地形学における模型実験の意義と問題点: ガリーの発達を一例として

Kashiwaya, Kenji; 柏谷, 健二

doi:10.4157/grj.49.497

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地形学における模型実験の意義と問題点: ガリーの発達を一例として

https://doi.org/10.24517/00053688

名前 / ファイル	ライセンス	アクション
SC-PR-KASHIWAYA-K-497.pdf (1.2 MB)

Item type

学術雑誌論文 / Journal Article(1)

公開日

2019-03-08

タイトル

地形学における模型実験の意義と問題点: ガリーの発達を一例として

タイトル

Model experiment in geomorphology: on the development of gully morphology

言語

jpn

資源タイプ

資源タイプ識別子

http://purl.org/coar/resource_type/c_6501

資源タイプ

journal article

ID登録

10.24517/00053688

ID登録タイプ

JaLC

著者

柏谷, 健二

WEKO 83632
e-Rad 30161029

	柏谷, 健二

Search repository

著者別表示

Kashiwaya, Kenji

提供者所属

内容記述タイプ

Other

内容記述

金沢大学環日本海域環境研究センター

書誌情報

地理学評論
en : Geographical review of Japan

巻 49, 号 7, p. 497-504, 発行日 1976-07

ISSN

収録物識別子タイプ

ISSN

収録物識別子

0016-7444

NCID

収録物識別子タイプ

NCID

収録物識別子

AN00148053

DOI

関連識別子

10.4157/grj.49.497

出版者

日本地理学会 = The Association of Japanese Geographers

抄録

内容記述タイプ

Abstract

内容記述

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.

権利

権利情報

著者版フラグ

出版タイプ

VoR

出版タイプResource

http://purl.org/coar/version/c_970fb48d4fbd8a85

関連識別子

http://ci.nii.ac.jp/naid/40002449948/