Fluid Dynamical Profiles and Constants of Motion from D-Branes

TL;DR

This paper explores the hidden symmetries and equivalence transformations in fluid mechanical systems derived from Nambu-Goto actions, revealing deeper geometric and dynamical structures.

Contribution

It uncovers the higher-dimensional Poincaré symmetry in fluid systems and explains their interconnections through equivalence transformations.

Findings

Identification of hidden Poincaré symmetry in fluid models

Demonstration of model equivalences via geometric transformations

Insight into the geometric origin of fluid dynamical constants

Abstract

Various fluid mechanical systems, governed by nonlinear differential equations, enjoy a hidden, higher-dimensional dynamical Poincar\'e symmetry, which arises owing to their descent from a Nambu-Goto action. Also, for the same reason, there are equivalence transformations between different models. These interconnections are discussed in this lecture, and are summarized in Fig. 3.