Modeling Sediment Deposition Patterns Arising From Suddenly Released Fixed-Volume Turbulent Suspensions

• Published in: Studies in applied mathematics (Cambridge) 2000-11, Vol.105 (4), p.333-359
• Main Authors: Moodie, T. B., Pascal, J. P., Bowman, John C.
• Format: Article
• Language: English
• Subjects: Classical and quantum physics: mechanics and fields; Classical mechanics of discrete systems: general mathematical aspects; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Mathematical analysis; Mathematics; Partial differential equations; Physics; Sciences and techniques of general use
• ISSN: 0022-2526; 1467-9590
• DOI: 10.1111/1467-9590.00154

Models presented in several recent papers [1–3] dealing with particle transport by, and deposition from, bottom gravity currents produced by the sudden release of dilute, well‐mixed fixed‐volume suspensions have been relatively successful in duplicating the experimentally observed long‐time, distal, areal density of the deposit on a rigid horizontal bottom. These models, however, fail in their ability to capture the experimentally observed proximal pattern of the areal density with its pronounced dip in the region initially occupied by the well‐mixed suspension and its equally pronounced local maximum at roughly the one‐third point of the total reach of the deposit. The central feature of the models employed in [1–3] is that the particles are always assumed to be vertically well‐mixed by fluid turbulence and to settle out through the bottom viscous sublayer with the Stokes settling velocity for a fluid at rest with no re‐entrainment of particles from the floor of the tank. Because this process is assumed from the outset in the models of [1–3], the numerical simulations for a fixed‐volume release will not take into account the actual experimental conditions that prevail at the time of release of a well‐mixed fixed‐volume suspension. That is, owing to the vigorous stirring that produces the well‐mixed suspension, the release volume will initially possess greater turbulent energy than does an unstirred release volume, which may only acquire turbulent energy as a result of its motion after release through various instability mechanisms. The eddy motion in the imposed fluid turbulence reduces the particle settling rates from the values that would be observed in an unstirred release volume possessing zero initial turbulent energy. We here develop a model for particle bearing gravity flows initiated by the sudden release of a fixed‐volume suspension that takes into account the initial turbulent energy of mixing in the release volume by means of a modified settling velocity that, over a time scale characteristic of turbulent energy decay, approaches the full Stokes settling velocity. Thereafter, in the flow regime, we assume that the turbulence persists and, in accord with current understanding concerning the mechanics of dense underflows, that this turbulence is most intense in the wall region at the bottom of the flow and relatively coarse and on the verge of collapse (see [22]) at the top of the flow where the density contrast is compositionally maintained. We