A numerical model for simulation of fluid mud with different rheological behaviors

Abstract

In this paper, a three-dimensional isopycnal approach is presented to simulate the dynamics of fluid mud covering the formation, development, transport, and disappearance of fluid mud. The basic assumption is the assignment of the fluid's density as the indicating parameter for the rheological behavior. Considering stable stratification, as is usually the case for fluid mud, layers of constant density discretize the vertical domain. The non-Newtonian dynamics of fluid mud is simulated by solving the Cauchy equations for general continuum dynamics. Instead of using a turbulent viscosity approach, the viscosity is allowed to vary according to the rheological behavior of mud suspensions. This apparent viscosity can be determined for different rheological formulations in dependence of the volume solid fraction and the shear rate. An existing threedimensional isopycnal hydrodynamic model was extended for vertical mass transport processes and was applied on a schematic system with hindered settling. For including the rheological behavior of fluid mud, the Worrall-Tuliani approach was parameterized and implemented. The resulting flow behavior is shown on a model application of fluid mud layers moving down an inclined plane. With these changes, it is demonstrated that the isopycnal model is capable of simulating fluid mud dynamics.

Response to comments of referee #1

“…FLOCMOD is a population model (Smoluchowski, 1917) based on a finite number of size classes with representative floc diameters D f (m). The model requires a relationship between floc size and floc density ρ f (kg m −3 ) that is related to the primary disaggregated particle diameter D p (m) and density ρ s (kg m −3 ) through a fractal dimension n f (dimensionless; Kranenburg, 1994) according to…”

“…where ρ w (kg m −3 ) is the density of the interstitial water in the flocs. The fractal dimension for natural flocs is typically close to 2.1 (Tambo and Watanabe, 1979;Kranenburg, 1994). Floc densities increase as n f increases, and at n f = 3, the flocs are solid particles with ρ f = ρ s .…”

“…The diameter, settling velocity, density, critical stress for erosion, and critical stress for deposition (described below) are required inputs for each sediment class, both cohesive and non-cohesive (see the Supplement). The present implementation requires a fractal relationship between floc diameter and floc density (Kranenburg, 1994), and we have assumed a Stokes settling velocity. Alternative relationships between diameter and settling velocity, such as a modified Stokes formula (e.g., Winterwerp, 2002;Winterwerp et al, 2002Winterwerp et al, , 2007Droppo et al, 2005;Khelifa and Hill, 2006), could be used by adjusting input parameters, but alternative relationships between diameter and floc density (Khelifa and Hill, 2006;Nguyen and Chua, 2011) would require changes to the aggregation and disaggregation terms in FLOCMOD.…”

A thermodynamically consistent constitutive model for fluid mud

“…So far no thermodynamically consistent model for fluid mud is available in literature [3][4][5]. Therefore, current hydrodynamic models describe the viscosity of fluid mud by rheological formulations of varying complexity [1,2,4,6], not directly accounting for the influence of the biological components. To overcome this restriction a three-dimensional, thermodynamically consistent constitutive formulation is to be found.…”

“…It can be classified as a structured fluid. Typically, its viscosity is modeled using Bingham-type rheological models of different complexity [1,2]. Here, the three-dimensional non-Newtonian constitutive behaviour will be modeled based on a visco-elasto-plastic model.…”