Ben-Dov Guy, Cohen Jacob
Faculty of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Phys Rev Lett. 2007 Feb 9;98(6):064503. doi: 10.1103/PhysRevLett.98.064503. Epub 2007 Feb 6.
Experimental results obtained over more than a century have shown that laminar flow in a circular pipe becomes naturally turbulent at a critical Reynolds number of Re approximately 2000. In this Letter a theoretical explanation, based on the minimum energy of an axisymmetric deviation (from the developed pipe flow profile), is suggested for this critical value. It is shown that for Re>1840 the minimum energy of the deviation, associated with the central part of the pipe, becomes a global minimum for triggering secondary instabilities. For Re<1840 the global minimum energy deviation is located next to the pipe wall. Previous experimental observations support this explanation.
一个多世纪以来的实验结果表明，圆形管道中的层流在临界雷诺数Re约为2000时会自然转变为湍流。在本信函中，基于轴对称偏差（相对于充分发展的管道流动剖面）的最小能量，对这一临界值提出了一种理论解释。结果表明，对于Re>1840，与管道中心部分相关的偏差最小能量成为触发二次不稳定性的全局最小值。对于Re<1840，全局最小能量偏差位于靠近管壁处。先前的实验观察结果支持这一解释。
