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2003 | Buch

Wind-Waves in Oceans

Dynamics and Numerical Simulations

verfasst von: Professor Dr. Igor V. Lavrenov

Verlag: Springer Berlin Heidelberg

Buchreihe : Physics of Earth and Space Environments

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Über dieses Buch

The study of sea waves has always been in the focus of mankind's atten­ tion. This is attributed not only to a desire to understand the behaviour in seas and oceans, but also, it has some practical necessity. Developing up-to­ date wind wave numerical methods requires detailed mathematical modelling, starting with wave generation, development, propagation and transformation on the surface in different water areas under quasi-stationary conditions, up to a synthesis of climatic features observed under different wave generation conditions in oceans, sea or coastal areas. The present monograph considers wind waves in terms of the most general formulation of the problem as a probable hydrodynamic process with wide spatial variability. It ranges between the global scale of the oceans, whose typical size is comparable with the Earth's radius, to the regional and local scales of the seas, including water areas limited in space with significant current or depth gradients in coastal zones, where waves cease their existence having propagated tens of thousand miles.

Inhaltsverzeichnis

Frontmatter
Introduction
Abstract
Surface gravity waves have always caused great interest, as they are an example of a well-known, but still very complicated phenomenon. They can easily be observed, but it is rather difficult to describe them mathematically. Sir Horace Lamb noted in his letter to the London Mathematical Society in 1904 that waves were almost the first hydrodynamic problem studied systematically on the basis of general equations. It gave an example of activity that provided efficient evidence of new and unusual analytical methods. Wave observations on the sea surface and their connection with wind have been performed from time immemorial. It was quite natural that the pioneers of theoretical hydrodynamics (J. Lagrange, G. Eiry, G. Stokes and J. Rayleigh) tried to find an explanation of the elementary properties of surface waves using the assumption of ideal fluid motion.
Igor V. Lavrenov
1. General Problem Formulation of Wind Wave Modelling in a Non-Uniform Ocean
Abstract
The evolution of wind waves should be considered as the self-consistent mo­tion of a two-layer water-air system under the corresponding dynamic and kinematic conditions in the two-media interface. The media motion is as­sumed to be determined by the laws of mass and momentum conservation. The former (i.e., the law of mass conservation) is written as:
(1.1)
where p i is the air (i = 1) or water (i = 2) density, respectively; U i is the velocity of the medium motion.
Igor V. Lavrenov
2. Mathematical Simulation of Wave Propagation at Global Distances
Abstract
Chapter 1 presents a general problem formulation of the evolution of the wind wave spectrum considering various determining factors. Due to the complexity of formulating the general problem, sphericity solution effects are considered in this chapter. The investigation is limited to the deep-water case, taking into consideration that the average ocean depth essentially exceeds the characteristic lengths of wind waves and swell.
Igor V. Lavrenov
3. Numerical Implementation of the Wave Energy Balance Equation
Abstract
Successful solution of the problem of hindcasting and forecasting a sea wind wave depends on the quality of the physical model, the numerical implementation of the wave energy balance equation and the accuracy of the wind field data. It should be noted that in general most modern wind wave models are not characterized by their high-level numerical implementation. The numerical imeplementation of the wave energy balance equation is principally important for accuracy and model efficiency (Lavrenov & Ryvkin, 1989; Ryvkin, 1990; Ryabinin, 1991a,b; Tolman, 1992). Numerical implementation errors are comparable with those obtained due to inaccuracy of wind data and imperfect parameterization of the mechanisms of the physical model.
Igor V. Lavrenov
4. Study of Physical Mechanisms Forming the Wind Wave Energy Spectrum in Deep Water
Abstract
As has been noted, the study of different physical mechanisms forming the wind wave spectrum is one of the central problems associated with wave simulation. The source function in the right-hand side of the wave energy balance equation reflects the formal representation of these mechanisms. At present there are many papers devoted to this problem. The most detailed description can be found, for example, in the latest monographs published in Russia (Problems of Research and Mathematical Modeling of Wind Sea, 1995) and in some other countries (Komen et al., 1994; Massel, 1996; Young, 1999). There is no need to present all these results in detail, but the most important aspects should be considered.
Igor V. Lavrenov
5. Wave Evolution in Non-uniform Currents in Deep Water
Abstract
The general formulation of the wind wave mathematical modelling problem in the ocean under the action of different factors forming the wind spectrum is presented in Chap. 1. The effects associated with wave spectrum transformation in a horizontal non-uniform current are investigated in this chapter.
Igor V. Lavrenov
6. Wave Transformation in Shallow Water
Abstract
The wave description given in Chap. 1 allows easy analysis of wind wave propagation in a coastal area,1 i.e. when relatively short sea waves propagate from deep to shallow water, approaching a coastline. In this case refraction plays a special role among the different factors affecting wave behavior. Due to depth variation it results in the evolution of wave parameters, namely, propagation direction, length, amplitude and wave profile. As noted in the Introduction, there are many papers devoted to the problem of wave transformation in a coastal area. An application of the spectral approach to this problem following from the general formulation is considered in this chapter.
Igor V. Lavrenov
7. Wave Transformation in Ice-Covered Water
Abstract
In the Arctic sea when the waves propagate from the open water surface into the region covered with ice, they meet ice of different density, reducing their intensity considerable. Now the cases of wave interaction with ice cases will be considered.
Igor V. Lavrenov
8. Conclusion
Abstract
Wind wave investigations in the World’s oceans are carried out by scientists in many countries. Now it is a subject of international research. This is manifested by a great number of papers and monographs (Komen et al., 1994; Problems of Research and Mathematical Modeling of Wind Sea. 1995; Massel, 1996; Young, 1999), published in the last few years and devoted to the study of wind waves and numerical simulation. The present monograph is a logical continuation of those publications. The main attention is paid to investigation of the effect of spatial inhomogeneous media on wind waves, including the effect of the Earth’s surface sphericity, the presence of non-uniform currents, uneven bottom, ice cover, etc, which affect wind wave spectral structure formation in the World’s oceans.
Igor V. Lavrenov
Backmatter
Metadaten
Titel
Wind-Waves in Oceans
verfasst von
Professor Dr. Igor V. Lavrenov
Copyright-Jahr
2003
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-662-05146-7
Print ISBN
978-3-642-07890-3
DOI
https://doi.org/10.1007/978-3-662-05146-7