１３：３０ から １５：００
場所: 京大 理学研究科５号館(物理学教室) ４０１号室
講師： Siddhartha Mukherjee (ICTS Bangalore)
講演題目： Aspects of Turbulence Organization: Emergent Structures, Vortex-Lines and Local Multifractality
The description of turbulence field organization from a “structures” perspective has been a long-standing challenge. While individual realizations of turbulence are rich in various kinds of structure, possibly “at all scales”, much of our knowledge is either limited to the statistical structure of ensembles of realizations, or to some eduction techniques suited for specialized applications. In this talk, I will take you through three aspects of turbulence structure and organization that we are trying to address. (1.) We shall see how a generalized correlations framework can be used to identify and seek insight about a range of velocity and vorticity field structures in turbulence. Coupling this with a Helmholtz-decomposition paradigm then allows disentangling individual structures and also entire fields from superposition. Such an exercise reveals some very intriguing features of the high kinetic energy structures, suggestive of an emergent nature in turbulence structures. (2.) We shall then move onto a vortex-lines based approach aimed at identifying coherent vortex-tubes. These long and slender objects can be in complex tangles, playing a key role in turbulence dynamics, via vortex-reconnections, stretching and interactions. Much of their geometrical features remain uncharted, like the distribution of their lengths, persistence profiles and links with dynamical aspects of the flow. We show how this can be solved by extracting individual vortex-lines. (3.) Finally, we shall move onto the subject of singular structures in turbulence fields, linked to intermittency and anomalous scaling and dissipation. While the multifractal formalism allows estimating a range of scaling exponents of the flow, the method remains largely reductive, and by its very construction precludes any conception of spatial variation in multifractality. We now show that this technique can be simply adapted as a local analysis, thereby revealing entire fields of generalized dimensions, and hence multifractal statistics of the small neighbourhood around any point in space. This throws up surprising findings that revise our understanding of the multifractal structure of the dissipation field. These topics, I hope, will make the case for studying individual fields in their own right to uncover their constituent structures, and inspire us to go beyond our usual set of lenses for studying turbulence.