Small Divisor Problem in the Theory of Three-Dimensional Water Gravity Waves PDF Download

Author: GŽrard Iooss
Publisher: American Mathematical Soc.
ISBN: 0821843826
Category : Science
Languages : en
Pages : 144

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Book Description
The authors consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity $g$ and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle $2\theta$ between them. Denoting by $\mu =gL/c^{2}$ the dimensionless bifurcation parameter ( $L$ is the wave length along the direction of the travelling wave and $c$ is the velocity of the wave), bifurcation occurs for $\mu = \cos \theta$. For non-resonant cases, we first give a large family of formal three-dimensional gravity travelling waves, in the form of an expansion in powers of the amplitudes of two basic travelling waves. ``Diamond waves'' are a particular case of such waves, when they are symmetric with respect to the direction of propagation. The main object of the paper is the proof of existence of such symmetric waves having the above mentioned asymptotic expansion. Due to the occurence of small divisors, the main difficulty is the inversion of the linearized operator at a non trivial point, for applying the Nash Moser theorem. This operator is the sum of a second order differentiation along a certain direction, and an integro-differential operator of first order, both depending periodically of coordinates. It is shown that for almost all angles $\theta$, the 3-dimensional travelling waves bifurcate for a set of ``good'' values of the bifurcation parameter having asymptotically a full measure near the bifurcation curve in the parameter plane $(\theta,\mu ).$

Author: Clark Little
Publisher: Ten Speed Press
ISBN: 1984859781
Category : Photography
Languages : en
Pages : 241

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Book Description
Instagram sensation Clark Little shares his most remarkable photographs from inside the breaking wave, with a foreword by world surfing champion Kelly Slater. “One of the world’s most amazing water photographers . . . Now we get to experience up-close these moments of bliss.”—Jack Johnson, musician and environmentalist Surfer and photographer Clark Little creates deceptively peaceful pictures of waves by placing himself under the deadly lip as it is about to hit the sand. "Clark's view" is a rare and dangerous perspective of waves from the inside out. Thanks to his uncanny ability to get the perfect shot--and live to share it--Little has garnered a devout audience, been the subject of award-winning documentaries, and become one of the world's most recognizable wave photographers. Clark Little: The Art of Waves compiles over 150 of his images, including crystalline breaking waves, the diverse marine life of Hawaii, and mind-blowing aerial photography. This collection features his most beloved pictures, as well as work that has never been published in book form, with Little's stories and insights throughout. Journalist Jamie Brisick contributes essays on how Clark gets the shot, how waves are created, swimming with sharks, and more. With a foreword by eleven-time world surfing champion Kelly Slater and an afterword by the author on his photographic practice and technique, Clark Little: The Art of Waves offers a rare view of the wave for us to enjoy from the safety of land.

Author: Christian Kharif
Publisher: Springer Science & Business Media
ISBN: 354088419X
Category : Science
Languages : en
Pages : 222

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Book Description
“It came from nowhere, snapping giant ships in two. No one believed the survivors . . . until now” —New Scientist magazine cover, June 30, 2001 Rogue waves are the focus of this book. They are among the waves naturally - served by people on the sea surface that represent an inseparable feature of the Ocean. Rogue waves appear from nowhere, cause danger, and disappear at once. They may occur on the surface of a relatively calm sea and not reach very high amplitudes, but still be fatal for ships and crew due to their unexpectedness and abnormal features. Seamen are known to be unsurpassed authors of exciting and horrifying stories about the sea and sea waves. This could explain why, despite the increasing number of documented cases, that sailors’ observations of “walls of - ter” have been considered ctitious for a while. These stories are now addressed again due to the amount of doubtless evidence of the existence of the phenomenon, but still without suf cient information to - able interested researchers and engineers to completely understand it. The billows appear suddenly, exceeding the surrounding waves by two times their size and more, and obtaining many names: abnormal, exceptional, extreme, giant, huge, s- den, episodic, freak, monster, rogue, vicious, killer, mad- or rabid-dog waves, cape rollers, holes in the sea, walls of water, three sisters, etc.

Author: Daniel D. Stancil
Publisher: Springer Science & Business Media
ISBN: 0387778659
Category : Technology & Engineering
Languages : en
Pages : 348

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Book Description
This book begins by introducing magnetism and discusses magnetic properties of materials, magnetic moments of atoms and ions, and the elements important to magnetism. It covers magnetic susceptibilities and electromagnetic waves in anisotropic dispersive media among other topics. There are problems at the end of each chapter, many of which serve to expand or explain the material in the text. The bibliographies for each chapter give an entry to the research literature.

Author: Konstantinos Kontis
Publisher: Springer Science & Business Media
ISBN: 3642256880
Category : Science
Languages : en
Pages : 860

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Book Description
The University of Manchester hosted the 28th International Symposium on Shock Waves between 17 and 22 July 2011. The International Symposium on Shock Waves first took place in 1957 in Boston and has since become an internationally acclaimed series of meetings for the wider Shock Wave Community. The ISSW28 focused on the following areas: Blast Waves, Chemically Reacting Flows, Dense Gases and Rarefied Flows, Detonation and Combustion, Diagnostics, Facilities, Flow Visualisation, Hypersonic Flow, Ignition, Impact and Compaction, Multiphase Flow, Nozzle Flow, Numerical Methods, Propulsion, Richtmyer-Meshkov, Shockwave Boundary Layer Interaction, Shock Propagation and Reflection, Shock Vortex Interaction, Shockwave Phenomena and Applications, as well as Medical and Biological Applications. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 28 and individuals interested in these fields.

Author: Jim Kempton
Publisher: Simon and Schuster
ISBN: 1643137255
Category : Sports & Recreation
Languages : en
Pages : 304

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Book Description
A captivating look at two centuries of surfing—"the Sport of Queens"—from Native Hawaiian royalty to the breakout style and jaw-dropping feats on the waves today. Few subjects in the world of sports and or the outdoors is more timely or compelling than women’s surfing. From smart, strong, fearless women shattering records on 80-foot waves to professional athletes fighting for equal pay and a more fair and just playing field, these amazing, wave-riding warriors provide an inspirational and aspirational cast of powerful role models for women (and men) across all backgrounds and generations. Over the past two-hundred years, and especially the past five decades, the surfing lifestyle have become the envy of people around the world. The perception of sun, sand, surf, strong young women and their inimitable style, has created a booming lifestyle and sports industry—and the sport that is set to make it’s Olympic exhibition debut in Tokyo 2021. A massive shift from when colonizers tried to extinguish all traces of Native Hawaiian surfing and its sacred culture. What is it about the surfing that intrigues people of all ages, from all corners of the world? The beaches and idyllic locations? The unique style and mystique that surfers project? These women, on the beach and riding giant waves, or in the media, have made their mark on not just their sport, but our wider culture. Women on Waves is filled with phenomenal athletic performance, breakthrough female achievements, and plenty of inspiration and fun to see us through until the time when we can all hit the surf once more! Spanning a millennia, From Hawaii to Malibu, New York to Australia, South Africa to the South Pacific and beyond, Jim Kempton presents a fascinating new narrative that will captivate anyone who loves sports and the outdoors.

Author: Leo H. Holthuijsen
Publisher: Cambridge University Press
ISBN: 1139462520
Category : Science
Languages : en
Pages : 9

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Book Description
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.

Author: Tobias H. JŠger
Publisher: American Mathematical Soc.
ISBN: 082184427X
Category : Mathematics
Languages : en
Pages : 120

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Book Description
The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.

Author: Emmanuel Kengne
Publisher: Springer Nature
ISBN: 981196744X
Category : Science
Languages : en
Pages : 525

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Book Description
This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.

Author: Shamil U. Galiev
Publisher: CRC Press
ISBN: 1000063976
Category : Science
Languages : en
Pages : 508

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Book Description
The theory of waves is generalized on cases of strongly nonlinear waves, multivalued waves, and particle–waves. The appearance of these waves in various continuous media and physical fields is explained by resonances and nonlinearity effects. Extreme waves emerging in different artificial and natural systems from atom scale to the Universe are explored. Vast amounts of experimental data and comparisons of them with the results of the developed theory are presented. The book was written for graduate students as well as for researchers and engineers in the fields of geophysics, nonlinear wave studies, cosmology, physical oceanography, and ocean and coastal engineering. It is designed as a professional reference for those working in the wave analysis and modeling fields.