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sommerfeld equation
相关语句
  sommerfeld方程
     A Complement of Extracting Solutions on Orr Sommerfeld Equation about the Analysis of Hydrodynamic Stability
     流体线性稳定性分析 Orr-Sommerfeld 方程求解的一点补充
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  “sommerfeld equation”译为未确定词的双语例句
     A rapid and effective method for solving Orr Sommerfeld equation′s neutral stability curve is presented.
     提出一种快速准确求解 Orr- Som merfeld(O- S)方程的中性曲线和临界雷诺数 Recr的方法。
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  相似匹配句对
     ON THE EQUATION
     关于方程ф(x)=ф(y)
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     equation
     方程(之3)
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     ACCURATE SOLUTION OF THE ORR-SOMMERFELD EIGENVALUE EQUATION
     Orr—Sommerfeld方程的数值解
短句来源
     THE SOLUTION OF THE EIGENVALUE PROBLEM OF THE ORR-SOMMERFELD EQUATION
     Orr-Sommerfeld方程的数值解法
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     On the Sommerfeld type integrals
     关于Sommerfeld型广义积分
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  sommerfeld equation
A temporal stability analysis based on the Orr-Sommerfeld equation has been performed.
      
The stability of this flow is investigated by solving the Orr-Sommerfeld equation for quasi-steady, onedimensional velocity profiles.
      
The analogue of Orr-Sommerfeld equation is derived for a generalized Newtonian fluid.
      
Solutions of the Orr-Sommerfeld equation are given as examples.
      
Analytic pseudoorthogonalization methods for linear two-point boundary value problems illustrated by the Orr-Sommerfeld equation
      
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The eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation, which is fundamental for the investigation of the problem of stability of laminar fluid motion, have been investigated by several authors, but the results are still imcomp-lete [6]. In this paper, this problem is reinvestigated, and some new results are obtained, which are: ( 1 ) The expansion series converges not only uniformly but also absolutely; ( 2 ) The coefficients of the expansion series satisfy an inequality...

The eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation, which is fundamental for the investigation of the problem of stability of laminar fluid motion, have been investigated by several authors, but the results are still imcomp-lete [6]. In this paper, this problem is reinvestigated, and some new results are obtained, which are: ( 1 ) The expansion series converges not only uniformly but also absolutely; ( 2 ) The coefficients of the expansion series satisfy an inequality of Paley-Wiener type, which is the natural extension of the well known Bessel equality of a complete orthogonal set.

Orr-Sommerfeld方程的特征值问题及展开定理,对于研究流体层流稳定问题具有重要意义,因此,有不少作者研究过.但据文献[6],这一问题还不能认为已完全解决.因此在本文中,我们进一步研究了这一问题,得到的具体结果是:展式的系数满足一个Paley-Wiener型不等式,它是通常完备正交系展式系数所满足的Bessel等式的一个推广:而且证明了展式是绝对一致收敛的.

In this paper, an alternative method has been presented to solve the Orr-Sommerfeld equation in the linear theory of stability. To begin with, we define a Green function which is expressed in terms of matrix. Subsequently, the reciprocity of it has been shown. Finally, a linear integral equation that is equivalent to the original Orr-Sommerfeld equation is derived. The method is applied to the cases with two solid walls and any velocity distribution of the main flow at any Reynolds number.

本文提出了一种求解线性稳定性理论Orr-Sommerfeld方程的方法.我们首先定义了该方程的Green函数,并将它表达成矩阵形式;然后证明了Green函数的互易性;最后导出了等价于原方程的线性积分方程.该方法适用于两固壁间任意Reynolds数下各种主流速度分布的情况.

In[1], Zhou extended some Liapounoff's theorems of the theory of stability in the case of plane laminar fluid flows In [ 2 ], Zhou and Li investigated the eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation, and obtained some new results. In this paper, based on the results of [ 1 ] and [ 2], we shall prove: (1) For the linearized problem the definition of stability according to the eigenvalues of Orr-Sommer-feld equation and that according to the perturbation energy...

In[1], Zhou extended some Liapounoff's theorems of the theory of stability in the case of plane laminar fluid flows In [ 2 ], Zhou and Li investigated the eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation, and obtained some new results. In this paper, based on the results of [ 1 ] and [ 2], we shall prove: (1) For the linearized problem the definition of stability according to the eigenvalues of Orr-Sommer-feld equation and that according to the perturbation energy are equivalent to each other; ( 2 ) The method of linearization is admissible for the stability problem of plane laminar fluid flows for sufficiently small initial disturbance.

本文是[1]的继续.在本文中,利用[1]的结果我们证明了,对于流体的层流运动稳定性而言,在线性化问题中,按特征值定义与按扰动能量定义二者是完全等价的,从外,借助于Ляпунов方法,我们又证明了,如果线性化问题是渐近稳定的,当考虑非线性影响时,只要扰动能量足够小,则仍然是渐近稳定的.

 
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