The present paper aims to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of velocity field turbulent flow. PDF PDE is highly non-linear parabolic-transport equation, which depends on two conditional statistical numerics important physical significance. general form classical Reynolds mean flow (O. Reynolds, Philos. Trans. R. Soc....

We show that small-amplitude periodic motion of a rigid plate causes point parts on the plate to move as if they are in a position-dependent velocity field. Further, we prove that every periodic plate motion maps to a unique velocity field. By allowing a plate to oscillate with six-degrees-of-freedom, we can create a large family of programmable velocity fields. We examine in detail sinusoidal ...

In this paper, we investigate the aggregation of a floating tracer into clusters. Motivated by observations dense patches buoyant material in real ocean (e.g., microplastic pollutants, plankton, and sargassum), develop an idealized model that can reproduce clustering process. A stochastic, kinematic 2D velocity field is chosen to represent turbulent oceanic surface currents, with weakly diverge...