Multi-Phase, Multi-Scale Mathematical Models of Splash Erosion
Global climate change, and the consequences for human civilisation, appears to be the latest in a long line of environmental problems at least partly due to the influence of human beings. As an example, consider that the partial desertification of ancient Greece was due to the unchecked roaming of domestic goats. No one now speculates that Greece was ever any different from the very arid place it is now. This problem was due to the presence of human beings who radically changed the environment. In other words the influence of human beings on the state of the environment is significant.
Today, one of the major concerns in both agriculture and the natural environment is soil erosion which is caused by the action of water and wind. Water erosion, initiated by the impact of a raindrop on soil, both breaks up and is able to eject soil particles away from the point of impact and, if sufficient water is present, this is followed by the water transport of the disturbed soil particles away from the region of impact. In other words soil is slowly lost from the surface and the soil surface becomes eroded. Typically, if this disturbed surface dries out leaving behind loose surface soil a strong wind can easily continue this process leading to the well known "dust bowl" of depression era America.
Clearly, it is vital that the soil erosion process be well understood. One of the best ways to further understand this process is to construct a mathematical model of it. Current models, either empirical or process based, do not study the initial raindrop impact process rather they rely on reasonable assumptions to predict larger scale phenomena. Of the two erosion processes it is the initial raindrop splash or rainsplash process which both initiates the whole process and is also the least understood. It is the purpose of this research proposal to develop a detailed mathematical model of the rainsplash phenomenon which is able to capture all of its significant features such as cratering: the compression and spreading of the drop and the soil by the raindrop, splash: the disruption of the raindrop as it impacts the soil surface leading to soil particle transport and the flow transport of loosened soil particles within a water-soil suspension flow.
Computer simulations of a properly constructed mathematical model can be both economic and avoid experimental difficulties while still capturing the vital characteristics of the problem. My own research has been involved with the computer solution of mathematical models involving the flow of multiple interacting fluids such as the splash of a raindrop. This approach is able to consider the entire process in a unified way by involving the complex rainsplash phenomenon as a three-phase process, two fluid phases, the air and the drop, and a third solid phase, the soil grains. It is also able to incorporate multiple physical forces such as gravity, inertia, frictional and elastic forces in a natural way while still solving a problem which involves both the small lengthscales of the soil particles and the larger scales of the drop. To my knowledge this model will represent the first attempt at solving the full rainsplash process.
The benefits of the modelling of this process are manifold, including: a proper understanding of soil surface detachment, particle flow transport and crater formation; validation or correction of previous empirical models; a way to test the influence of individual forces affecting the process and so determine how these forces interact and a way to derive previously used assumptions for parameters of the rainsplash process. (see proposal_2.pdf)
Today, one of the major concerns in both agriculture and the natural environment is soil erosion which is caused by the action of water and wind. Water erosion, initiated by the impact of a raindrop on soil, both breaks up and is able to eject soil particles away from the point of impact and, if sufficient water is present, this is followed by the water transport of the disturbed soil particles away from the region of impact. In other words soil is slowly lost from the surface and the soil surface becomes eroded. Typically, if this disturbed surface dries out leaving behind loose surface soil a strong wind can easily continue this process leading to the well known "dust bowl" of depression era America.
Clearly, it is vital that the soil erosion process be well understood. One of the best ways to further understand this process is to construct a mathematical model of it. Current models, either empirical or process based, do not study the initial raindrop impact process rather they rely on reasonable assumptions to predict larger scale phenomena. Of the two erosion processes it is the initial raindrop splash or rainsplash process which both initiates the whole process and is also the least understood. It is the purpose of this research proposal to develop a detailed mathematical model of the rainsplash phenomenon which is able to capture all of its significant features such as cratering: the compression and spreading of the drop and the soil by the raindrop, splash: the disruption of the raindrop as it impacts the soil surface leading to soil particle transport and the flow transport of loosened soil particles within a water-soil suspension flow.
Computer simulations of a properly constructed mathematical model can be both economic and avoid experimental difficulties while still capturing the vital characteristics of the problem. My own research has been involved with the computer solution of mathematical models involving the flow of multiple interacting fluids such as the splash of a raindrop. This approach is able to consider the entire process in a unified way by involving the complex rainsplash phenomenon as a three-phase process, two fluid phases, the air and the drop, and a third solid phase, the soil grains. It is also able to incorporate multiple physical forces such as gravity, inertia, frictional and elastic forces in a natural way while still solving a problem which involves both the small lengthscales of the soil particles and the larger scales of the drop. To my knowledge this model will represent the first attempt at solving the full rainsplash process.
The benefits of the modelling of this process are manifold, including: a proper understanding of soil surface detachment, particle flow transport and crater formation; validation or correction of previous empirical models; a way to test the influence of individual forces affecting the process and so determine how these forces interact and a way to derive previously used assumptions for parameters of the rainsplash process. (see proposal_2.pdf)
proposal_2.pdf | |
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