水动力学中的能量变分原理和能量积分

VARIATIONAL AND INTEGRAL PRINCIPLE ON ENERGY IN HYDRODYNAMICS OF THE VISCOUS FLOW

本文针对粘性不可压缩水流建立了拉格朗日观点下的能量泛函，通过变分法论证了能量泛函的一阶变分为零等价于水流运动的基本方程式，即动量方程式。在恒定流的条件下，利用拉格朗日函数导出了推广的伯努利方程，从而说明了寻找的能量泛函的正确性。

In this paper, on the basis of Lagrange's point of view, the energy functional for incompressible viscous flow is established. By the use of variational method,it could be proved that the first-order variation of the energy functional equals zero,is equivalent to the basic equations of the flow movement, i. e. the momentum equations. That the extended Bernoullian equations can be derived from the Lagrangian function under the condition of the flow being steady, demonstrates that the energy functional presented in this paper is valid.