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.
|Number of pages||17|
|Journal||IMA Journal of Applied Mathematics|
|Publication status||Published - 14 Feb 2007|
- strongly nonlinear analysis
- Reynolds averaging