An introduction to Navier-Stokes equation and oceanography

More about the book

In the spring of 1999, I taught a graduate course on Partial Differential Equations Models in Oceanography at Carnegie Mellon University and created lecture notes for my students. These notes were later shared online and distributed at a Summer School in Lisbon in July 1999. After some time, I decided to publish a revised version to reach a broader audience. While there seems to be a growing interest in the Navier–Stokes equation, many who express this interest lack a fundamental understanding of continuum mechanics, raising questions about the depth of their engagement. The renewed focus may be linked to the Clay Millennium Prizes; however, the conjectures associated with this prize appear to have been selected by individuals not deeply versed in continuum mechanics, as they lack significant physical relevance. Although invariance by translation or scaling is mentioned, the omission of rotational invariance and Galilean invariance is notable. The latter is crucial for understanding that, in ordinary fluid dynamics where velocities are much smaller than the speed of light, relativistic corrections are unnecessary, and thus Galilean invariance should be applied. However, it's important to recognize that the mathematical formulation does not guarantee that solutions will adhere to velocities limited by the speed of light.