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The shape of submarine levees: exponential or power law?

Published online by Cambridge University Press:  25 January 2009

V. K. BIRMAN ,
E. MEIBURG  and
B. KNELLER
V. K. BIRMAN
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
E. MEIBURG*
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
B. KNELLER
Affiliation:
Department of Geology & Petroleum Geology, University of Aberdeen, Aberdeen AB24 3FX, UK
*
†Email address for correspondence: meiburg@engineering.ucsb.edu
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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 as 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 of the shallow water model, thus validating the assumptions underlying the model, and demonstrating its predictive abilities.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 619 , 25 January 2009 , pp. 367 - 376
Copyright
Copyright © Cambridge University Press 2008

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