Simple Internal Waves and Bores

Abstract

A simple surface wave develops, for example, after a dam break in a reservoir, or when water is suddenly withdrawn from one end of a long open channel. The present contribution is on simple internal waves, which can develop at the thermocline of a stratified reservoir when a sudden change of the inflow rate occurs due to man‐made or natural causes. Use is made of the fact that the interface along a simple wave advances with the local long‐wave speed, and of flow continuity. General analytical solutions for the velocity difference between the upper and lower layers along simple waves, and for their shape, are derived for Boussinesq flows. Also, the conditions are outlined under which a simple wave becomes unstable, and an internal bore develops. An example is provided for the shape and extent of a simple wave, which is due to a sudden dense inflow into a stratified reservoir. Such a wave is stable.