A comparison of the modern Lie scaling method to classical scaling techniques
In the past 2 decades a new modern scaling technique has emerged from the highly developed theory on the Lie group of transformations. This new method has been applied by engineers to several problems in hydrology and hydraulics, including but not limited to overland flow, groundwater dynamics, sedi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2016-07-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | http://www.hydrol-earth-syst-sci.net/20/2669/2016/hess-20-2669-2016.pdf |
| Summary: | In the past 2 decades a new modern scaling technique has emerged from the
highly developed theory on the Lie group of transformations. This new method
has been applied by engineers to several problems in hydrology and
hydraulics, including but not limited to overland flow, groundwater dynamics,
sediment transport, and open channel hydraulics. This study attempts to
clarify the relationship this new technology has with the classical scaling
method based on dimensional analysis, non-dimensionalization, and the
Vaschy–Buckingham-Π theorem. Key points of the Lie group theory, and the
application of the Lie scaling transformation, are outlined and a comparison
is made with two classical scaling models through two examples: unconfined
groundwater flow and contaminant transport. The Lie scaling method produces
an invariant scaling transformation of the prototype variables, which ensures
the dynamics between the model and prototype systems will be preserved. Lie
scaling can also be used to determine the conditions under which a complete
model is dynamically, kinematically, and geometrically similar to the
prototype phenomenon. Similarities between the Lie and classical scaling
methods are explained, and the relative strengths and weaknesses of the
techniques are discussed. |
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| ISSN: | 1027-5606 1607-7938 |