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Ellipsoidal Vortices in Compressible Rotating Fluidтезисы доклада
- Авторы: Rozanova O.S., Turzynsky M.K/
- Сборник: BOOK OF ABSTRACTS, Eleventh International Conference on Application of Mathematics in Technical and Natural Sciences 20-25 June 2019, Albena, Bulgaria
- Тезисы
- Год издания: 2019
- Место издания: Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences Sophia
- Первая страница: 77
- Последняя страница: 77
- Аннотация: We study vortices in 2D polytropic uniformly rotating compressible fluid within the class of motions with uniform deformation. In the Eulerian coordinates, it implies that the velocity is a linear function of coordinates and the level lines of the pressure are ellipses. It is shown that this class of solutions is completely defined by a system of quadratically nonlinear ODEs of a higher order. Under certain assumption this system is integrable. In particular, it happens for the adiabatic index equal to 2. Formally this case corresponds to the case of shallow water on a rotating plane. The equilibria of this system form two families. One of them is one-parametric, it corresponds to a vortex, and the parameter is the intensity of vortex. We show that the nonlinear stability of these steady vortices for the physically meaningful adiabatic indices depends only on the ratio between the parameter of intensity of the vortex and the Coriolis parameter. It is shown that if the rotation of the coordinate frame presents, the domain of stability exists both for anticyclonic and cyclonic cases, nevertheless it shrinks if the Coriolis parameter tends to zero. Another family is two-parametric, it corresponds to the shear, and the equilibria are always unstable. Both families of equilibria are prototypic for elementary atmospheric structures like cyclone/anticyclone and trough/ridge.
- Добавил в систему: Розанова Ольга Сергеевна