Modulations of Deep Water Waves and Spectral Filtering
Modulations of deep water waves are studied by a new formalism of spectral filtering. For single‐mode dynamics, spectral filtering results in computable equations, which are counterpart to the nonlinear Schrödinger (NLS) equations. An essential feature of new equations is that bandwidth limitation i...
Saved in:
Published in | Studies in applied mathematics (Cambridge) Vol. 111; no. 3; pp. 301 - 313 |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK
Blackwell Publishing, Inc
01.10.2003
Blackwell |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Modulations of deep water waves are studied by a new formalism of spectral filtering. For single‐mode dynamics, spectral filtering results in computable equations, which are counterpart to the nonlinear Schrödinger (NLS) equations. An essential feature of new equations is that bandwidth limitation is decoupled from small‐amplitude assumption. The filtered equations have a substantially broader range of validity than the NLS equations, and may be viewed as intermediate between the NLS and Zakharov equations. The new single‐mode equations reproduce exactly the conditions for nonlinear four‐wave resonance (“figure 8” of Phillips [1]) even for bandwidths greater than unity. Sideband instability for uniform Stokes waves is limited to finite bandwidths only, and agrees well with exact results of McLean [2]. |
---|---|
Bibliography: | ArticleID:SAPM235 istex:F01E6192CA66DE0397759D77E0ECDD92059612CE ark:/67375/WNG-MRTHWPFQ-S ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0022-2526 1467-9590 |
DOI: | 10.1111/1467-9590.t01-1-00235 |