Asymptotic Expansion of Navier-Stokes Solutions in Three Dimensions for Large Distances

Citation

Childress, William Stephen (1961) Asymptotic Expansion of Navier-Stokes Solutions in Three Dimensions for Large Distances. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/A77G-P071. https://resolver.caltech.edu/CaltechETD:etd-12082005-113027

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis studies the stationary flow field at large distances from a finite obstacle moving uniformly in a viscous, incompressible fluid. The principal results consist of asymptotic expansions, uniformly valid for large distance, of the velocity and the pressure of the flow field. The expansion procedure employed is based upon the introduction of a small, extraneous parameter; the construction is thus recast as a perturbation for small values of the parameter. Owing to the presence of a viscous wake, the perturbation is in general a singular one, and is treated accordingly, using methods developed for related hydrodynamical problems. The calculated results include the following: for the case of axially-symmetric flow, a uniformly valid expansion of the velocity to order [...] inclusive, and of the pressure to order [...] inclusive, r being the distance from the obstacle; for the general case, an expansion of the velocity to order [...] and of the pressure to order [...], inclusive.

Thesis Files