Environmental Fluid Mechanics

, Volume 17, Issue 1, pp 159–186 | Cite as

Froude scaling limitations in modeling of turbidity currents

  • Jasim Imran
  • Sadia M. Khan
  • Carlos Pirmez
  • Gary Parker
Original Article


The scaling problem associated with the modeling of turbidity currents has been recognized but is yet to be explored systematically. This paper presents an analysis of the dimensionless governing equations of turbidity currents to investigate the scale effect. Three types of flow conditions are considered: (i) conservative density current; (ii) purely depositional turbidity current; and (iii) mixed erosional/depositional turbidity current. Two controlling dimensionless numbers, the Froude number and the Reynolds number, appear in the non-dimensional governing equations. When densimetric Froude similarity is satisfied, the analysis shows that the results would be scale-invariant for conservative density current under the rough turbulent condition. In the case of purely depositional flows, truly scale-invariant results cannot be obtained, as the Reynolds-mediated scale effects appear in the bottom boundary conditions of the flow velocity and sediment fall velocity. However, the scale effect would be relatively modest. The Reynolds effect becomes more significant for erosional or mixed erosional/depositional turbidity currents as Reynolds-mediated scale effects also appear in the sediment entrainment relation. Numerical simulations have been conducted at three different scales by considering densimetric Froude scaling alone as well as combined densimetric Froude and Reynolds similarity. Simulation results confirm that although the scaling of densimetric Froude number alone can produce scale-invariable results for conservative density currents, variations occur in the case of turbidity currents. The results become scale invariant when densimetric Froude and Reynolds similarities are satisfied simultaneously.


Scale effect Reynolds number Froude number Densimetric Froude number Particle Reynolds number Numerical modeling Turbidity currents Turbulence modeling 



Funding support from NSF Marine Geology and Geophysics Program (OCE 1061244) and Shell is gratefully acknowledged. The opinion and conclusions or recommendations expressed in this paper are those of the authors and do not reflect the views of the funding agencies. The paper benefited from the helpful suggestions of guest editor Professor Bombardelli and the anonymous reviewers.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of South CarolinaColumbiaUSA
  2. 2.City of CharlotteCharlotteUSA
  3. 3.Shell International Exploration and Production Inc.RomeItaly
  4. 4.Department of Civil & Environmental Engineering, Department of GeologyUniversity of Illinois Urbana-ChampaignUrbanaUSA

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