Bed roughness induced entrainment in a high Richardson number underflow

Field data, collected in a shallow underflow into a medium-sized reservoir, show that the dimensionless entrainment, E, is non-negligible at high Richardson numbers. For such underflow, the field data demonstrate that E is mainly dependent on the stress generated at the bottom, directly determined by the relative bed roughness and the properties of the current. The flow is shown to quickly reach a condition of normal flow where Ri is constant; the value of Ri being a strong function of the bottom slope. An entrainment law is presented, in terms of both Richardson number and bottom drag coefficient, written as E = E(Ri, C-D), that shows good agreement with the values of E measured in the field.