Forces and torques in two-dimensional turbulence and their applications

Abstract

Since the discovery of two-dimensional (2D) turbulence in Faraday waves a decade ago, understanding of such phenomena has advanced greatly. The discovery of coherent bundles in such flows introduced a new way of exploiting 2D turbulence. This led to the development of devices capable of self-propelling in turbulent flows and offered novel ways of extracting energy stored in the inertial range of turbulence. Forces and torques acting on solid objects in turbulence require better understanding to optimise these methods for practical applications. Here I study the interaction forces acting between two solid objects, and torques acting on solid disks of different diameters in 2D turbulence. I demonstrate how the improved understanding of these interactions helps to control the growth of bacterial cellulose (BC) in the Faraday wave-driven turbulence.

Understanding forces generated in nonequilibrium systems is a significant challenge in statistical and biological physics. The generation of forces between passive inclusions in nonequilibrium systems underpins many phenomena in nature. The most celebrated of these fluctuation-induced forces is the quantum Casimir force. The phenomenon of force generation observed in other systems, has not yet been studied in classical hydrodynamic turbulence. Here, we present evidence of the attractive force mediated via turbulent fluctuations by using two walls which locally confine 2D turbulence. An optical fibre is used as a force probe in these studies, which provides a simple, reliable and accurate method for measuring such forces. In such a strongly nonlinear system, dominated by the energy cascades and spatiotemporal chaos, we show that the long-range interaction is a function of the wall separation and the energy injection rate into the turbulent flow. The magnitude of the attractive force increases with the turbulence kinetic energy. As the wall spacing decreases, the confined flow becomes less energetic and more anisotropic in the bounded domain, producing stronger attraction. We propose a model to calculate the attraction force using turbulence parameters. The mechanism of force generation is rooted in a nontrivial fluid-wall coupling where coherent flow structures are guided by the cavity in between the walls. For the narrowest cavities studied, a resonance phenomenon at the flow forcing scale leads to a complex short-range interaction.

Complementary to studying force acting on straight walls, we experimentally study the rotational dynamics of a circular disk in 2D turbulence. A stochastic process can describe the dynamics of the angular motion. The effect of the forcing scale on the measured rotational motion is studied. It is found that the mean-squared angular displacement (MSAD) is diffusive at long times. We demonstrate how the rotational dynamics of a disk with a diameter smaller than the forcing scale of turbulence couples with coherent bundles. The rotational kinetic energy of the disk is determined, and the change of this parameter with the ratio of the disk size over the forcing scale in the 2D turbulence is demonstrated. The results highlight the importance of interactions between meandering bundles of fluid particles, recently found in such a turbulence.

Based on the understanding obtained from studying the interacting forces of passive particles, we introduce living organisms to such flow condition. Bacterial cellulose (BC), a biopolymer synthesised by bacteria, has attracted much attention recently as a potential sustainable biomaterial. In this work, under the influence of surface wave-driven turbulent flow, the bacterial cellulose forms spherical beads whose diameter is determined by the characteristic scale of the flow. This ability, to alter the properties and the structure of the BC, will potentially broaden its industrial applications in, for example, tissue engineering, paper manufacturing, electronics, and filtration membranes. Show more