Copyright © Randal Ferman

Introduction into Hydrodynamics

The present repository is a freely available copy of lecture notes on the Mathematical Hydrodynamics with a particular emphasis on variational methods. Basically, this material has been gathered together to serve as students's support for various lectures that the Author has been invited to deliver. The manuscript is currently constantly evolving. So, please, check this web page from time to time for the updated versions.

Moreover, if you have any questions, suggestions or corrections to this document, please do not hesitate to contact the Author (preferably by e-mail).

---

Author

• Dr. Denys Dutykh (CNRS - INSMI - LAMA UMR #5127 - Université Savoie Mont Blanc)
• Home page: http://www.denys-dutykh.com/
• E-mail: " Denys . Dutykh at univ-savoie . fr "

---

Acknowledgements

The contributions of these people are greatly acknowledged:

• Prof. Didier Clamond (LJAD - Université de Nice Sophia Antipolis, Nice, France)
• Dr. Dimitrios Mitsotakis (School of Mathematics, Statistics and Operations Research - Victoria University of Wellington, Wellington, New Zealand)
• Dr. Ashkan Rafiee (Carnegie Wave Energy, Perth, Australia)

---

Changelog

V0.0.5: 2015/09/01

• An extra section on Maxwell equations is added
• A section on Poincare lemma is added to Appendix (relation between exact and closed differential forms)
• A quotation of Yukawa and another one of Dirac are added
• Stokes equations are described
• Bernoulli's theorem is added
• Section on isentropic flows is rewritten and the circulation theorem is added

V0.0.4: 2015/08/01

• A new Chapter on Vorticity will be added in the future (already created in TOC)
• Mini tables of contents are added at the beginning of each Chapter
• The Chapter on Fluid Dynamics equation derivation is further cleaned
• Feynman's blackboard picture is added
• List of figures is added (and List of Tables, without tables present in the text for the moment)

V0.0.3: 2015/06/01

• Portraits of Lagrange, Hamilton & Zakharov were added
• CERN Mug is added to illustrate the use of Lagrangians in Theor. Physics
• Paper layout changed to european format a5

V0.0.3: 2015/05/01

• General Lagrangian formulation for Euler and Navier-Stokes equations
• Dimensional analysis, pi-theorem
• SPH method
• Various small improvements

V0.0.2: 2015/04/08

• Derivation of basic Fluid Mechanics equations in the Eulerian description
• Appendix on differential forms

V0.0.1: 2014/11/21

• The very first preliminary structure of the manuscript.