| Prandtl边界层方程推导中的尺度化分析 |
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| 引用本文： | 樊福梅,梁平,龙新峰.Prandtl边界层方程推导中的尺度化分析[J].华南理工大学学报(自然科学版),2003,31(10):61-64. |
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| 作者姓名： | 樊福梅 梁平 龙新峰 |
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| 作者单位： | 1. 华南理工大学,电力学院,广东,广州,510640
2. 华南理工大学,化工学院,广东,广州,510640 |
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| 摘 要： | 针对Navier-Stokes方程中的各项微商，通过选择内禀参考尺度，并根据连续函数的若干性质，在结合实验观察结果的基础上，确定其数量级的大小，再进一步对方程中的各项进行尺度化分析，使得方程中各项的数量级无量纲化，并评估方程中各项微商的数量级大小，略去数量级小于1的项，从而成功推导出了Prandtl边界层微分方程．该方法在一定程度上揭示了边界层微分方程的数学物理实质．
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| 关 键 词： | 边界层 尺度化 数量级 |
| 文章编号： | 1000-565X(2003)10-0061-04 |
| 修稿时间： | 2003年4月14日 |
Scaling Analysis for Inducing Prandtl Boundary Layer Equation |
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| Fan Fu mei,Liang Ping,Long Xin feng.Scaling Analysis for Inducing Prandtl Boundary Layer Equation[J].Journal of South China University of Technology(Natural Science Edition),2003,31(10):61-64. |
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| Authors: | Fan Fu mei Liang Ping Long Xin feng |
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| Institution: | Fan Fu mei 1 Liang Ping 1 Long Xin feng 2 |
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| Abstract: | By selecting intrinsic reference scaling, and according to some related properties of continuous function, the magnitude of each tiny quotient in Navier Stokes equation was determined based on some experimental materials. Then scaling analysis was carried out to make each part of the equation non dimensional, and the magnitude of each tiny quotient of the equation was evaluated. By removing the parts whose magnitude was less than 1, Prandtl boundary layer differential equation was induced successfully. To a certain extent, this method discloses the mathematical and physical essence of boundary differential equation. |
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| Keywords: | boundary layer scaling magnitude |
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