Celerity and amplification of supercritical surface waves

The amplification of supercritical waves in steep channels is examined analytically using a one-dimensional dynamic solution of the Saint-Venant equations. Existing methods were modified to describe the amplification of surface waves over a normalized channel length rather than over a single wavelength. The results are strikingly different, and a generalized graph shows that short waves amplify the most over a fixed channel length. The maximum amplification parameter over a normalized channel length is 0.53 when F=3.44. Applications to the flood drainage channel F1 in Las Vegas indicate that the amplitude of waves shorter than 100 m would increase by 65% over a channel length of 543 m. These theoretical results await field verification. Supercritical waves could be dampened by increasing channel roughness to reduce the Froude number below 1.5.