Journal of Fluid Mechanics

Self-accelerating turbidity currents

Gary  Parker a1, Yusuke  Fukushima a2 and Henry M.  Pantin a3
a1 St Anthony Falls, Hydraulic Laboratory, University of Minnesota, Minneapolis, Minnesota 55414, USA
a2 Faculty of Engineering, Technological University of Nagaoka, Niigata, Japan
a3 British Geological Survey, Keyworth, Nottingham NG12 5GG UK

Article author query
parker g   [Google Scholar] 
fukushima y   [Google Scholar] 
pantin hm   [Google Scholar] 


Approximate layer-averaged equations describing the mechanics of turbid underflows are derived. Closure of the equations describing the balance of fluid mass, sediment mass, and mean flow momentum provides for the delineation of a three-equation model. A description of sediment exchange with the bed allows for the possibility of a self-accelerating turbidity current in which sediment entrainment from the bed is linked to flow velocity. A consideration of the balance of the mean energy of the turbulence yields a constraint on physically realistic solutions to the three-equation model. It is shown that the self-acceleration predicted by the three-equation model is so strong that the energy constraint fails to be satisfied. In particular, the turbulent energy consumed in entraining new bed sediment exceeds the supply of energy to the turbulence, so that the turbulence, and thus the turbidity current, must die. The problem is rectified by the formulation of a four-equation model, in which an explicit accounting is made of the mean energy of the turbulence. Sediment entrainment from the bed is linked to the level of turbulence in the four-equation model. Self-acceleration is again predicted, although it is somewhat subdued compared with that predicted by the three-equation model. The predictions of both models are summarized over a wide range of conditions.

(Published Online April 21 2006)
(Received May 25 1984)
(Revised March 24 1986)