## Abstract

Rigorously derived shallow water equations (SWEs) are applied to results of large eddy simulation (LES) of a continuously fed gravity current in order to assess (1) sensitivity of current depth results to its definition; (2) coefficients in depth-averaged continuity and momentum equation due to the nonuniformity of density and velocity profiles; and (3) sensitivity of entrainment coefficient to definition of current depth. It is shown that using different definitions of the current depth may produce significantly different numerical results. The coefficients due to nonuniformity in the continuity equation are very close to unity, whereas the coefficients in the momentum flux and the pressure term in the momentum equation are different from unity by a margin that is very sensitive to the definition of current depth. The entrainment coefficient is more sensitive to the selected parameterization than to the definition of the current depth.

Original language | English |
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Article number | 1868 |

Number of pages | 11 |

Journal | Journal of Hydraulic Engineering |

Volume | 147 |

Issue number | 5 |

Early online date | 12 Mar 2021 |

DOIs | |

Publication status | Published - 1 May 2021 |

### Bibliographical note

AcknowledgmentsThe first author acknowledges support from the Swiss National Science Foundation (SNSF Grant No. 200021_159249). The second author acknowledges support from the Binks Trust Foundation. The authors would like to acknowledge the associate editor and the two anonymous reviewers for the constructive comments, which allowed significant improvement of the earlier version of this article

## Keywords

- Current depth definition
- Gravity currents
- Shallow water equations (SWEs)
- Shape factors