On the Lamb Vector and the Hydrodynamic Charge

Abstract

This work is an attempt to test the concept of hydrodynamic charge (analogous to the electric charge in Electromagnetism) in the simple case of a coherent structure such as the Burgers vortex. We provide experimental measurements of both the so-called Lamb vector and its divergence (the charge) by two-dimensional Particle Image Velocimetry. In addition, we perform a Helmholtz-Hodge decomposition of the Lamb vector in order to explore its topological features. We compare the charge with the well-known Q criterion in order to assess its interest in detecting and characterizing coherent structure. Usefulness of this concept in studies of vortex dynamics is demonstrated.