A study of the interactions between uniform and pointwise vortices in an inviscid fluid

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2016-03-01 DOI:10.1515/caim-2016-0016

G. Riccardi

引用次数: 1

Abstract

Abstract The planar interactions between pair of vortices in an inviscid fluid are analytically investigated, by assuming one of the two vortices pointwise and the other one uniform. A novel approach using the Schwarz function of the boundary of the uniform vortex is adopted. It is based on a new integral relation between the (complex) velocity induced by the uniform vortex and its Schwarz function and on the time evolution equation of this function. They lead to a singular integrodifferential problem. Even if this problem is strongly nonlinear, its nonlinearities are confined inside two terms, only. As a consequence, its solution can be analytically approached by means of successive approximations. The ones at 0th (nonlinear terms neglected) and 1st (nonlinear terms evaluated on the 0-order solution) orders are calculated and compared with contour dynamics simulations of the vortex motion. A satisfactory agreement is keept for times which are small with respect to the turn-over time of the vortex pair.

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无粘流体中均匀涡与点状涡相互作用的研究

摘要在无粘流体中，假设两个涡旋中的一个为点向，另一个为均匀涡旋，对涡旋对之间的平面相互作用进行了解析研究。采用了一种利用均匀涡边界的Schwarz函数的新方法。它是基于均匀涡诱导的(复)速度与其Schwarz函数之间的一种新的积分关系以及该函数的时间演化方程。它们导致一个奇异的积分微分问题。即使这个问题是强非线性的，它的非线性也仅限于两项。因此，它的解可以用逐次逼近的方法解析逼近。计算了第0阶(非线性项忽略)和第1阶(非线性项在0阶解上求值)的涡场，并与涡旋运动的轮廓动力学模拟进行了比较。对于相对于旋涡对的翻转时间较小的时间，保持令人满意的一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.