Dynamics of floating objects at high particulate Reynolds numbers

The motion of high Reynolds number objects at free surfaces is a general problem that has many industrial and ecological applications, such as hazard assessment due to driftwood in rivers or motion of plastic patches in the oceans. Modeling such object trajectories in a flow can be done assuming the object to be a tracer or using Newton's second law in the form of the Basset-Boussinesq-Oseen equation. In many studies, however, the latter approach can be difficult to implement due to the presence of complex forces at play and a high computational cost, thus knowing the validity of the tracer model can be very useful for practical applications. In this work, we study theoretically and experimentally the dynamics of high Reynolds number floating objects in one- and two-dimensional free surface flows. We first verify that the two-dimensional surface version of the Basset-Boussinesq-Oseen equation can accurately model floating object trajectories. Following our theoretical analysis, we introduce a characteristic response distance noted λ that scales the acceleration distance of a floating object, and we show that it is about two to four times the body length in the streamwise direction. The dimensionless parameter λ^★ obtained by normalizing λ by a flow length scale then plays a role analogous to that of the Stokes number at low particulate Reynolds number. Moreover, we show that once the floating object reaches the flow velocity, or if at any given time its velocity is equal to that of the flow, the floating object behaves like a tracer, regardless of λ^★. These results can greatly simplify the analyses and computations of the motion of floating objects at high particulate Reynolds number, first by identifying a characteristic distance λ scaling the length of the acceleration phase, and then by showing that once the flow velocity is reached, the object is transported as a passive tracer.