Author: Roberto FeolaPublisher: American Mathematical Society
ISBN: 1470468778
Category : Mathematics
Languages : en
Pages : 170
Book Description
View the abstract.
Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
Author: Roberto FeolaPublisher: American Mathematical Society
ISBN: 1470468778
Category : Mathematics
Languages : en
Pages : 170
Book Description
View the abstract.
Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves
Author: Massimiliano BertiPublisher: American Mathematical Soc.
ISBN: 1470440695
Category : Education
Languages : en
Pages : 171
Book Description
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.
Small Divisor Problem in the Theory of Three-Dimensional Water Gravity Waves
Author: Grard IoossPublisher: American Mathematical Soc.
ISBN: 0821843826
Category : Science
Languages : en
Pages : 144
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 $(\theta,\mu ).$
Applied Mechanics Reviews
Author: Twenty-Second Symposium on Naval Hydrodynamics
Author: National Research CouncilPublisher: National Academies Press
ISBN: 0309065372
Category : Science
Languages : en
Pages : 1039
Book Description
The Twenty-Second Symposium on Naval Hydrodynamics was held in Washington, D.C., from August 9-14, 1998. It coincided with the 100th anniversary of the David Taylor Model Basin. This international symposium was organized jointly by the Office of Naval Research (Mechanics and Energy Conversion S&T Division), the National Research Council (Naval Studies Board), and the Naval Surface Warfare Center, Carderock Division (David Taylor Model Basin). This biennial symposium promotes the technical exchange of naval research developments of common interest to all the countries of the world. The forum encourages both formal and informal discussion of the presented papers, and the occasion provides an opportunity for direct communication between international peers.
The Water Waves Problem
Author: David LannesPublisher: American Mathematical Soc.
ISBN: 0821894706
Category : Mathematics
Languages : en
Pages : 347
Book Description
This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.
Nonlinear Waves in Fluids: Recent Advances and Modern Applications
Author: Roger GrimshawPublisher: Springer Science & Business Media
ISBN: 3211380256
Category : Technology & Engineering
Languages : en
Pages : 202
Book Description
Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.
The Interaction of Ocean Waves and Wind
Author: Peter JanssenPublisher: Cambridge University Press
ISBN: 0521465400
Category : Science
Languages : en
Pages : 310
Book Description
This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.
Waves in Fluids
Author: Sir M. J. LighthillPublisher: Cambridge University Press
ISBN: 9780521010450
Category : Mathematics
Languages : en
Pages : 528
Book Description
This comprehensive text describes the science of waves in fluids.
Gravity-Capillary Free-Surface Flows
Author: Jean-Marc Vanden-BroeckPublisher: Cambridge University Press
ISBN: 0521811902
Category : Mathematics
Languages : en
Pages : 331
Book Description
Experienced and well-respected author; essential monograph for applied mathematicians and engineers.