Probing Geometric Structure of Turbulence via Direct Measurements of Vorticity Field
Abstract
Despite of significant advancement in our ability to model turbulent flows in the recent decades, our understanding of turbulence at phenomenological level has not been fundamentally improved and deepened from the notion of Richardson and Kolomogorov more than a half century ago. Enhancing such understanding can help us establish a consistent framework on how turbulence behaves under various complex and dynamic external forcings (e.g. stratification and wind gust, etc.) and when interacts with dispersed phases (e.g. sand storms). This framework serves as a crucial step for developing effective prediction tools and a priori control strategies for turbulent flows under realistic settings relevant to a number of army operations. This proposed project aims to elevate our fundamental understanding of turbulence by probing into its geometric structure through direct measurements of its vorticity field. Based on 3D digital inline holographic (DIH) imaging, we will first develop a robust diagnostic technique that can quantify the vorticity field from the Kolmogorov scale to the integral scale of turbulence by tracking the rotation and the translation of a large number of individual spherical tracers in a sample volume. Successively, we will implement the developed technique to measure the vorticity field of two canonical turbulent flows, i.e., homogeneous isotropic turbulence and smooth-wall channel flow. The data will be first analyzed to gain understanding of the small-scale geometric structure of turbulence. Specifically, we will identify the presence of intense vortex filaments in turbulence and quantify their spatial and temporal characteristics through the spatial distribution and evolution of vorticity vectors measured from a group tracers. We will also explore the interaction between neighboring vortex filaments and between the filaments and the strain rate field as well as the connection between filaments and small-scale turbulence statistics. In addition, using the same dataset, we will construct vorticity field at multiple scales through bandpass filtering (coarse graining), and examine the geometric representation of eddy interaction and energy cascading across different scales. Finally, we will further investigate the effect of external forcing at integral scale on the geometric structure of turbulence. The proposed project will develop a unique diagnostic technique that allows the direct measurement of the vorticity field at Kolmogorov scale for the first time. The implementation of such measurements on two canonical turbulent flows will provide benchmark datasets for the fundamental study of turbulence using theoretical and numerical approaches. The proposal has the potential to significantly enhance our fundamental understanding of turbulence by providing more quantitative information and more detailed characterization of the phenomenology of turbulence, particularly at small scales. Such knowledge can provide deep insight into the geometric characteristics of Navier-Stokes equations, and may yield a new class of approaches, beyond conventional statistical averaging and stochastic dynamics, to interpret, model (e.g. new Lagrangian structure-based subgrid-scale models for large eddy simulation) or even control turbulence in practice.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010098
Entities
People
- Jiarong Hong
Organizations
- Army Contracting Command
- United States Army
- University of Minnesota