TY - JOUR
T1 - Role of internal structures within a vortex in helicity dynamics
AU - Shen, Weiyu
AU - Yao, Jie
AU - Hussain, Fazle
AU - Yang, Yue
N1 - Funding Information:
This work has been supported by the National Natural Science Foundation of China (Grant Nos. 11925201 and 11988102), the National Key R&D Program of China (No. 2020YFE0204200) and the Xplore Prize.
Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.
PY - 2023/9/4
Y1 - 2023/9/4
N2 - Helicity, an invariant under ideal-fluid (Euler) evolution, has a topological interpretation in terms of writhe and twist for a closed vortex tube, but accurately quantifying twist is challenging in viscous flows. With a novel helicity decomposition, we present a framework to construct the differential twist that establishes the theoretical relation between the total twisting number and the local twist rate of each vortex surface. This framework can characterize coiling vortex lines and internal structures within a vortex - important in laminar-turbulence transition, and in vortex instability, reconnection and breakdown. As a typical example, we explore the dynamics of vortex rings with differential twist via direct numerical simulation (DNS) of the Navier-Stokes equations. Two twist waves with opposite chiralities propagate towards each other along the ring and then collide whence the local twist rate rapidly surges. Local vortex surfaces are squeezed into a disk-like dipole structure containing coiled vortex lines, leading to vortex bursting. We derive a Burgers-equation-like model to quantify this process, which predicts a bursting time that agrees well with DNS.
AB - Helicity, an invariant under ideal-fluid (Euler) evolution, has a topological interpretation in terms of writhe and twist for a closed vortex tube, but accurately quantifying twist is challenging in viscous flows. With a novel helicity decomposition, we present a framework to construct the differential twist that establishes the theoretical relation between the total twisting number and the local twist rate of each vortex surface. This framework can characterize coiling vortex lines and internal structures within a vortex - important in laminar-turbulence transition, and in vortex instability, reconnection and breakdown. As a typical example, we explore the dynamics of vortex rings with differential twist via direct numerical simulation (DNS) of the Navier-Stokes equations. Two twist waves with opposite chiralities propagate towards each other along the ring and then collide whence the local twist rate rapidly surges. Local vortex surfaces are squeezed into a disk-like dipole structure containing coiled vortex lines, leading to vortex bursting. We derive a Burgers-equation-like model to quantify this process, which predicts a bursting time that agrees well with DNS.
KW - topological fluid dynamics
KW - vortex dynamics
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U2 - 10.1017/jfm.2023.620
DO - 10.1017/jfm.2023.620
M3 - Article
AN - SCOPUS:85171134959
SN - 0022-1120
VL - 970
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - A26
ER -