Comments on “Flux‐Averaged and Volume‐Averaged Concentrations in Continuum Approaches to Solute Transport” by J. C. Parker and M. Th. van Genuchten

Abstract

In a recent paper, Parker and van Genuchten [1984] follow Brigham [1974] and Kreft and Zuber [1978] by introducing two concepts of concentration to dispersive flow. It seems that some comments on that paper may clarify certain points.In a flowing fluid the concentration of a solute may be defined in two ways, depending on the definitions of the representative elementary volume of the fluid. where C(x, s) is the Laplace transform of C(x, t) and ['/n is the nth normalized moment about the origin. Similarly, the change of moments A/• n between two observation points Xl and x2 can be found by using the following formula'

Study of hydraulic parameters in heterogeneous gravel beds: Constructed wetland in Nowa Słupia (Poland)

“…Significant mathematical differences between models arise from different formulations of boundary and initial conditions. These issues were thoroughly discussed for practical applications by Kreft and Zuber (1978, 1979, 1986 and Parker and van Genuchten (1984). This paper provides a quantitative description of flow characteristics in the constructed wetland in Nowa Słupia, Poland.…”

Solute and sediment transport at laboratory and field scale: Contributions of J.-Y. Parlange

“…As noted by Parlange et al [1992], a zero-or first-order sink term added to the right side of equation (1) leaves it unchanged under equation (2) [Kreft and Zuber, 1986].…”

A simple predictive approach to solute transport in layered soils

“…where C, [M L-3] is a solute flux concentration (Kreft & Zuber, 1986) and C, is the concentration of the applied solution; i [L3 T-'1 is an irrigation/drainage rate, constant at the rate i,; z is a depth below the surface in a layer of soil of length L (= 16 cm); and t is the experimental time scale. The above conditions permit a TFM to be written in the form: where C,(z,t) is the concentration leaving an output surface at depth z and time t, and g,(t) is the probability density function (pdf) [T-I] describing the distribution of travel times to depth z.…”

“…Dyson & White (1987), Equation (20). C, [M L-'1 is a resident solute concentration, which is conceptually different from a solute flux concentration (Kreft & Zuber, 1986); zI and z2 are depths below the soil surface, for z2>z,; the numerator on the RHS of Equation (6) is the solute influx minus the efflux of the depth interval, and the denominator is the volume of water in the interval, where a is the column radius. The mass of nitrate retained in a depth interval is thus calculated from the estimate of C, (zl, z2; t ) multiplied by the volume of water in the interval.…”