Keywords

Fluid impulse, incompressible fluid, compressible fluid

Abstract

The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the importance of the study of fluid impulse. In chapters two and three we will derive the Kuz'min, E & Liu, Maddocks & Pego and the Zero gauges for the evolution equation of the impulse density, as well as their properties. The first three of these gauges have been named after their authors. Chapter four will study two exact solutions in the impulse formulation. Physical interpretations are examined in chapter five. In chapter six, we will begin with the generalization to the compressible case for the Kuz'min gauge, based on Shivamoggi et al. (2007), and we will derive similar results for the remaining gauges. In Chapter seven we will examine physical interpretations for the compressible case.

Notes

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Graduation Date

2007

Semester

Fall

Advisor

Shivamoggi, Bhimsen

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0001907

URL

http://purl.fcla.edu/fcla/etd/CFE0001907

Language

English

Release Date

December 2007

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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Included in

Mathematics Commons

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