NDLI: Weak or strong nonlinearity: the vital issue

Content Provider	Springer Nature Link
Author	Rainey, R. C. T.
Copyright Year	2007
Abstract	Marine hydrodynamics is characterised by both weak nonlinearities, as seen for example in drift forces, and strong nonlinearities, as seen for example in wave breaking. In many cases their relative importance is still a controversial matter. The phenomenon of particle escape, seen in linear theory, appears to offer a guide to when strongly nonlinear effects will start to become important, and what will happen when they do.In the case of the “ringing” of vertical cylinders in steep waves, particle escape is shown to correspond approximately to local wave breaking, which leads to the cavitation responsible for “ringing”. Another example is rogue waves, where recent results from weakly nonlinear theory are disappointing, and also fail to explain the rogue waves seen in relatively shallow water, as in the data from the Draupner and Gorm platforms. Recent laboratory experiments, too, show wave crests continuing to grow in height after all frequency components have come into phase, which is inconsistent with weakly nonlinear theory. Particle escape, which is more frequent in shallow water, offers a simple alternative explanation for these observations, as well as for the violent motion at the wave crests, which often confuses rogue-wave data. Extreme wave crests have long been known to be strongly nonlinear, so it appears possible that rogue waves are primarily a strongly nonlinear phenomenon.Fully nonlinear computations of two interacting regular waves are presented, to explore further the connection between particle escape and wave breaking. They are combined with Monte-Carlo simulations of particle escape in hurricane conditions, and the very few measurements of large breaking waves during hurricanes. It is concluded that large breaking waves will have occurred about once per hour, and once per 100 h, respectively, in the recent hurricanes LILI and IVAN. These findings call into question the use of non-breaking wave models in the design codes for fixed steel offshore structures.
Starting Page	229
Ending Page	249
Page Count	21
File Format	PDF
ISSN	00220833
Journal	Journal of Engineering Mathematics
Volume Number	58
Issue Number	1-4
e-ISSN	15732703
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2007-03-10
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Freak waves Hurricane damage Offshore structures Rogue waves Wave breaking Numeric Computing Mathematical Modeling and Industrial Mathematics Analysis Applications of Mathematics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mathematics Engineering

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