An Inverse Method to Estimate the Source-Sink Term in the Nitrate Transport Equation

2007 ◽  
Vol 71 (1) ◽  
pp. 26-34 ◽  
Author(s):  
Jianchu Shi ◽  
Qiang Zuo ◽  
Renduo Zhang
Keyword(s):  
Transport Equation ◽  
Inverse Method ◽  
Nitrate Transport ◽  
Sink Term ◽  
Source Sink

Nitrate leaching from a drained, sheep-grazed pasture. II. Modelling nitrate leaching losses

Soil Research ◽  
1998 ◽  
Vol 36 (6) ◽  
pp. 963 ◽  
Author(s):  
R. E. White ◽  
L. K. Heng ◽  
G. N. Magesan
Keyword(s):  
Nitrate Leaching ◽  
Preferential Flow ◽  
Pulse Input ◽  
Grazed Pasture ◽  
Sink Term ◽  
Chloride Leaching ◽  
Loam Soil ◽  
Rain Events ◽  
Transport Volume ◽  
Source Sink

Nitrate (NO-3 ) concentrations in 0·5-mm increments of drainage from adjacent mole- and pipe-drained paddocks of a silt loam soil under pasture near Palmerston North, New Zealand, were measured during 2 winters. The data were simulated using a simple analytical transfer function model (TFM). Urea fertiliser applied at the rate of 120 kg N/ha to one paddock was treated as a pulse input to the pool of resident soil NO-3. A source{sink term was included for plant uptake and net mineralisation (including any effect of denitrification). During the first winter (1990), a TFM using either a 1-parameter Burns probability density function (pdf) for solute travel, or a 2-parameter lognormal pdf, satisfactorily simulated the NO-3 concentration trends and predicted the total amounts of N leached. The pdf parameters were derived from previous chloride leaching data for this site. The best-fit value for the transport volume θst, the key parameter in the Burns pdf, was set at 0·37 m3 /m3 in 1990, as used in previous modelling of sulfate leaching. However, a value of 0 ·25 m3 /m3 in the Burns pdf gave better simulations of the 1991 data. This was probably due to more intense rain events during the early part of the drainage season in 1991 compared with 1990, which resulted in more preferential flow through the soil and a lower value for θst. The simulations for both years showed that ≥50% of the total leachable NO-3 was retained in the soil, despite normal winter drainage of about 300 mm. Ideally, the appropriate value of st should be determined by independent measurement. It may need to be adjusted according to the likely incidence of preferential flow early in the winter when NO-3 concentrations are highest. Provided the average initial soil NO-3 concentration can be estimated and a net source{sink term defined, the amount of NO-3 leached in drained soils can be satisfactorily modelled using the TFM approach with a 1-parameter pdf. Duplex soils which have a fluctuating watertable in the A horizon over an impermeable B horizon may prove to be an analogous system.

The interaction effect between two neutron absorbers using Wallace's method

2000 ◽  
Vol 78 (12) ◽  
pp. 1035-1054 ◽  
Author(s):  
M MR Williams
Keyword(s):  
Integral Equation ◽  
Transport Equation ◽  
Absorption Rate ◽  
Exact Result ◽  
Integral Form ◽  
High Accuracy ◽  
Approximation Procedure ◽  
Plate Separation ◽  
Source Sink ◽  
Constant Source

The dependence of Galanin's constant on fuel-plate separation is studied. Galanin's constant arises in the source–sink method of lattice calculations and normally its value for an isolated fuel plate is used. Our calculations therefore enable the accuracy of that assumption to be assessed. To illustrate the problem, two absorbing and scattering plates, embedded in an infinite moderator and separated by a distance b are considered, with a source in the moderator region. The calculations are carried out via the integral form of the transport equation using the little-known method of Wallace. This approach enables the integral equation to be cast into a particularly useful form for evaluation of the flux and absorption rate in the plates. A variational method and a numerical solution provide results that show that there are significant deviations from the isolated plate approximation. Tables and figures are provided to illustrate these conclusions. In addition to the main result, we take the opportunity to show how Wallace's method can be used to simplify the transport equation for an infinitely reflected slab reactor. We also obtain results for the flux in a half-space in which there is a constant source, using a novel approximation procedure. Comparison with the exact result shows high accuracy.

Model of Salt Flow in Soil with a Source-sink Term

1977 ◽  
Vol 41 (1) ◽  
pp. 29-33 ◽  
Author(s):  
D. Melamed ◽  
R. J. Hanks ◽  
L. S. Willardson
Keyword(s):  
Sink Term ◽  
Source Sink ◽  
Salt Flow

Leaching of copper from contaminated soil following the application of EDTA. I. Repacked soil experiments and a model

Soil Research ◽  
2003 ◽  
Vol 41 (2) ◽  
pp. 323 ◽  
Author(s):  
T. Thayalakumaran ◽  
I. Vogeler ◽  
D. R. Scotter ◽  
H. J. Percival ◽  
B. H. Robinson ◽  
...  
Keyword(s):  
Contaminated Soil ◽  
Coming Out ◽  
Sandy Loam ◽  
Soil Columns ◽  
Volcanic Origin ◽  
Sink Term ◽  
Loam Soil ◽  
Copper Contaminated ◽  
Source Sink ◽  
Similar Soil

The EDTA-enhanced remediation of copper contaminated sandy-loam soil of volcanic origin was investigated. The soil, from an orchard, was contaminated with about 250 mg/kg of copper due to the extensive use of copper sprays. Copper-contaminated soil was packed into 100-mm-long columns, and solutions of Na2H2EDTA with CaCl2, raised to a pH of 6.2, were applied at a flow rate of 24 mm/h. Application of an excess of 0.01 M EDTA leached about half the acid-extractable copper from the soil; most of it coming out in the first 3 liquid-filled pore volumes (PV). Also a 0.5 PV pulse of 0.001 M EDTA was applied to similar soil columns and then either leached immediately with 0.005 M CaCl2, or left for periods of up to 1 month before leaching. With immediate leaching, 70% of the EDTA applied was complexed with copper in the leachate, but after a month's delay only 24% was complexed with copper in the leachate, the rest being complexed with iron. There was no evidence of EDTA retardation or adsorption. The experimental results were simulated using the convection–dispersion equation, incorporating a source/sink term. This described the competing time-dependent reactions of copper and iron with EDTA, and the reversion of CuEDTA2– to adsorbed Cu2+ and Fe(III)EDTA– in solution. Reasonable simulations were achieved, mostly within errors of observation.

scholarly journals On the Lamb vector divergence in Navier–Stokes flows

2008 ◽  
Vol 610 ◽  
pp. 261-284 ◽  
Author(s):  
CURTIS W. HAMMAN ◽  
JOSEPH C. KLEWICKI ◽  
ROBERT M. KIRBY
Keyword(s):  
Transport Equation ◽  
Rate Of Change ◽  
Coherent Motion ◽  
Navier Stokes ◽  
Time Rate ◽  
Wall Flows ◽  
Ejections And Sweeps ◽  
Turbulent Wall ◽  
Source Sink ◽  
Development And Evolution

The mathematical and physical properties of the Lamb vector divergence are explored. Toward this aim, the instantaneous and mean dynamics of the Lamb vector divergence are examined in several analytic and turbulent flow examples relative to its capacity to identify and characterize spatially localized motions having a distinct capacity to effect a time rate of change of momentum. In this context, the transport equation for the Lamb vector divergence is developed and shown to accurately describe the dynamical mechanisms by which adjacent high- and low-momentum fluid parcels interact to effect a time rate of change of momentum and generate forces such as drag. From this, a transport-equation-based framework is developed that captures the self-sustaining spatiotemporal interactions between coherent motions, e.g. ejections and sweeps in turbulent wall flows, as predicted by the binary source–sink distribution of the Lamb vector divergence. New insight into coherent motion development and evolution is found through the analysis of the Lamb vector divergence.

scholarly journals Reconstructing the Nd oceanic cycle using a coupled dynamical – biogeochemical model

2009 ◽  
Vol 6 (3) ◽  
pp. 5549-5588 ◽  
Author(s):  
T. Arsouze ◽  
J.-C. Dutay ◽  
F. Lacan ◽  
C. Jeandel
Keyword(s):  
Isotopic Composition ◽  
River Discharge ◽  
Thermohaline Circulation ◽  
Exchange Process ◽  
Global Scale ◽  
Biogeochemical Model ◽  
Sink Term ◽  
Crucial Information ◽  
Atmospheric Inputs ◽  
Source Sink

Abstract. The decoupling of behaviour observed between Nd isotopic composition (Nd IC, also referred as εNd) and Nd concentration has led to the notion of a "Nd paradox". While εNd behaves in a quasi-conservative way in the open ocean, leading to its broad use as a water-mass tracer, Nd concentration displays vertical profiles that increase with depth together with a deep water enrichment along the global thermohaline circulation, non-conservative behaviour typical of nutrients affected by scavenging in surface waters and remineralisation at depth. In addition, recent studies suggested that the only way to reconcile both concentration and Nd IC oceanic budgets, is to invoke a "Boundary Exchange" process (BE, defined as the co-occurrence of transfer of elements from the margin to the sea with removal of elements from the sea by Boundary Scavenging) as a source-sink term. However, these studies did not simulates the real input/output fluxes of Nd to the ocean, and therefore did prevent from crucial information to apprehend the "Nd paradox". In this study, we investigate this paradox on a global scale using for the first time a fully prognostic coupled dynamical/biogeochemical model and an explicit representation of the sources and sinks to simulate the Nd oceanic cycle. Sources considered are dissolved river fluxes, atmospheric dusts and margin sediment re-dissolution. Sinks are scavenging by settling particles. This model satisfyingly simulate the global Nd oceanic cycle, and produces realistic distribution of Nd concentration and isotopic composition, though a slight overestimation of Nd concentrations in the deep Pacific Ocean, likely revealing an underestimation of the particle fields by the biogeochemical model. Our results underlines that 1) vertical cycling (scavenging/remineralisation) is absolutely necessary to satisfyingly simulate both concentration and εNd, and 2) BE is the dominant Nd source to the ocean. The estimated BE flux (1.1×1010 g(Nd)/yr) is much higher than both dissolved river discharge (2.6×108 g(Nd)/yr) and atmospheric inputs (1.0×108 g(Nd)/yr) that play negligible role in the water column but are necessary to reconcile Nd IC in surface and subsurface. This leads to a recalculated residence time of Nd in the ocean of 360 yrs. The BE flux requires the dissolution of only 3 to 5% of the annually flux of material weathered on the continent and deposited via the solid river discharge on the continental margin.

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