帕隆藏布河流纵剖面演化的最小功模式

Model of Minimum Energy Dissipation in Evolution of Longitudinal Profile of Polongzangbu River

河流地貌最小功原理表明河流纵剖面形态将向力求使流速增大的方向演化 ,据此推导出矩形流域全程流速的平均值 (懕)与河流纵剖面形态指数 (N)的关系式 :懕∝ｆ(N) ={ 1/ 2 - 1/ [(N +1) (N +2 ) ]} 1/ 2 ,f(N)被称为流速函数。这一最小功模式表明河流纵剖面演化方向是N由小变大 ,纵剖面形态由上凸抛物线经直线向下凹抛物线发展。在侵蚀旋回中 ,河流各发育阶段的f(N)值也由小变大。以西藏帕隆藏布中上游流域系统、干流全程及Ⅰ级阶地为例 ,由最小功模式计算的全程流速均值与实测值相吻合 。

It is indicated with theory of minimum energy dissipation in river geomorphology that impelling velocity to increase is evolution direction of river longitudinal profile.Accordingly, a relation formula between average value (ū) of velocity along the river and forming index (N) of the river longitudinal profile , ū∝f(N)={1/2-1/[(N+1)(N+2)]} 1/2(the f(N) is a velocity function), is inquired.The mathematical model of minimum energy dissipation indicates that to increase value N is evolution direction of river longitudinal profile, and that shape of the longitudinal profile develop to a concave parabola pattern from a convex one.Further, the values f(N)which it is increase in every evolution stages of an erosional cycle is calculated.As examples with middle and upper reaches, whole main stream and its No.I terrace of Polongzangbu rive, average values of velocity along the river calculated by the model of minimum energy dissipation conforms to measured value.Thus, the theory and mathematical model of minimum energy dissipation are examined.