially converted into compatible solutes such as proline. This is accompanied by lower rates of both nitrate reduction and de novo amino acid biosynthesis. Protective proteins (e.g., dehydrins, chaperones, antioxidant enzymes or the key enzyme for proline biosynthesis) play an important role in leaves and may be present at higher levels under water deprivation or high temperatures. On the whole plant level, effects on long-distance translocation of solutes via xylem and phloem and on leaf senescence (e.g., anticipated, accelerated or delayed senescence) are important. The factors mentioned above are relevant for the overall performance of crops under drought and heat and must be considered for genotype selection and breeding programs.

Trends of mean and extreme temperature indices since 1874 at low-elevation sites in the Southern Alps

We describe the recovery of three daily meteorological records for the southern Alps (Domodossola, Riva del Garda, and Rovereto), all starting in the second half of the nineteenth century. We use these new data, along with additional records, to study regional changes in the mean temperature and extreme indices of heat waves and cold spells frequency and duration over the period 1874–2015. The records are homogenized using subdaily cloud cover observations as a constraint for the statistical model, an approach that has never been applied before in the literature. A case study based on a record of parallel observations between a traditional meteorological window and a modern screen shows that the use of cloud cover can reduce the root-mean-square error of the homogenization by up to 30% in comparison to an unaided statistical correction. We find that mean temperature in the southern Alps has increased by 1.4°C per century over the analyzed period, with larger increases in daily minimum temperatures than maximum temperatures. The number of hot days in summer has more than tripled, and a similar increase is observed in duration of heat waves. Cold days in winter have dropped at a similar rate. These trends are mainly caused by climate change over the last few decades.

Wave height (regular and irregular waves) reduction in 2m water depth over a 40-m-long salt marsh test section in a large scale laboratory flume

Coastal communities around the world face increasing risk from flooding as a result of rising sea level, increasing storminess, and land subsidence. Salt marshes can act as natural buffer zones, providing protection from waves during storms. However, the effectiveness of marshes in protecting the coastline during extreme events when water levels and waves are highest is poorly understood. Here, we experimentally assess wave dissipation under storm surge conditions in a 300-m-long wave flume that contains a transplanted section of natural salt marsh. We find that the presence of marsh vegetation causes considerable wave attenuation, even when water levels and waves are high. From a comparison with experiments without vegetation, we estimate that up to 60% of observed wave reduction is attributed to vegetation. We also find that although waves progressively flatten and break vegetation stems and thereby reduce dissipation, the marsh substrate remained remarkably stable and resistant to surface erosion under all conditions.The effectiveness of storm wave dissipation and the resilience of tidal marshes even at extreme conditions suggest that salt marsh ecosystems can be a valuable component of coastal protection schemes.

Extreme super-resolution using the spherical geodesic waveguide

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 superresolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ/500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.