Abstract
We consider the rotation of tangent vectors and the mutual rotation of two particles undergoing motion in a random two-dimensional velocity field. We look at random fields whose laws are invariant under translations and rotations, but not reflections. These polarized fields are intermediate between homogeneous and isotropic fields, and may possess a preferred sense of rotation. The covariance of such a field must have a certain form which we describe. In a Brownian flow based on a polarized random field, we show that tangent vectors can rotate at a constant asymptotic rate, and that under certain conditions, two particles will rotate about each other at the same asymptotic rate. For illustration we present simulations of a polarized Gaussian field and of particles moving in a polarized Brownian flow.
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