In Newtonian fluids the relationship between shear rate and shear stress is linear and passes though the origin. Non-Newtonian fluids have a shear rate vs shear stress relationship which can be nonlinear and/or does not pass though the origin. A wide range natural flows present non-Newtonian properties including mudflows, debris flows, lahars, and snow avalanches. The USACE has well established hydraulic hydrologic tools for simulating Newtonian flows but the tools available for non-Newtonian flows are quite limited. Hyperconcentrated flows present physical present properties between clear-water and solid mass movements which complicate their computational modeling. Hyperconcentrations range from approximately 5-60%. Most hydraulic and sediment transport simulations assume that the transporting fluid has "Newtonian" properties.
A Newtonian Fluid has two properties,
a linear stress-strain relationship and
a zero stress-strain intercept.
This assumption appropriate for most fluids, including sediment laden fluids with volumetric concentrations up to 30%. However, as sediment concentrations increase, they begin to affect the fluid properties, which alter the stress-strain relationship. There are many constitutive equations describing the shear-strain relationship in literature which have had some degree of success for different situations. However, due to the complex nature of the fluid-solid mixtures, these equations and their parameters have a large degree of uncertainty.
The mathematical models used to simulate non-Newtonian flows may be classified as single- and two-phase models. Single-phase models describe the properties of the mixture and solve conservation equations for the mixture (e.g. Hergarten and Robl 2015; Hunger and McDougall 2009). Two-phase models consider the fluid and solid phases of the mixture and solve conservation equations for both the mixture and each phase (e.g. Bozhinskiy and Nazarov 200; Iverson and Denlinger 2001). The mathematical approaches developed in HEC-RAS follow a single-phase approach.
This video summarizes some of the principles and equations in this manual: