### Abstract

Original language | English |
---|---|

Pages (from-to) | 424-430 |

Number of pages | 7 |

Journal | Journal of Hydraulic Research |

Volume | 56 |

Issue number | 3 |

Early online date | 31 Jul 2017 |

DOIs | |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

- gravity currents
- pressure term
- shallow water equations
- varying density
- reduced gravity
- celerity

### Cite this

*Journal of Hydraulic Research*,

*56*(3), 424-430. https://doi.org/10.1080/00221686.2017.1335245

**Depth-averaged momentum equation for gravity currents with varying density : coefficient in pressure term.** / Pokrajac, Dubravka; Venuleo, Sara; Franca, Mario J.

Research output: Contribution to journal › Article

*Journal of Hydraulic Research*, vol. 56, no. 3, pp. 424-430. https://doi.org/10.1080/00221686.2017.1335245

}

TY - JOUR

T1 - Depth-averaged momentum equation for gravity currents with varying density

T2 - coefficient in pressure term

AU - Pokrajac, Dubravka

AU - Venuleo, Sara

AU - Franca, Mario J

N1 - The second author is funded by the Swiss National Science Foundation (grant 200021 159249).

PY - 2018

Y1 - 2018

N2 - Gravity currents are often modeled by means of shallow water equations (SWEs). In these models, simplifications such as the consideration of a constant layer-averaged density are common. This note presents the complete and general derivation of 2D depth-averaged momentum equation for gravity currents with density and velocity varying in the bed-normal direction. Special attention is given to the pressure term which is evaluated for constant, linear and exponential density profile. The shape of the density profile has implications for the momentum balance: the assumption of constant density leads to an overestimation of the driving force due to pressure gradient by a factor of 33% for linear density profile and up to 50% for an exponential profile. It also leads to an overestimation of celerity in numerical models based on traditional SWEs by factor of 22% and around 40% for linear end exponential density profiles respectively.

AB - Gravity currents are often modeled by means of shallow water equations (SWEs). In these models, simplifications such as the consideration of a constant layer-averaged density are common. This note presents the complete and general derivation of 2D depth-averaged momentum equation for gravity currents with density and velocity varying in the bed-normal direction. Special attention is given to the pressure term which is evaluated for constant, linear and exponential density profile. The shape of the density profile has implications for the momentum balance: the assumption of constant density leads to an overestimation of the driving force due to pressure gradient by a factor of 33% for linear density profile and up to 50% for an exponential profile. It also leads to an overestimation of celerity in numerical models based on traditional SWEs by factor of 22% and around 40% for linear end exponential density profiles respectively.

KW - gravity currents

KW - pressure term

KW - shallow water equations

KW - varying density

KW - reduced gravity

KW - celerity

U2 - 10.1080/00221686.2017.1335245

DO - 10.1080/00221686.2017.1335245

M3 - Article

VL - 56

SP - 424

EP - 430

JO - Journal of Hydraulic Research

JF - Journal of Hydraulic Research

SN - 0022-1686

IS - 3

ER -