Depth-averaged momentum equation for gravity currents with varying density: coefficient in pressure term

Dubravka Pokrajac, Sara Venuleo, Mario J Franca

Research output: Contribution to journalArticle

7 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)424-430
Number of pages7
JournalJournal of Hydraulic Research
Volume56
Issue number3
Early online date31 Jul 2017
DOIs
Publication statusPublished - 2018

Fingerprint

momentum
Momentum
Gravitation
gravity
Pressure gradient
Water
Numerical models
shallow-water equation
pressure gradient

Keywords

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

Cite this

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

In: Journal of Hydraulic Research, Vol. 56, No. 3, 2018, p. 424-430.

Research output: Contribution to journalArticle

@article{b8d0ef240017426c9089e72346260e0b,
title = "Depth-averaged momentum equation for gravity currents with varying density: coefficient in pressure term",
abstract = "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.",
keywords = "gravity currents, pressure term, shallow water equations, varying density, reduced gravity, celerity",
author = "Dubravka Pokrajac and Sara Venuleo and Franca, {Mario J}",
note = "The second author is funded by the Swiss National Science Foundation (grant 200021 159249).",
year = "2018",
doi = "10.1080/00221686.2017.1335245",
language = "English",
volume = "56",
pages = "424--430",
journal = "Journal of Hydraulic Research",
issn = "0022-1686",
publisher = "Taylor & Francis",
number = "3",

}

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 -