Navier-Stokes Solutions at Large Distances from a Finite Object

Citation

Chang, I-Dee (1959) Navier-Stokes Solutions at Large Distances from a Finite Object. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SMPS-TA29. https://resolver.caltech.edu/CaltechETD:etd-02062006-083016

Abstract

The asymptotic expansion of the Navier-Stokes solutions at fixed Reynolds numbers and large distances from a finite object for an incompressible, stationary and two-dimensional flow is studied. The expansion is a coordinate-type expansion and differs in many mathematical aspects from the more familiar parameter-type expansions for large and small Reynolds number flows. These differences are noted and discussed in some detail. The technique chosen for dealing with the problem is that of the use of an artificial parameter. This is one possible method for using some of the techniques of parameter-type expansions. In particular, at large distances from the object one may distinguish a viscous wake region and a potential ("outer") flow region. The relation between these regions is very similar to the relation between the viscous boundary layer and the potential flow region for flow at large Reynolds numbers. Several terms of the expansion are computed. However, the main emphasis is placed on discussing the methods for deriving these terms. The special features of expansions in artificial parameters are discussed in detail. The role of various properties of Navier-Stokes solutions, such as validity of integral theorems and rapid decay of vorticity is also brought out. The original motivation of the study was an attempt to understand the Filon's paradox which historically was an error in evaluating the momentum, integral of the asymptotic flow field. The present study, however, deals with the general problem of the flow at large distances from a finite object, and, more generally, with expansion techniques for similar problems. The author's explanation of Filon's paradox is only an incidental result.

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