Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case
Author(s):
Kilin A. A., Gavrilova A. M., Artemova E. M.
This paper is concerned with the plane-parallel motion of an elliptic foil with an
attached vortex of constant strength in an ideal fluid. Special attention is given to the case in
which the vortex lies on the continuation of one of the semiaxes of the ellipse. It is shown that
in this case there exist no attracting solutions and the system is integrable by the Euler – Jacobi
theorem. A complete qualitative analysis of the equations of motion is carried out for cases where
the vortex lies on the continuation of the large or the small semiaxis of the ellipse. Possible
types of trajectories of an elliptic foil with an attached vortex are established: quasi-periodic,
unbounded (going to infinity) and periodic trajectories.
Keywords:
ideal fluid, elliptic foil, point vortex, integrable system, bifurcation analysis
✖
Мы используем cookie-файлы и сервис Яндекс.Метрики для анализа работы сайта, статистики и улучшения его работы. Продолжая использовать данный сайт, Вы соглашаетесь с условиями Пользовательского соглашения и условиями использования сервиса Яндекс.Метрика, а также выражаете своё согласие на использование cookie-файлов и на обработку своих персональных данных в соответствии с Политикой конфиденциальности. Вы можете запретить обработку cookies в настройках браузера.
We use cookies and Yandex.Metrica service to analyze the usage of our web-site and improve its performance. By continuing to use this website, you agree to the terms of the User Agreement and the terms of Yandex.Metrica service, and give your consent to the Cookies Policy and to the processing of your personal data in accordance with the Privacy Policy. You may deactivate cookies in your browser settings.