 |
| Titel |
Mode composition and fine spectrum of fully nonlinear simulated waves trapped by an opposing current |
| VerfasserIn |
Alexey Slunyaev, Victor Shrira |
| Konferenz |
EGU General Assembly 2015
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250108587
|
| Publikation (Nr.) |
 EGU/EGU2015-8350.pdf |
|
|
|
|
|
| Zusammenfassung |
| The modal approach for efficient description of nonlinear wave patterns on opposing jet
currents suggested in [1] allows one to derive nonlinear evolution equations for interacting
modes from the primitive Euler equations. In many important situations the resulting theory
enables simplified description (even exact solutions are available). In particular, for a single
trapped mode its evolution on a realistically weak current is governed by the nonlinear
Schrodinger equation. Strongly nonlinear simulations within the primitive Euler equations of
the representative solutions (uniform trapped waves, modulational instability of trapped
waves, envelope solitons of trapped waves) reported in [2] confirm adequacy of the developed
weakly nonlinear modal theory.
In this paper to understand better the range of validity of modal description we consider in
detail the mode composition of solutions presented in [2], making use of the vast amount of
data available in numerical simulations. We compute numerically the spectra of trapped
modes (the spectrum in longitudinal wavenumbers, frequencies, and Ï - k spectrum),
including the fine comb-shaped structure of the spectrum due to the discrete character of
trapped mode frequencies. Thus, we explicitly confirm the existence and observability of
localized modes trapped by jet currents. The analysis reveals that in the simulations of single
modes and envelope solitons the excited modes hold energy for long time even when waves
are steep; there is no evidence of noticeable energy leakage from the energetic mode.
In the situation of modulationally unstable trapped mode train, only at the final
stage of the evolution, when waves start to break, the energy is being transferred to
many trapped modes. Thus only for breaking waves the unimodal regime becomes
invalid.
[1] Shrira, V.I., Slunyaev, A.V. Trapped waves on jet currents: asymptotic modal
approach. J. Fluid Mech. 738, 65-104 (2014).
[2] Shrira, V.I., Slunyaev, A.V. Nonlinear dynamics of trapped waves on jet currents and
rogue waves. Phys. Rev. E. 89, 041002(R) 1–5 (2014). |
|
|
|
|
|
|