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The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. [1] It is a quasilinear partial differential equation ; its analytical solution is often limited to specific initial and boundary conditions. [ 2 ]
The molecules in a drop of food coloring added to water will eventually disperse throughout the entire medium, where the effects of molecular diffusion are more evident. However, stirring the mixture with a spoon will create turbulent flows in the water that accelerate the process of dispersion through convection-dominated dispersion.
Dispersion is a process that occurs in soils that are particularly vulnerable to erosion by water. In soil layers where clays are saturated with sodium ions ("sodic soils"), soil can break down very easily into fine particles and wash away. This can lead to a variety of soil and water quality problems, including:
The sodium adsorption ratio (SAR) is an irrigation water quality parameter used in the management of sodium-affected soils.It is an indicator of the suitability of water for use in agricultural irrigation, as determined from the concentrations of the main alkaline and earth alkaline cations present in the water.
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
Water retention curve is the relationship between the water content, θ, and the soil water potential, ψ. The soil moisture curve is characteristic for different types of soil, and is also called the soil moisture characteristic. It is used to predict the soil water storage, water supply to the plants (field capacity) and soil aggregate stability.
In unconfined aquifers, the solution to the 3D form of the equation is complicated by the presence of a free surface water table boundary condition: in addition to solving for the spatial distribution of heads, the location of this surface is also an unknown. This is a non-linear problem, even though the governing equation is linear.
The drainage formula can be amplified [10] to account for (see figure on the right): the additional energy associated with the incoming percolation water , see groundwater energy balance; multiple soil layers; anisotropic hydraulic conductivity, the vertical conductivity (Kv) being different from the horizontal (Kh)