.png){kind=icon}
返回
On vortex-sheet evolution beyond singularity formation
.png){kind=icon}
PRE
AI
DOI：10.1017/jfm.2023.880.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
We consider the evolution of a spatially periodic, perturbed vortex sheet for small times after the formation of a curvature singularity at time t = t(c) as demonstrated by Moore (Proc. R. Soc. Lond. A, vol. 365, issue 1720, 1979, pp. 105-119). The Moore analysis is extended to provide the small-amplitude, full-sheet structure at t = t(c) for a general single-mode initial condition in terms of polylogarithmic functions, from which its asymptotic form near the singular point is determined. This defines an intermediate evolution problem for which the leading-order, and most singular, approximation is solved as a Taylor-series expansion in tau = t - t(c), where coefficients are calculated by repeated differentiation of the defining Birkhoff-Rott (BR) equation. The first few terms are in good agreement with numerical calculation based on the full-sheet solution. The series is summed, providing an analytic continuation which shows sheet rupture at circulation F = 0(+), tau > 0(+), but with non-physical features owing to the absence of end-tip sheet roll up. This is corrected by constructing an inner solution with Gamma < tau, as a perturbed similarity form with small parameter tau (1/2). Numerical solutions of both the inner, nonlinear zeroth-order and first-order linear BR equations are obtained whose outer limits match the intermediate solution. The composite solution shows sheet tearing at tau = 0(+) into two separate, rolled up algebraic spirals near the central singular point. Branch separation distance scales as tau with a non-local, tau(3/2) correction. Properties of the intermediate and inner solutions are discussed.
Keyword:
vortex dynamics
期刊
IF:
3.9
论文数:
2.0W
被引数:
9.4W
机构
引用论文
Self-similar roll-up of a vortex sheet driven by a shear flow: Hyperbolic double spiral.png)
PHYSICS OF FLUIDS
PHYSICS OF FLUIDSIF4.3
PREAI
分享收藏ODIN-WIND: An Overview of the Decommissioning Process for Offshore Wind TurbinesODIN-WIND：海上风力涡轮机退役过程概述MARE-WINT
MARE-WINTIF0
PREAI
分享收藏An upper bound on Pluto's heat flux from a lack of flexural response of its normal faults由于缺乏正常故障的弯曲响应，冥王星的热通量上限Icarus
IcarusIF0
PREAI
分享收藏分享收藏A Novel Immune Evasion Mechanism of LMP-1, an EBV-Primary Oncogene, in Nasopharyngeal CarcinomaEBV原发性致癌基因LMP-1在鼻咽癌中的一种新型免疫逃逸机制
OAAI
OAAI分享收藏
查看更多内容