Undular Bore - in Hydraulics

In Hydraulics

The term "bore" is also used to describe positive surges advancing in shallow waters. When the surge's Froude number is less than 1.4 to 1.7 (i.e. above unity and below a number somewhere in the range 1.4 to 1.7), the advancing front is followed by a train of well-defined free-surface undulations (called "whelps"). The surge is then called an undular surge or undular bore.

The undulations form a standing wave pattern, relative to the undular bore front. So, the phase velocity (propagation velocity relative to still water) of the undulations is just high enough to keep the undulations stationary relative to the bore front. Now, in water waves, the group velocity (which is also the energy-transport velocity) is less than the phase velocity. Therefore, on average, wave energy of the undulations is transported away from the front, and contributing to the energy loss in the region of the front.

A related occurrence of positive surges is the tidal bore in estuaries.