Tracking of the development of a vortex ring in isotropic turbulence

Document Type : Original Article

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1 Department of Mathematics Suez University, Suez, Egypt

2 Department of Mathematics, Suez University, Suez, Egypt

3 Department of Mathematics, Suez University, Suez, Egypt.

Abstract

In the current study, the isotropic turbulence, and the lattice Boltzmann method (LBM) are utilized as helpful tools to track the development of a vortex ring in isotropic turbulence. A vortex ring is isolated from a decaying turbulent flow with a resolution of 〖128〗^3, and three different approaches are considered to deal with the single vortex ring. The first case has started at null velocity, considering the vortex ring as a forcing source where the velocity modes at low wavenumbers are calculated using the stored vorticity data from the Poisson equation ∇ ⃑×w ⃑=-∇^2 u ⃑ in the Fourier space. Then, large tubular vortices are found, and the ring has broken as a result of being an external force every time step. In the second case, the vortex ring is used as an initial state and left to dissipate, and large tubular vortices are formed around the ring due to the presence of a tube source. Finally, an initial state from a forced turbulent flow is used, and the vortex ring is also utilized as a forcing source every time step in the LBM. The vortex ring has broken and interacted with the tubular vortices from the forced turbulence forming a variety of thin tubular vortices. The three cases are studied and compared, moreover, some statistical features of the flow field are calculated such as the Taylor-Reynolds number〖 R〗_λ, the Taylor micro-scale λ, the Kolmogorov micro-scale η, and the energy spectrum function E(k).

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