Topics in Fluid Dynamics: Dimensional Analysis, the Coriolis force, and Lagrangian and Eulerian Representations

A graph demonstrating Lagrangian trajectories.

Five day-long Lagrangian trajectories observed by freely-drifting floats (green worms) and the Eulerian horizontal current vector measured by a fixed current meter (black vector) that is scaled similarly. The approximate equality of these measurements is a demonstration of the Fundamental Principle of Kinematics. These data are a snapshot from a four month-long period that is animated in the cover page of the essay on Lagrangian and Eulerian representations of fluid flow. (Image by James F. Price. Used with permission.)


James F. Price

    Resource Description

    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 (MATLABĀ® and Fortan) that allows some application and experimentation. They should be suitable for self study.

    Technical Requirements

    Special software is required to use some of the files in this course: .m, .fortran.