Dynamics of a nonlinear dipole vortex

J.S. Hesthaven, Jens-Peter Lynov, A.H. Nielsen, J. Juul Rasmussen, M.R. Schmidt, E.G. Shapiro, S.K. Turitsyn

    Research output: Contribution to journalJournal articleResearch

    Abstract

    A localized stationary dipole solution to the Euler equations with a relationship between the vorticity and streamfunction given as omega=-psi+psi(3) is presented. By numerical integration of the Euler equations this dipole is shown to be unstable. However, the initially unstable dipole reorganizes itself into a new nonlinear dipole, which is found to be stable. This new structure has a functional relationship given as omega=alpha psi+beta psi(3)-gamma psi(5). Such dipoles are stable to head-on collisions and they are capable of creating tripolar structures when colliding off axis. The effects of increasing Newtonian viscosity on the nonlinear dipole is studied revealing that even though the nonlinearity is weakening, the dipole does not relax towards a Lamb dipole. (C) 1995 American Institute of Physics.
    Original languageEnglish
    JournalPhysics of Fluids
    Volume7
    Issue number9
    Pages (from-to)2220-2229
    ISSN1070-6631
    DOIs
    Publication statusPublished - 1995

    Cite this

    Hesthaven, J. S., Lynov, J-P., Nielsen, A. H., Juul Rasmussen, J., Schmidt, M. R., Shapiro, E. G., & Turitsyn, S. K. (1995). Dynamics of a nonlinear dipole vortex. Physics of Fluids, 7(9), 2220-2229. https://doi.org/10.1063/1.868470
    Hesthaven, J.S. ; Lynov, Jens-Peter ; Nielsen, A.H. ; Juul Rasmussen, J. ; Schmidt, M.R. ; Shapiro, E.G. ; Turitsyn, S.K. / Dynamics of a nonlinear dipole vortex. In: Physics of Fluids. 1995 ; Vol. 7, No. 9. pp. 2220-2229.
    @article{2de741a9c5c742d6b3ed3f3ae20168ae,
    title = "Dynamics of a nonlinear dipole vortex",
    abstract = "A localized stationary dipole solution to the Euler equations with a relationship between the vorticity and streamfunction given as omega=-psi+psi(3) is presented. By numerical integration of the Euler equations this dipole is shown to be unstable. However, the initially unstable dipole reorganizes itself into a new nonlinear dipole, which is found to be stable. This new structure has a functional relationship given as omega=alpha psi+beta psi(3)-gamma psi(5). Such dipoles are stable to head-on collisions and they are capable of creating tripolar structures when colliding off axis. The effects of increasing Newtonian viscosity on the nonlinear dipole is studied revealing that even though the nonlinearity is weakening, the dipole does not relax towards a Lamb dipole. (C) 1995 American Institute of Physics.",
    keywords = "Energimaterialer og ny energiteknologi",
    author = "J.S. Hesthaven and Jens-Peter Lynov and A.H. Nielsen and {Juul Rasmussen}, J. and M.R. Schmidt and E.G. Shapiro and S.K. Turitsyn",
    year = "1995",
    doi = "10.1063/1.868470",
    language = "English",
    volume = "7",
    pages = "2220--2229",
    journal = "Physics of Fluids",
    issn = "1070-6631",
    publisher = "American Institute of Physics",
    number = "9",

    }

    Hesthaven, JS, Lynov, J-P, Nielsen, AH, Juul Rasmussen, J, Schmidt, MR, Shapiro, EG & Turitsyn, SK 1995, 'Dynamics of a nonlinear dipole vortex', Physics of Fluids, vol. 7, no. 9, pp. 2220-2229. https://doi.org/10.1063/1.868470

    Dynamics of a nonlinear dipole vortex. / Hesthaven, J.S.; Lynov, Jens-Peter; Nielsen, A.H.; Juul Rasmussen, J.; Schmidt, M.R.; Shapiro, E.G.; Turitsyn, S.K.

    In: Physics of Fluids, Vol. 7, No. 9, 1995, p. 2220-2229.

    Research output: Contribution to journalJournal articleResearch

    TY - JOUR

    T1 - Dynamics of a nonlinear dipole vortex

    AU - Hesthaven, J.S.

    AU - Lynov, Jens-Peter

    AU - Nielsen, A.H.

    AU - Juul Rasmussen, J.

    AU - Schmidt, M.R.

    AU - Shapiro, E.G.

    AU - Turitsyn, S.K.

    PY - 1995

    Y1 - 1995

    N2 - A localized stationary dipole solution to the Euler equations with a relationship between the vorticity and streamfunction given as omega=-psi+psi(3) is presented. By numerical integration of the Euler equations this dipole is shown to be unstable. However, the initially unstable dipole reorganizes itself into a new nonlinear dipole, which is found to be stable. This new structure has a functional relationship given as omega=alpha psi+beta psi(3)-gamma psi(5). Such dipoles are stable to head-on collisions and they are capable of creating tripolar structures when colliding off axis. The effects of increasing Newtonian viscosity on the nonlinear dipole is studied revealing that even though the nonlinearity is weakening, the dipole does not relax towards a Lamb dipole. (C) 1995 American Institute of Physics.

    AB - A localized stationary dipole solution to the Euler equations with a relationship between the vorticity and streamfunction given as omega=-psi+psi(3) is presented. By numerical integration of the Euler equations this dipole is shown to be unstable. However, the initially unstable dipole reorganizes itself into a new nonlinear dipole, which is found to be stable. This new structure has a functional relationship given as omega=alpha psi+beta psi(3)-gamma psi(5). Such dipoles are stable to head-on collisions and they are capable of creating tripolar structures when colliding off axis. The effects of increasing Newtonian viscosity on the nonlinear dipole is studied revealing that even though the nonlinearity is weakening, the dipole does not relax towards a Lamb dipole. (C) 1995 American Institute of Physics.

    KW - Energimaterialer og ny energiteknologi

    U2 - 10.1063/1.868470

    DO - 10.1063/1.868470

    M3 - Journal article

    VL - 7

    SP - 2220

    EP - 2229

    JO - Physics of Fluids

    JF - Physics of Fluids

    SN - 1070-6631

    IS - 9

    ER -