Stability isn't everything in fluid dynamics or is it?

Lets consider a prismatic channel with the following data:
Length of the channel = 100 km
Width of the rectangular cross-section = 100 m
Bed slope = 1%
Manning’s roughness n = 0.035

The downstream boundary condition is a rating curve shown below:
Depth Discharge
(m) (m3/s)
0.0 0.0
0.5 142.8
1.0 450.5
1.5 900.0
2.0 1426.6
2.5 2100.0
>3.0 2797.0

The discharge hydrograph at the upstream boundary point is shown in the following figure

One way to estimate the appropriate time step for the simulation is to look at the Courant-
Friedrich-Levy (CFL) criterion. This criterion is usually applied to explicit numerical schemes but the CFL criterion may nevertheless serve as a guideline for implicit algorithms.
dt < (dx / v)

A realistic peak velocity could be guessed as twice or three times the steady velocity (v=4.64 m/s).

Chosen numerical parameters:

dx= 5 km

dt= 10 min

In HEC-RAS 4.0, an intermediate theta (a.k.a. numerical damping parameter) was chosen in order to ensure a compromise between accuracy and stability: theta=0.5 is the Crank-Nicholson method and theta=1.0 fully implicit scheme. Also, the model needs some warm-up time at the beginning of the simulation to adjust to initial and boundary conditions.

So, here we have the expected results at X= 50 km (the midpoint):

Neither the computed depth nor the velocity seem realistic and the HEC-RAS implicit algorithm is unable to calculate the magnitude and exact period of the steep water waves. Any solution?