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Global Regularity for 2d Water Waves with Surface Tension
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves
system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An
important point of our analysis is to develop a sufficiently robust method, based on energy estimates and dispersive analysis, which
allows us to deal simultaneously with strong singularities arising from time resonances in the applications of the normal form method
and with nonlinear scattering. As a result, we are able to consider a suitable class of perturbations with finite energy, but no other
momentum conditions.
Part of our analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is
of independent interest. As a consequence, the results in this paper are self-contained.
eBook
Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in
fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves,
we can consider solutions such that the curvature of the initial free surface does not belong to
The
proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and
Hölder estimates. We first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then we use the dispersive
properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.
eBook
Waves in Oceanic and Coastal Waters
Waves in Oceanic and Coastal Waters describes the observation, analysis and prediction of wind-generated waves in the open ocean, in shelf seas, and in coastal regions with islands, channels, tidal flats and inlets, estuaries, fjords and lagoons. Most of this richly illustrated book is devoted to the physical aspects of waves. After introducing observation techniques for waves, both at sea and from space, the book defines the parameters that characterise waves. Using basic statistical and physical concepts, the author discusses the prediction of waves in oceanic and coastal waters, first in terms of generalised observations, and then in terms of the more theoretical framework of the spectral energy balance. He gives the results of established theories and also the direction in which research is developing. The book ends with a description of SWAN (Simulating Waves Nearshore), the preferred computer model of the engineering community for predicting waves in coastal waters.
eBook
Tropical Cyclone Characteristics Represented by the Ocean Wave-Coupled Atmospheric Global Climate Model Incorporating Wave-Dependent Momentum Flux
Understanding the systematic characteristics of tropical cyclones (TCs) represented in global climate models (GCMs) is important for reliable climate change impact assessments. The atmospheric GCM (AGCM) and ocean wave models were coupled by incorporating the wave-dependent momentum flux. Systematic impacts of wave-dependent momentum flux on TC characteristics were estimated by analyzing 100 historical TCs that occurred in the western North Pacific Ocean. Wave-dependent momentum flux parameterization considering wind and wave direction misalignment was used for assessing the wave–atmosphere interaction. The larger the wave age and misalignment are, the larger the drag coefficient is. The drag coefficient at the left-hand side of the TC was enhanced by the wave condition. It was found that the wave-dependent momentum flux did not have any impact on peak TC intensity. On the other hand, the wave-dependent momentum flux showed a significant impact on TC development during the early development stage. Although systematic differences in TC intensity at most developed stages were not detected, systematic differences in TC tracks between experiments were observed. The TC tracks of the wave-coupled AGCM tend to pass in a relatively eastward direction in comparison with those from the uncoupled AGCM. This is because the wave-dependent momentum flux in the coupled AGCM altered the environmental steering flow and the smaller beta effect of smaller TC at the early developing stage. Systematic differences in TC tracks have significant impacts on climate change assessments, such as extreme sea level changes in coastal regions due to climate change.
Journal Article
Numerical Simulation of Wave Characteristics off Kulasekharapatnam, Southeast Coast of India
Waves are important driving forces that have significant implications in deep and shallow waters. To achieve further understanding of the characteristics of wind waves in the Gulf of Mannar, an attempt is made based on the measured data off Kulasekharapatnam for the period from January 2006 to May 2007. The integrated third-generation ocean wave models, WAM and SWAN, are implemented to simulate the significant wave parameters. Simulations were carried out using ECMWF ERA-Interim winds over the deep waters (30°E–120°E; 70°S–30°N and 76°E–80°E; 6°N–10°N) domains. Comparison of the ECMWF ERA-Interim wind data against the field measured data demonstrates that the overall trend and dominant directions are consistent with the observational data. The validation of significant wave parameters exhibited very high correlation (
R
> 0.9) at the study location. Wave heights are high in the Gulf of Mannar during the southwest monsoon period and the waves are from south-southwest. The study also shows that swells are predominant (24%) in the Gulf of Mannar during non-monsoon period and during rest of the year, wind sea (75.9%) dominates. The study also demonstrates the sensitivity of the SWAN model towards different GEN3 physics options and bottom friction formulations by forcing the model with QuikSCAT/NCEP Blended winds off Kulasekharapatnam. The simulations obtained using different GEN3 physics options and bottom friction formulations have been compared with the buoy data. The study indicates that the SWAN model with Janssen and Komen physics options simulates the significant wave height and mean wave period, respectively, with a fairly high degree of accuracy. Similarly, the JONSWAP formulation for bottom friction reproduced the buoy signals at the study location with good accuracy for both significant wave height and mean wave period. The study demonstrates that the simulations are sensitive to the choice of GEN3 physics and bottom friction formulations off Kulasekharapatnam, and hence effective for obtaining more accurate wave predictions.
Journal Article
Fractional Calculus with Applications in Mechanics
The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscillations of a body attached to a rod, impact and variational principles of a Hamiltonian type. The books will be useful for graduate students in mechanics and applied mathematics, as well as for researchers in these fields.Part 1 of this book presents an introduction to fractional calculus. Chapter 1 briefly gives definitions and notions that are needed later in the book and Chapter 2 presents definitions and some of the properties of fractional integrals and derivatives.Part 2 is the central part of the book. Chapter 3 presents the analysis of waves in fractional viscoelastic materials in infinite and finite spatial domains. In Chapter 4, the problem of oscillations of a translatory moving rigid body, attached to a heavy, or light viscoelastic rod of fractional order type, is studied in detail. In Chapter 5, the authors analyze a specific engineering problem of the impact of a viscoelastic rod against a rigid wall. Finally, in Chapter 6, some results for the optimization of a functional containing fractional derivatives of constant and variable order are presented.
eBook
Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
eBook
An atmosphere–wave regional coupled model: improving predictions of wave heights and surface winds in the southern North Sea
The coupling of models is a commonly used approach when addressing the complex interactions between different components of earth systems. We demonstrate that this approach can result in a reduction of errors in wave forecasting, especially in dynamically complicated coastal ocean areas, such as the southern part of the North Sea – the German Bight. Here, we study the effects of coupling of an atmospheric model (COSMO) and a wind wave model (WAM), which is enabled by implementing wave-induced drag in the atmospheric model. The numerical simulations use a regional North Sea coupled wave–atmosphere model as well as a nested-grid high-resolution German Bight wave model. Using one atmospheric and two wind wave models simultaneously allows for study of the individual and combined effects of two-way coupling and grid resolution. This approach proved to be particularly important under severe storm conditions as the German Bight is a very shallow and dynamically complex coastal area exposed to storm floods. The two-way coupling leads to a reduction of both surface wind speeds and simulated wave heights. In this study, the sensitivity of atmospheric parameters, such as wind speed and atmospheric pressure, to the wave-induced drag, in particular under storm conditions, and the impact of two-way coupling on the wave model performance, is quantified. Comparisons between data from in situ and satellite altimeter observations indicate that two-way coupling improves the simulation of wind and wave parameters of the model and justify its implementation for both operational and climate simulations.
Journal Article
Finite Element and Boundary Methods in Structural Acoustics and Vibration
A unique and in-depth presentation of the finite element method (FEM) and the boundary element method (BEM) in structural acoustics and vibrations, this book illustrates the principles using a logical and progressive methodology, which leads to a thorough understanding of their physical and mathematical principles and their implementation to solve a wide range of problems in structural acoustics and vibration. This book helps readers to understand the principles, use of the FEM, and the BEM in structural acoustics and vibrations.
eBook