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Topics in Fluid Dynamics: Dimensional Analysis, the Coriolis Force, and Lagrangian and Eulerian Representations
by James F. Price

This collection of three essays was developed from the author's experience teaching Fluid Dynamics of the Atmosphere and Ocean, 12.800, offered to graduate students entering the MIT/WHOI Joint Program in Oceanography. The goal of this course is to help each student master the concepts and mathematical tools that make up the foundation of classical and geophysical fluid dynamics. Three topics --- the subject of these essays --- proved to be the most difficult for most students: 1) dimensional analysis, 2) the Coriolis force and 3) Lagrangian and Eulerian representations. These essays treat these topics in considerably greater depth than a comprehensive fluids textbook can afford, and they are accompanied by data files (MATLAB® and Fortan) that allows some application and experimentation. They should be suitable for self study.

Cover of the Topics in Fluid Dynamics. (Image courtesy of James F. Price.)

Technical Requirements

The essays are accompanied by MATLAB® and Fortran source code. Special software is required if you choose to run the code: .m, and .fortran.

Topics In Fluid Dynamics contents

  • Table of Contents (all three essays) (PDF)

  • Author's Preface (PDF)

ESSAY 1: Dimensional Analysis of Models and Data Sets: Similarity Solutions and Scaling Analysis
Summary (PDF)
Complete Essay 1 (PDF - 1.5 MB)
MATLAB® file:
danalysis.m (M)
ESSAY 2: A Coriolis Tutorial
Summary (PDF)
Complete Essay 2 (PDF - 2.2 MB)
MATLAB® files:
arrow3h.m (M)
Coriolis.m (M)
partslope.m (M)
geoadjPE.m (M)
ESSAY 3: Lagrangian and Eulerian Representations of Fluid Flow: Kinematics and the Equations of Motion
Summary (PDF)
Complete Essay 3 (PDF - 2.6 MB)
MATLAB® files:
gwavemovie.m (M)
basinlook.m (M)
basintracks.m (M)

Fortran files:
basin.f (F)
basinsubs.f (F)


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