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A theory of laminar flow stability

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Abstract

The success enjoyed by a laminar flow stability parameter that I previously developed as a generalization of the critical Reynolds number of laminar turbulent transition has occasioned considerable interest in the phenomenological theory underlying the parameter. In this paper an analysis of laminar flow stability is presented which leads naturally to the parameter in a much different manner than originally proposed. The stability parameter is seen to represent the coupling ratio between the rate of change of angular momentum of a deforming fluid element and its rate of loss of momentum by frictional drag. At a certain critical value of this coupling ratio, the element becomes unstable to rotational disturbances. If such disturbances are present, the basic nonlinearity of the momentum transfer process guarantees rapid amplification and generation of a turbulent eddy. The consequnces of the theory are examined for two special fixed boundary classes of motion. The physical interpretation of the parameter is compared with conventional interpretations of the Reynolds number and found to be more fundamentally sound. The application of the theory to moving boundary flows, such as the Couette viscometer, is also discussed and an important physical difference is pointed out.

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