The dynamic evolution of helicity and twist, and their role in vortex instabilities
Abstract
Vortical structures constitute the core of fluid flows, and their fundamental dynamics and interactions are of interest to many natural and engineering applications. An effective understanding of vortex dynamics can be obtained by analyzing the geometry of the vorticity field lines, specifically their mutual linking or intertwining. The central concept in this perspective is the flowÕs helicity, a topological measure of the winding of vortex lines, which was discovered as an invariant of the inviscid flow equations only around sixty years ago. However, even flows with zero helicity can contain locally twisted vortex lines, implying that the geometric perspective can be applied to a broad class of vortex dynamics phenomena. In this proposal we intend to use high-fidelity direct numerical simulations to systematically analyze the dynamics of helicity and twist in a set of non-trivial vortical flows that are beyond the reach of current theories and experimental measurements. Numerically, the structure of the vorticity field lines is available at any time, and their winding can be computed for any vortex surface around the vortex tube centerline. Further, simulations provide the possibility to probe arbitrary initial conditions, and analyze the precise twist and writhe dynamics of vortex tubes in isolation, as well as in an external strain field. We fully exploit these capabilities of numerical simulations by developing a parametrized set of initial conditions with tunable twist, writhe, and core profile; a set of post-processing tools for extracting the geometric characteristics of arbitrary vortical flows; and an inviscid vortex filament solver to better characterize the effect of viscosity. Using this framework, we intend to investigate the structure and dynamics of twist, and its interaction with centerline writhe and external straining flows. The total helicity of isolated vortex tubes is often decomposed into a component due to the writhe of the centerline, and a component due to the twisting of vortex lines around the centerline. The dynamic evolution of helicity in viscous flows can then be interpreted as a transfer between twist and writhe, which is an inviscid phenomenon, combined with the viscous dissipation of the twist component of helicity. However, the assumptions underlying this interpretation have not been extensively verified beyond basic flow configurations, and this proposal aims to further investigate to what extent this perspective can be applied to non-trivial flows. Further, we will use our numerical tools to address a particularly interesting case of vortex dynamics where twist plays a critical role. This flow originates from a zero-helicity vortex tube with periodic undulations in its core size, which evolves by generating opposite-signed twist waves. The collision between two such twist waves gives rise to so-called vortex bursting, and is accompanied by an increase in energy dissipation rate, generation of small-scale structures, and significant radial fluid transport. We wish to characterize this process to determine its relevance in dissipating and breaking up vortical structures, which in turn has relevance for our understanding of vortical and turbulent flows. Moreover, we intend to investigate vortex bursting as a prototypical mechanism for uncovering non-trivial twist dynamics with broader relevance to practical flows. This proposal will validate and extend existing modeling techniques based on the twist/writhe decomposition of helicity, as well as provide data and analysis that can lead to new reduced-order modeling approaches for local twist wave dynamics.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 07, 2021
- Source ID
- W911NF2110332
Entities
People
- Willem Van Rees
Organizations
- Army Contracting Command
- Massachusetts Institute of Technology
- United States Army