On the covariant formulation of the law of motion of passive particles in a field of turbulence
Abstract
The tensor calculus of curvilinear coordinates has been applied to the problem of the dynamics of particle transfer in a turbulence field in order to record in covariant form the interaction of particles in a fluid and of particles in a solid admixture. A covariant derivative of the Lagrangian velocity field was used to construct covariant expressions which were relative to any coordinate transformation. The condition of covariance, when constructed in this way does not contain any other functions, is restricting, and leads to a negative scalar curvature of the Riemann manifold representing the states of the system. Restrictions imposed on the velocity field introduced a static metric of the manifold into the analysis. The special case of a nonstationary metric is considered in order to obtain a more general expression of the covariant derivative of the velocity field.
 Publication:

Travaux Geophysiques
 Pub Date:
 1984
 Bibcode:
 1984TraGe..29..325H
 Keywords:

 Flow Stability;
 Particle Diffusion;
 Turbulent Diffusion;
 Two Phase Flow;
 Covariance;
 EulerLagrange Equation;
 Flow Velocity;
 Geodesic Lines;
 Markov Processes;
 Riemann Manifold;
 Tensor Analysis;
 Turbulent Flow;
 Turbulent Mixing;
 Fluid Mechanics and Heat Transfer