Newton's Shear Flow Applied to Infiltration and Drainage in Permeable Media

Abstract

The paper argues that universal approaches to infiltration and drainage in permeable media that pivot around capillarity and that led to dual porosity, non-equilibrium, or preferential flow need to be replaced by a dual process approach. One process has to account for relatively fast infiltration and drainage based on Newton's shear flow, while the other one is responsible for storage and relatively slow redistribution of soil water by focusing on capillarity. Already Schumacher (1864) postulated two separate processes. However, Buckingham's (1907) and Richards' (1931) apparent universal capillary-based approach to flow and storage of water in soils dominated. The paper introduces the basics of Newton's shear flow in permeable media. It presents experimental support for the four presumptions of (i) sharp wetting shock fronts; (ii) that move with constant velocities; (iii) atmospheric pressure prevails behind the wetting shock front; (iv) laminar flow. It further discusses the scale tolerance of the approach, its relationship to Darcy's (1856) law, and its extension to solute transport.

Potential of a Gravity‐Driven Film Flow Model to Predict Infiltration in a Catchment for Diverse Soil and Land Cover Combinations

“…This would enable for the full applicability of film flow with kinematic wave theory (Germann & Karlen, 2016). If the kinematic wave theory could be applied, it would help to model longer rain events with varying intensities by superimposition of multiple waves from single homogenous rain pulses (Germann, 2014; Germann & Karlen, 2016). Also rivulets routing down waves with different properties (F and L) could then be applied (Germann et al., 2007).…”

“…The film flow model represents a 1D steady‐state viscous film flow with gravity being the only force against the viscous momentum dissipation, without any pressure or capillary forces being considered (Germann, 2014). The gravity‐driven film flow approach was derived from Newton's shear flow hypothesis (Germann & Di Pietro, 1999) and is a special form of the kinematic wave (Jarvis et al., 2017), therefore also displaying kinematic properties (Di Pietro et al., 2003; Germann et al., 2007).…”

“…The following section briefly introduces the main concepts relevant to this study. The full derivation of the theory can be found for example in Germann (2014). The subsequent section follows the derivations of Germann and Karlen (2016) and Germann and Prasuhn (2018).…”

“…Integrating the differential volume flux density of a water film from the solid‐water to the water‐air interface (for details see Germann, 2014 or Germann & Di Pietro, 1999), we obtain the volume flux density of the water film q [L T −1 ]: where η is the kinematic viscosity of water [L 2 T −1 ] and g the acceleration due to gravity [L T −2 ].…”

“…DEMAND AND WEILER 10.1029/2019WR026988 4 of 24 Integrating the differential volume flux density of a water film from the solid-water to the water-air interface (for details see Germann, 2014or Germann & Di Pietro, 1999, we obtain the volume flux density of the water film q [L T −1 ]:…”