Abstract
Two-dimensional gravity-capillary waves can be modeled by the forced Korteweg-de Vries (fKdV) equation in subcritical flows when the Bond number is greater than one third. Four steady symmetric depression wave solutions and two elevation wave solutions for the fKdV equation have been found and time evolutions of their magnitude or spatial perturbations have been observed. We approach the fKdV equation as a stochastic equation by modeling the perturbation as a random variable and examine the stabilities of the steady solutions based on the polynomial chaos expansion framework. Polynomial chaos also provides surfaces, which encompass random fluctuations of unstable waves. The effects of several parameters on the stabilities and the surfaces have been also considered.
| Original language | English |
|---|---|
| Pages (from-to) | 71-86 |
| Number of pages | 16 |
| Journal | European Journal of Mechanics, B/Fluids |
| Volume | 39 |
| DOIs | |
| Publication status | Published - 2013 May |
Bibliographical note
Funding Information:The authors are grateful to the anonymous referees for their valuable comments and suggestions. This research of Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 20120003004 ).
Keywords
- Forced KdV
- Polynomial chaos
- Solitary waves
- Stability
ASJC Scopus subject areas
- Mathematical Physics
- General Physics and Astronomy