An Analytical Model for Vertical Profiles in Submarine Channels

Turbidity currents are the primary agents carrying sediments from the continental shelf to the deep-sea. They are the counterpart of fluvial currents in the deep-sea environment and are responsible for the shaping of submarine channels. Due to the unpredictability of events and to their ability to destroy installed monitoring instruments, only a few attempts to directly measure the properties of turbidity currents in submarine channels has proved to be successful (Xu et al., 2004; Xu, 2010). Consequently the vast majority of the studies concerning the vertical structure of turbidity currents were either laboratory experiments or numerical models. In spite of the relevance of the problem, related to the consequences of flow field on sedimentary deposits, at present an ongoing debate still exist on similarities and differences between submarine and fluvial channels related in particular to the orientation of the helical flow in channel bends. Here we expand on the above ideas and develop an analytical theory for flow and suspended sediment transport in submarine channels able to describe vertical profiles of both flow field and suspendend sediment concentration. The turbulence closure needed to account for density stratification is adapted from the model of Mellor and Yamada (1982). Solutions are found for both straight and constant curvature channels. In the latter case, in order to evaluate the secondary flow induced by curvature, we take advantage of the fact that the ratio of flow depth to radius of curvature is typically small in the field, which leads to a solution of the governing equations through an appropriate asymptotic expansion. Steady fully developed flow conditions in a bend of constant width are considered. Results for longitudinal velocity and concentration profiles in straight channels are then compared with experimental observations of Sequeiros et al. (2010) providing good agreement. We also expect to find under which values of the controlling parameters the orientation of secondary flow in submarine channels can be reversed with respect to the case of fluvial channels hopefully clarifying the ongoing debate. References Mellor, G.L. and Yamada, T. (1982). Development of a Turbulence Closure Model for Geophysical Fluid Problems. Rev. Geophys. Space Phys., 20(4), 851-875. Sequeiros O.E., B. Spinewine, R. T. Beaubouef, T. Sun, M. H. García, and G. Parker, (2010). Characteristics of Velocity and Excess Density Profiles of Saline Underflows and Turbidity Currents Flowing over a Mobile Bed, J. Hydr. Engrg. 136, 412. Xu, J. P., M. A. Noble, and L. K. Rosenfeld (2004), In-situ measurements of velocity structure within turbidity currents, Geophys. Res. Lett., 31, L09311. Xu, J. P., (2010)., Normalized velocity profiles of field-measured turbidity currents, Geology, v. 38; no. 6; p. 563-566.