The Geometry and Topology of Turbulent Blobs
Abstract
Improving our understanding of how turbulence develops and decays and finding ways to control its dynamics, is of both fundamental and significant practical interest. In its essence, turbulence is a tangle of vortical flow, with vortex lines winding in seemingly random directions. As such, the turbulent state can take many forms. Correspondingly, experimental investigations rely on carefully characterized model systems, such as flow past grids, or flow between counter-rotating boundaries, each ideally suited to study specific aspects of turbulence. In this proposal we focus on the geometry and topology of turbulence. By geometry, we mean the shape of the boundary of a turbulent region, embedded in a quiescent fluid, and by topology, we mean the knottiness of the tangled vortex lines within a region of turbulence. In particular, we seek to develop an ideal experimental platform for the study of both aspects. Our proposed design features a turbulent region that evolves while embedded in an otherwise quiescent fluid, with a knottedness that can be tuned. From simple considerations, such as the shape of a vortex tangle and the fuzziness of its boundaries, to more intricate measures, such as the helicity (or knottiness ) of the vorticity field, the geometry and topology of turbulence has proven challenging to access in existing model systems. Yet geometry and topology are an inescapable aspect of the problem: however turbulence may be generated, regions of tangled flow mix, expand, and diffuse into the surrounding fluid. How a turbulent region immersed in an otherwise quiescent fluid spreads and decays, or whether its growth, spreading and decay can be controlled by tuning the knottiness its vortex lines, are thus key issues. Many of the experimental model systems for the study of turbulence, such as grids, counter-rotating paddles, jets and convection setups generate turbulence at hard boundaries, and subsequently either confine it, as in the case of counter-rotating paddles, or advect it away, as in the case of grids in wind tunnels. While these model systems have enabled extensive exploration of the statistical properties of homogeneous isotropic turbulence,. the onset of turbulence near walls, and the effects of mean flows on turbulent development, they are less well suited to the study of geometric aspects because the generation of turbulence at boundaries makes it hard to control the amount of knottedness that is injected, while confinement by boundaries, or strong advection make it hard to follow the evolution of the edge of a turbulent region. We propose to research a new method of generation of turbulence that is well suited to our aims: by rapidly colliding vortex loops, we r construct a turbulent region that is embedded in quiescent fluids. This design allows characterization of the turbulent font, dynamics of growth and decay, and the shape and topology of the turbulent tangle. The method utilizes new techniques for the generation of vortices with controlled geometry and topology, enabling us to tune the properties of the flow that feeds the turbulent region. Preliminary results suggest that rapidly-fired vortex loops can spontaneously weave into a turbulent state that self-confines into a turbulent blob . We will characterize the properties of this new model system and subsequently use it to study turbulence s self-confining properties, its decay far from any walls, and the effect of knotting the injected vortices. The proposed research has promise for significantly advancing our experimental handle on the geometry of turbulent flows, leading to new ways of controlling the effects of turbulence.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 07, 2018
- Source ID
- W911NF1810046
Entities
People
- William T. M. Irvine
Organizations
- Army Contracting Command
- United States Army
- University of Chicago