What can we learn from large bodies moving in a turbulent fluid?

Abstract

In this paper we describe simulations of the dynamics of two floating bodies in a turbulent fluid with the aim of determining to what extent their motion replicates the motion of the fluid. The fluid moves under gravity in a two dimensional region where the turbulence is driven by a stirrer. The bodies are neutrally buoyant with a diameter comparable to the Taylor length of the turbulence. Because the upper surface is free, and the perturbations to it can be large, we use the numerical method SPH which handles the motion of a free surface and moving bodies very easily. The time correlation functions of the velocity calculated from the paths and dynamics of the bodies are remarkably similar to those for the turbulent fluid. The spatial correlation of the velocity calculated from the motion of the bodies has the same form as that calculated using the 22,500 particles of the SPH simulation. The variation with time of the separation of the two bodies agrees with the appropriate theory for two dimensional turbulence until it reaches a scale comparable to the width of the fluid region when the separation drops rapidly to the initial separation then increases as before. This cycle is then repeated. Results for the correlation functions of spin of the bodies and its variation with time are also given.