Laminar bottom gravity currents: friction factor–Reynolds number relationship

Abstract

This study elucidates a relationship between the Fanning friction factor and the Reynolds number for the laminar propagation of constant-flux gravity currents. The particular motivation for this study was related to the pipeline disposal of dredged fluid-mud where non-Newtonian bottom gravity currents form. The power-law rheology model, which has been shown to model fluid-mud rheology well, was incorporated in the theoretical analysis. The proposed Fanning friction factor-Reynolds number relationship includes a proportionality constant (henceforth, the shape factor) that considers the shape of the current. For non-Newtonian fluid-mud gravity currents, a relationship for the shape factor was developed through laboratory experiments. Different potential applications of the developed friction factor-Reynolds number relationship are discussed. In this regard, a new viscous propagation model was developed and evaluated through comparisons with laboratory experimental data for fluid-mud gravity currents. The approach presented in this manuscript can be extended for currents of different fluids propagating over smooth and rough bottoms.

Anatomy and propagation dynamics of continuous-flux release bottom gravity currents through emergent aquatic vegetation

“…5, exhibited a similar trend as the viscous propagation trend, the data were more closely correlated to the wall jet propagation. 7,45 The phase transition times and distances are tabulated in Table III. Table II indicates that the total viscous force (including both the bottom shear and vegetation drag forces) dominated over the inertia force at the instant when the current transitioned into the drag-dominated phase for all of our experimental runs.…”

“…In these calculations, the Fanning friction factor was estimated using the formulation of Ref. 45  . The summation of these friction and pressure drag coefficients gives the total drag coefficient for an isolated cylinder in an infinite fluid medium.…”

“…The fluid mud mixtures used in this study have non-Newtonian rheological characteristics. The Ostwald power-law model, which relates the shear stress τ and the shearing strain rate ∂u/∂z as τ = m(∂u/∂z) n [here, n is the flow behavior index and m is the consistency index] provides an accurate, yet simple formulation for the rheology of the non-Newtonian fluid mud suspensions with concentrations up to approximately 300 g / l. 44,45 In our experiments, the initial fluid mud concentration values were between 100 and 250 g/l; hence, we used the power-law rheology model for fluid mud. The empirical relationships for the flow behavior index (n) and the consistency index (m) in terms of the volumetric concen-…”

A dipole solution for power-law gravity currents in porous formations

“…It approximately describes the behaviour of timeindependent non-Newtonian fluids over an intermediate range of shear rates and in the absence of yield stress and has been successfully adopted to describe the flow of polymer solutions, foams and crude oils in porous media. Environmental contaminants such as slurries or dredged fluid mud (Yilmaz, Testik & Chowdury 2014) and carriers for remediation agents (Tosco et al 2014) are usually represented either via the power-law model, or using more complex constitutive equations including a yield stress; even in the latter case however, the adoption of a pure power-law model (approximating the Herschel-Bulkley constitutive equation for vanishing values of the yield stress) permits mathematical predictions that are upper bounds for the exact solution, or may work as benchmarks for numerical codes.…”