Froude Number is not the Critical Factor in Behavior of Long Run-Out Turbidity Currents

Abstract

Turbidity currents are capable of transporting suspended sand over many hundreds of kilometers along submarine channels. The mean velocity structure and turbulence distribution in turbidity currents is generally considered to be largely the result of two competing factors; the formation of Kelvin-Helmholtz (K-H) instabilities along the upper boundary of the current, and the damping of these instabilities by the stable density stratification. Much of the loss of energy of the current, as well as entrainment of ambient fluid, is a consequence of the K-H instabilities that are thus responsible for ‘turbulent drag’ which leads to the current's dissipation. Several authors have recently suggested that the behavior of turbidity currents is largely determined by their bulk (depth-averaged) densimetric Froude number, Fr', which represents the ratio between inertial and gravitational forces. It is clear that many turbidity currents on the slope are supercritical, and have velocity profiles that clearly indicate the presence of K-H instabilities. However, K-H instabilities are also present in most subcritical currents (ie Fr' < 1), both in nature and the laboratory, which should thus should decay fairly rapidly on low slopes. The critical criterion for the formation of K-H instabilities is the ratio between the effect of gravity on the density stratification and the fluid shear, expressed as a dimensionless number, the gradient Richardson number, Rig. Above a critical value of 0.25, K-H instabilities are strongly damped. We show numerically that turbulent dissipation, the drag on the upper boundary of the current and the entrainment of ambient seawater fall almost to zero in the absence of instabilities, and suggest necessary conditions for stable density stratification. We propose that it is this absence of instabilities on low slopes that allows turbidity currents to flow so far on low gradients in the ocean. Thus it is the gradient Richardson number, not the Froude number, that is the primary determinant of turbidity current behavior; bulk Froude number is an inappropriate descriptor of these density stratified currents. Based on LES simulations, a straightforward scaling argument equating the dissipated energy to the loss of potential energy suggests that slope angles below 0.1 degrees suffice to maintain turbidity currents.

AAPG Datapages/Search and Discovery Article #90216 ©2015 AAPG Annual Convention and Exhibition, Denver, CO., May 31 - June 3, 2015