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Title: | Stochastic differential equation models of vortex merging and reconnection |
Authors: | Kevlahan, N.K.-R. |
Keywords: | vortex;reconnection;stochastic differential equations |
Publication Date: | 3-Jun-2005 |
Publisher: | American Institute of Physics |
Citation: | Kevlahan, N.K.-R. 2005 Stochastic differential equation models of vortex merging and reconnection. Phys. Fluids. 17, 064107 (16 pp). |
Series/Report no.: | Phys. Fluids;065107 |
Abstract: | We show that the stochastic differential equation SDE model for the merger of two identical two-dimensional vortices proposed by Agullo and Verga “Exact two vortices solution of Navier– Stokes equation,” Phys. Rev. Lett. 78, 2361 1997 is a special case of a more general class of SDE models for N interacting vortex filaments. These toy models include vorticity diffusion via a white noise forcing of the inviscid equations, and thus extend inviscid models to include core dynamics and topology change e.g., merger in two dimensions and vortex reconnection in three dimensions. We demonstrate that although the N=2 two-dimensional model is qualitatively and quantitatively incorrect, it can be dramatically improved by accounting for self-advection. We then extend the two-dimensional SDE model to three dimensions using the semi-inviscid asymptotic approximation of Klein et al. “Simplified equations for the interactions of nearly parallel vortex filaments,” J. Fluid Mech. 288, 201 1995 for nearly parallel vortices. This model is nonsingular and is shown to give qualitatively reasonable results until the approximation of nearly parallel vortices fails. We hope these simple toy models of vortex reconnection will eventually provide an alternative perspective on the essential physical processes involved in vortex merging and reconnection. |
URI: | http://hdl.handle.net/11375/16834 |
Identifier: | DOI:10.1063/1.1932310 |
Appears in Collections: | Mathematics & Statistics Publications |
Files in This Item:
File | Description | Size | Format | |
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physfluids_v17.pdf | Main article | 689.2 kB | Adobe PDF | View/Open |
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