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  1. Myanmar Maritime University
  2. Department of Port and Harbour Engineering

The Most Unstable Conditions of Modulation Instability

http://hdl.handle.net/20.500.12678/0000007088
http://hdl.handle.net/20.500.12678/0000007088
da22875f-f426-4152-8e9c-f53241a34825
25c43c36-3c1b-439b-93f3-af353b4fbc67
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Publication type
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Publication
Title
Title The Most Unstable Conditions of Modulation Instability
Language en
Publication date 2012-03-26
Authors
Mee Mee Soe
Description
Modulation instability is one of the most ubiquitous types of instabilities in nature. As one of the
key characteristics of modulation instability, the most unstable condition attracts lots of attention.
The most unstable condition is investigated here with two kinds of initial wave systems via a
numerical high-order spectral method HOS for surface water wave field. Classically, one carrier
wave and a pair of sidebands are implied as the first kind of initial wave system: “seeded” wave
system. In the second kind of initialwave system: “un-seeded”wave system, only one carrier wave
is implied. Two impressive new results are present. One result shows that the grow rates of lower
and upper sideband are differentwithin the “seeded”wave system. Itmeans that, for a given wave
steepness, the most unstable lower sideband is not in pair with the most unstable upper sideband.
Another result shows the fastest growing sidebands are exactly in pair from “unseeded” wave
system. And the most unstable conditions of “unseeded” wave system are more or less the mean
value of those derived from the lower sidebands and upper sidebands within the “seeded” wave
system.
1.
Keywords
Modulation instability, most unstable condition, high-order spectral method, fastest-growing-sidebands
Identifier doi:10.1155/2012/656873
Journal articles
Hindawi Publishing Corporation
Journal of Applied Mathematics
11
2012, Article ID 656873
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