Shallow Wave Propagation in Open Channel Flow

The propagation characteristics of various types of shallow water waves in open channel flow are calculated on the basis of linear stability theory. The celerity and attenuation functions of kinematic, diffusion, convective dynamic, dynamic and gravity waves, are derived. For the most general case, i.e., the dynamic wave model, the propagation characteristics are expressed as a function of the steady uniform flow Froude number and the dimensionless wave number of the unsteady component of the motion. For the dynamic model, the wave number spectrum is divided into three bands: 1)A gravity band corresponding to large wave number, where the wave celerity is the gravity wave celerity; 2)a kinematic band corresponding to a small wave number where the wave celerity is the kinematic wave celerity; and 3)a dynamic band corresponding to mid-spectrum values of the wave number, where the wave celerity falls between the gravity and kinematic celerity values.