### Abstract

Field observations indicate that the height Of Submarine levees decays with distance from the channel either exponentially or according to a power law. This investigation clarifies the flow conditions that lead to these respective shapes, via a shallow water model for the overflow Currents that govern the levee formation. The model is based on a steady state balance of sediment supply by the turbidity current, and sediment deposition onto the levee, with the settling velocity and the entrainment rate appearing its parameters. It demonstrates that entrainment of ambient fluid is the determining factor for the levee shape. For negligible entrainment rates, levee shapes tend to exhibit exponential profiles, while constant rates of entrainment or detrainment result in power law shapes. Interestingly, whether a levee has an exponential or a power law shape is determined by kinematic considerations only, viz. the balance laws for sediment mass and fluid volume. We find that the respective coefficients governing the exponential or power law decay depend on the settling speeds of the sediment grains, which in turn is a function of the grain size. Two-dimensional, unsteady Navier-Stokes simulations confirm the emergence of a quasi-steady state, The depositional behaviour of this quasi-steady state is consistent with the predictions or the shallow water model, thus validating the assumptions underlying the model, and demonstrating its predictive abilities.

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

Pages (from-to) | 367-376 |

Number of pages | 10 |

Journal | Journal of Fluid Mechanics |

Volume | 619 |

DOIs | |

Publication status | Published - 25 Jan 2009 |

### Keywords

- driven gravity currents
- deep-sea fan
- turbidity currents
- turbulent entrainment
- deposition
- channel
- flows
- California
- boundaries
- slopes

### Cite this

*Journal of Fluid Mechanics*,

*619*, 367-376. https://doi.org/10.1017/S0022112008004862

**The shape of submarine levees : exponential or power law?** / Birman, V. K.; Meiburg, E.; Kneller, B.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 619, pp. 367-376. https://doi.org/10.1017/S0022112008004862

}

TY - JOUR

T1 - The shape of submarine levees

T2 - exponential or power law?

AU - Birman, V. K.

AU - Meiburg, E.

AU - Kneller, B

PY - 2009/1/25

Y1 - 2009/1/25

N2 - Field observations indicate that the height Of Submarine levees decays with distance from the channel either exponentially or according to a power law. This investigation clarifies the flow conditions that lead to these respective shapes, via a shallow water model for the overflow Currents that govern the levee formation. The model is based on a steady state balance of sediment supply by the turbidity current, and sediment deposition onto the levee, with the settling velocity and the entrainment rate appearing its parameters. It demonstrates that entrainment of ambient fluid is the determining factor for the levee shape. For negligible entrainment rates, levee shapes tend to exhibit exponential profiles, while constant rates of entrainment or detrainment result in power law shapes. Interestingly, whether a levee has an exponential or a power law shape is determined by kinematic considerations only, viz. the balance laws for sediment mass and fluid volume. We find that the respective coefficients governing the exponential or power law decay depend on the settling speeds of the sediment grains, which in turn is a function of the grain size. Two-dimensional, unsteady Navier-Stokes simulations confirm the emergence of a quasi-steady state, The depositional behaviour of this quasi-steady state is consistent with the predictions or the shallow water model, thus validating the assumptions underlying the model, and demonstrating its predictive abilities.

AB - Field observations indicate that the height Of Submarine levees decays with distance from the channel either exponentially or according to a power law. This investigation clarifies the flow conditions that lead to these respective shapes, via a shallow water model for the overflow Currents that govern the levee formation. The model is based on a steady state balance of sediment supply by the turbidity current, and sediment deposition onto the levee, with the settling velocity and the entrainment rate appearing its parameters. It demonstrates that entrainment of ambient fluid is the determining factor for the levee shape. For negligible entrainment rates, levee shapes tend to exhibit exponential profiles, while constant rates of entrainment or detrainment result in power law shapes. Interestingly, whether a levee has an exponential or a power law shape is determined by kinematic considerations only, viz. the balance laws for sediment mass and fluid volume. We find that the respective coefficients governing the exponential or power law decay depend on the settling speeds of the sediment grains, which in turn is a function of the grain size. Two-dimensional, unsteady Navier-Stokes simulations confirm the emergence of a quasi-steady state, The depositional behaviour of this quasi-steady state is consistent with the predictions or the shallow water model, thus validating the assumptions underlying the model, and demonstrating its predictive abilities.

KW - driven gravity currents

KW - deep-sea fan

KW - turbidity currents

KW - turbulent entrainment

KW - deposition

KW - channel

KW - flows

KW - California

KW - boundaries

KW - slopes

U2 - 10.1017/S0022112008004862

DO - 10.1017/S0022112008004862

M3 - Article

VL - 619

SP - 367

EP - 376

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -