Sketch profile: mild, steep with gate, mild

Terms: NDL = normal depth line ($y_n$); CDL = critical depth line ($y_c$). On a mild slope $y_n > y_c$ (NDL above CDL); on a steep slope $y_n < y_c$ (NDL below CDL). Subcritical flow is controlled from downstream; supercritical flow is controlled from upstream.

Step by step

1. Mild reach (upstream). The flow far upstream is uniform at $y_n$ (subcritical). At the break to the steep slope the flow must pass through critical depth. The profile is a drawdown, M2, falling from the NDL to the CDL at the break.
2. Steep reach, before the gate. Flow leaves the break at $y_c$ and falls towards the steep NDL as an S2 curve (supercritical, accelerating). The sluice gate is an artificial control: it holds the water behind it at a depth above $y_c$. Supercritical flow at $y_n$ cannot meet this deeper water smoothly, so a hydraulic jump forms and the deep water behind the gate is an S1 curve rising to the gate.
3. Steep reach, after the gate. The jet from the gate (vena contracta) is shallower than $y_n$, so the depth increases gradually towards the NDL as an S3 curve.
4. Steep to mild break. The supercritical flow at $y_n$ (steep) enters a mild slope where the uniform depth is the deeper $y_n$ (mild). It rises gradually as M3 and then a hydraulic jump raises it to the mild normal depth, after which flow is uniform. (If the mild tailwater is high enough, the jump moves up to the break and the M3 curve disappears.)

 MILD |          STEEP (gate)           | MILD
 -----+---- NDL1 ....................... NDL3 (high)
  \   |                       gate        _____
   \M2|  S2        J  S1       |G|  S3  J/ M3
 CDL..\._________  /''''''      |_|__   /
 NDL2      yn ..\_/......        yn_/_/