# 3D Turbulence

Recent theoretical and experimental work suggests that the dynamics of turbulent flows

are guided by unstable solutions to the Navier-Stokes equation (Suri et al. 2017; Suri et al. 2018; Hof et al. 2004). These solutions, known as Exact Coherent Structures (ECS), are special non-chaotic solutions that are stable along most dimensions in its infinite (or in practice extremely high) dimensional state space and weakly unstable only along a few dimensions. The underlying geometry, or structure, of state space is set by the details of these solutions. So, in order to forecast where the turbulent flow will go next in state space, information about these ECS is needed. Finding these dynamically relevant solutions is challenging. The tools necessary to find these solutions in an efficient manor either are still in their infancy or simply to not exist. Developing the tools necessary to make this dynamical systems approach to turbulence practical requires comparing numerically computed ECS to highly resolved, high fidelity, fully time resolved 3D turbulent velocity measurements in a volume.

In this lab we are currently searching for evidence of ECS in experimentally realized 3D turbulence. Our experimental efforts are complimented by the efforts of Roman Grigoriev’s Dynamics and Control Group. The specific system we work in is known as “Taylor-Couette flow,” which refers to the flow of a fluid in the annular gap between two concentric cylinders. Taylor-Couette flow has been studied for decades and is known to exhibit a myriad of different stable flow regimes for various flow parameters. We are working in a regime where the flow is moderately turbulent where no stable non-turbulent flow states exist.

In order to measure the 3D velocity field in the entire volume of the flow domain, we constructed a small aspect ratio Taylor-Couette system (see figure above) that is entirely transparent and both filled and cooled with index matched fluid. The flow is seeded with fluorescent tracer particles made in house and illuminated and viewed from bellow by 8 cameras. The data from these cameras a streamed to disk so that long duration of data can be collected. The particle images are then analyzed using a 4D particle tracking technique (4D as apposed to 3D because it also uses time) to obtain a fully time resolved 3D velocity field in the entire flow domain.