MODEL EXPERIMENT IN GEOMORPHOLOGY:on the development of gully morphology
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概要
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For an appropriate explanation of geomorphological features, it is necessary to study both the characters of materials which constitute the features and the transformation of the features. Model experiments dealt in this paper offer one effective method to analyze the latter i. e., to examine the laws on the transformation of the features and their fundamental equations. If the experiment is to be considered from the point of view of investigating the fundamen-tal equations, numerical experiments operated by computor today have the similar meaning with model experiments. In either case the features in the prototype should be reproduced in the experiment. Numerical experiments are often useful when proper controlling factors and the laws of their working mechanism are well known. On the other hand, model experiments are sometimes operated in cases where their laws are not well known, because they can be operated with some knowledge on controlling factors in the trial and error steps. As to geomorphological phenomena, generally it is difficult to obtain proper equations for them, and then model experiments may be used to estimate the basic relations among them. The first problem in carrying out the model experiments on geomorphological pheno-mena is that the appropriate dynamic similarity conditions should be observed. The fundamental conditions for satisfying the similarity laws are P1/m1=P2/m2=……=Pn/mn (1) or Pi/Pj=mi/mj (i, j=1, 2, …, n) (2) Setting Pi/Pj=πp, mi/mj=πm we obtain πp=πm (3) where p is a physical factor in the prototype, and m that in the model. Eq. (3) indicates that pr-numbers in the prototype must be equal to those in the model for the phenomenon to reappear in the model. But it is seldom possible that all π-numbers in the model are in conformity with those in the prototype. This is the limitation of the model experiment. In some cases, however, it is possible to operate the experiment by easing the similarity law i. e., dividing a pheno-menon into some local regions in space and time. In the model experiment on gully morphology, the eroding force by surface runoff was assumed to be a dominant factor. The fundamental equation of surface erosion is given by Horton (1945), which may be written as follows dmp/dtp=kepApτep (4) with m: eroded mass, t: time, ke: erosion proportionality factor, A:area, τe: eroding force per unit area, and suffix p: prototype. The scaling relations are developed simply by postulating that the fundamental equation be valid in the prototype as well as in the model. Hence Eq. (4) becomes dmm/dtm=kemAmτem (5) in the model. Here the suffix m indicates the model. As the physical factors in the model and those corresponding in the prototype are related by scaling ratios, the ratio of Eq. (4) to Eq. (5) may be written as follows dmp/dmm dtm/dtp=kep/kem Ap/Am τep/τem (6) Using m ∝ ρ8l3, A ∝ l2 and τe ∝ ρwV2, Eq. (6)become s ρwp/ρsp kevp=ρwm/ρsm kemVm (7) with ρs: the density of soil, l: length, ρw: the density of water, and v: velocity. Here, all variables are expressed by representative quantity.
- The Association of Japanese Geographersの論文
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