Nonlinear Standing Waves in a Tube

Theory of lossless nonlinear standing waves in tubes is extended to the case when dissipation exists due to the boundary layer inside the tube. And the viscous loss is taken care of with a complex wave number. The solutions thus obtained for the nonlinear standing wave satisfy exactly the hydrodynamic equations. The unusual situations encountered in developing the formulae of the field parameters into their frequency components are discussed and solutions proposed.