Abstract
Original explicit modulation equations are determined for cnoidal waves of the Korteweg-deVries (KdV)-Burgers equation. This formal asymptotic analysis is used to demonstrate that there is no single partial differential equation for the leading-order mean velocity. The technique of Reynolds averaging is also employed to determine an equation for the mean velocity with the familiar closure problem being encountered. The Reynolds-averaged KdV-Burgers equation is shown to be a counterexample to the existence of a closure associated with a convective nonlinearity.
| Original language | English |
|---|---|
| Pages (from-to) | 163-179 |
| Number of pages | 17 |
| Journal | IMA Journal of Applied Mathematics |
| Volume | 72 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 14 Feb 2007 |
Keywords
- strongly nonlinear analysis
- Reynolds averaging