Hydrodynamics, Geometric Optics, and Classical Mechanics

Abstract

In the investigation of the general properties of vortex lines, a significant role is played by the equation

$$ \frac{{\partial u}}{{\partial t}} = rot\left( {u \times \upsilon } \right), $$

(1.1)

where v(x, t) is the velocity of the particles of a medium in the three-dimensional Euclidean space E ³ = {x} and u(x, t) is a solenoidal vector field, div u = 0. The physical meaning of the field u is determined by the specific problem under investigation. Integral curves of the vector field u (at a fixed instant t) are called vortex lines.