Modulation theory solution for resonant flow over topography
Abstract
The nearresonant flow of a stratified fluid over topography is considered in the weakly nonlinear, longwave limit, this flow being governed by a forced Kortewegde Vries equation. It is proved from the modulation equations for the Kortewegde Vries equation, which apply away from the obstacle, that no steady state can form upstream of the obstacle. This has been noted from previous experimental and numerical studies. The solution upstream and downstream of the topography is constructed as a simple wave solution of the modulation equations. Based on similarities between the method by which this solution is found and the quarter plane problem for the Kortewegde Vries equation, the solution to the quarter plane problem is found for the special case in which a positive constant is specified at x = 0.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 January 1987
 DOI:
 10.1098/rspa.1987.0007
 Bibcode:
 1987RSPSA.409...79S
 Keywords:

 Flow Theory;
 KortewegDevries Equation;
 Stratified Flow;
 Topography;
 Cnoidal Waves;
 Flow Velocity;
 Modulation;
 Resonant Frequencies;
 Fluid Mechanics and Heat Transfer