HYDRODYNAMIC THEORY FOR THE FORMATION OF MISSISSIPPI BIRDSFOOT AND TIE CHANNELS

On the lower Mississippi Delta two fundamentally different channel patterns can be observed: at Wax Lake, channels bifurcate by mouth bar deposition to create a branching distributary network; on the Birdsfoot, elongate channels persist for long distances without bifurcating. Mississippi Delta restoration schemes propose to construct new delta lobes through diversion of water and sediment, however an understanding of what causes elongate vs. bifurcating channels is lacking. Elongate channels can also be seen in tie channels connecting floodplain lakes to rivers, and they appear to grow under conditions of rapid levee deposition and progradation relative to mouth bar growth. Beginning from this observation, we propose a hydrodynamic theory for levee deposition at river mouths that seeks to predict the conditions under which such elongate channels form. Sediment-laden river flows debouch into quiescent water in the form of a turbulent jet that decelerates and expands rapidly, causing sediment deposition. Turbulent jet spreading may be characterized as a Gaussian velocity profile that flattens and widens downstream as a result of shearing and lateral mixing at the jet margins. Recent experiments have demonstrated that this Gaussian shape controls the time-averaged sedimentation pattern at jet margins. In our new approach we model this velocity pattern using the vertical component of the flow vorticity, ζ, which allows the description of the flow field to be reduced to one dimension without losing generality. We show how both shearing and lateral spreading can be directly related to ζ. In order to study resulting sediment deposition from the jet we introduce a new kind of potential vorticity that incorporates sediment concentration. By means of the Ertel potential vorticity theorem, the result is a new dynamic equation that can be solved analytically to model the flow pattern at a river mouth. The potential vorticity model is consistent with available theoretical and field observations, and appears to explain key aspects of levee deposition. Our theory predicts that high potential vorticity is a necessary condition for the creation of elongate channels such as the Mississippi Birdsfoot.