Implications of experiments on the weak undular bore

Abstract

The behavior of the nonlinear dispersive waves observed behind weak undular bores is studied using available experimental information. Calculations on cnoidal wave theory using the measured wavelengths and amplitudes lead to the unexpected result that in bore-fixed coordinates the energy and momentum of the flow under the waves are larger than in the upstream flow. This can only be due to the action in the experiments of the unsteady boundary layer on the channel bottom, for this boundary layer has a negative momentum thickness. Therefore, the dissipation near the front that is known to be a necessary condition for the existence of the steady periodic waves is shown to occur on the bottom of the channel.