Instructions: No online consultation; no notes. Answer only 10 questions. Submit your pdf file with answers, to the course email by FRIDAY 211210 1730.

1. Explain why the unsteady flow feature of HEC-RAS is not likely to be useful for the calculation of flood stages for channel design.

2. What flow variable is a constant in an inherently stable channel? Why is the inherently stable channel impractical as a solution for the control of roll waves?

3. According to Craya, what is a necessary condition for the development of roll waves in open-channel flow? Explain the physical meaning.

4. Explain why the Vedernikov criterion is necessary but not sufficient to produce roll waves in steep channels. What scale of waves (large, medium, or large dimensionless wavenumber σ_*) is more likely to be subject to amplification?

5. What is the definition of the Vedernikov number in terms of the exponent of the rating β and the Froude number? What is the value of β corresponding to a neutral-stability Froude number equal to 25?

6. What two kinds of errors arise in numerical modeling? Which one is related to stability, and which one to convergence. Explain.

7. Why is numerical modeling always a compromise between stability and convergence? Explain.

8. What is the effect of the weighting factor θ in implicit numerical modeling of unsteady open-channel flow using the Preissmann scheme? How does θ work in controlling the stability of the model? What value of θ is recommended for use in practice?

9. Why is the backward-in-time/backward-in-space discretization of the kinematic wave equation (the Li model) not suited for practical computations? Why and how does the Muskingum-Cunge solution achieve grid independence?

10. Under what (hydrologic and hydraulic) conditions is runoff diffusion (spreading of the flow in time) produced in watershed flow?

11. In what direction (upstream or downstream) does a negative bed wave (created by sand mining in an alluvial river) travel? What type of analysis will show downstream propagation? What can happen if the downstream propagation is allowed to progress without control?

12. What physical process(es) (or governing equation term or terms) produce(s) circulation in two-dimensional depth-averaged flow models? Why is circulation dependent on problem scale? How can circulation be effectively modeled while neglecting the effective stresses due to their intractability?