Lin, Chia-Chiao (1944) On the development of turbulence. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06232004-140148
The stability of two-dimensional parallel flows of an incompressible fluid is investigated, based upon a study of the equation of Orr and Sommerfeld along the lines initiated by Heisenberg. The theory of Heisenberg is carefully examined and further developed to obtain several general and specific results on hydrodynamic stability. Most of the disputes in the existing theories are clearly brought out and carefully settled. It is further shown that all symmetrical and all boundary-layer types of velocity distributions are unstable above a certain minimum critical Reynolds number, whose approximate value can be easily calculated from equations (12.24) and (12.25) respectively. General characteristics of the curve of neutral stability are obtained (Fig. 9). Complete numerical calculations of this curve have been carried through for the plane Poiseuille flow and the Blasius flow. In the first case, the minimum critical Reynolds number is found to be 16000, based upon the maximun velocity and the width of the channel. In the second case, the number is 400, based upon the free stream velocity and the displacement thickness of the boundary layer. Physical interpretations of the results obtained are given, based upon the conservation of vorticity in a perfect fluid and its diffusion by viscous forces. Indications are also given to connect the stability theory with Taylor's theory of transition to turbulence. It is hoped that this work may remove all the doubts of applying the theory of small oscillations to the treatment of hydrodynamic stability using Navier-Stokes equations for an incompressible fluid.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Engineering and Applied Science|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 February 1944|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||24 Jun 2004|
|Last Modified:||26 Dec 2012 02:53|
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