Energy conservation properties of Ritter solution for idealized dam break flow

ABSTRACT

We examine different aspects of energy conservation in the case of the analytical solution of Ritter for idealized dam break flow in a horizontal frictionless and dry channel. We detail the application of the unsteady Bernoulli equation in this case and highlight that the inertial effects cancel out when averaged over the whole flow region. We also show that the potential and kinetic contributions to the total mechanical energy in the flow region have a distinct and constant relative importance: potential energy accounts for 60%, and kinetic energy for 40% of the total mechanical energy. These properties of Ritter solution are rarely emphasized while they may be of practical relevance, particularly for the verification of numerical schemes with respect to their ability to ensure energy conservation.

Keywords:

• Dam break flow
• energy conservation
• mechanical energy
• specific energy
• unsteady Bernoulli equation

Acknowledgements

The Authors gratefully acknowledge three anonymous reviewers and the Associate Editor for their valuable comments.

ORCID

Benjamin Dewals http://orcid.org/0000-0003-0960-1892

Martin Bruwier http://orcid.org/0000-0001-6596-1273

Additional information

Funding

This research was partly funded through the ARC grant for Concerted Research Actions, financed by the Wallonia-Brussels Federation.