Wednesday, March 20, 1985 12:00 p.m.
Professor Mark F. Hamilton
Department of Mechanical Engineering
The University of Texas at Austin
Finite amplitude propagation of higher order modes in a rectangular waveguide is analyzed by decomposing the modes into plane waves. Two types of nonlinear interactions may then be considered. The self interaction of an individual plane wave generates harmonics that propagate in the same direction. Such interactions are unaffected by dispersion because each harmonic propagates at the same speed, although in a different mode. The second type includes noncollinear interactions between plane waves. In this case geometric dispersion prevents efficient transfer of energy between the interacting components.
A single transverse mode excited at a frequency not far from cutoff is composed of two plane waves propagating in very different directions. The noncollinear interactions are then so highly dispersive that as a first approximation they may be ignored. The remaining, nondispersive interactions were modeled using a modified Burgers equation that accounts for tube wall absorption of each mode. Theoretical results for this case agree well with experiment. Second order dispersive interactions characterized by spectral components that oscillate in space were also measured and shown to agree very well with theoretical predictions.