Redesigning Compound Weirs as Polynomial Weirs (Baddour 2019)
Compound weirs shown below have straight edges and sharp corners. These features produce instabilities in the head-discharge equation. This problem was documented in a report by USBR (1963).
Another compound weir from OpenChannelFlow
The following statement in USBR (1963) describes the instability observed at the level of the abrupt change of width of a compound weir.
A solution to the compound weir instability problem is simply to redesign the compound weir as a polynomial weir by creating smooth variations of width with height.