A preliminary investigation of the pseudo-spectral method numerical solution of the Perkins instability equations in the homogeneous TEC case

Qina Zhou, John David Mathews, Qiang Du, Clark A. Miller

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    A pseudo-spectral method code is developed to simulate the electrodynamic instability (spread-F) behavior of the mid-latitude ionosphere by numerically solving two of the Perkins (J. Geophys. Res. 78 (1973) 218) equations. This work follows that of Miller (On gravity waves and the electrodynamics of the mid-latitude ionosphere, Ph.D. Thesis, Cornell University, 1996) and provides extensions in both the solution method-resulting in more precise, efficient and robust solutions-and in the range of solutions investigated. In the linear instability-development stage, the simulation result is consistent with the Perkins (1973) predictions, yielding relative differences of less than 0.6%. A random initial condition case like that of Miller (1996) is carried out with the result agreeing with Miller's result obtained in a different manner. In addition, the effect of non-linearity of the equation system is observed. The range of initial conditions investigated indicates that over a large wavelength range, self-similar ionospheric instability structures (Geophys. Res. Lett. 28 (2001) 4167) can be generated in conductivity and potential (the field-line integrated electron concentration is constant). Further, by using dual-wave-mode excitation with suitable parameters, saturation of the instability process is observed. Some dual-mode excitation processes are very different from the single-mode excitation case in many respects-especially in wavelength dependence. The turbulent saturation is observed in simulation to be caused by the E×B instability that requires a sharp conductivity gradient at the backside of the drift movement. On the other hand, other dual-mode excitation processes do not display a saturation state. In this case, the process converges to and then follows the path of the corresponding single-mode excitation example.

    Original languageEnglish (US)
    Pages (from-to)325-335
    Number of pages11
    JournalJournal of Atmospheric and Solar-Terrestrial Physics
    Volume67
    Issue number4
    DOIs
    StatePublished - Mar 1 2005

    Fingerprint

    spectral methods
    numerical method
    electrodynamics
    excitation
    saturation
    ionospheres
    ionosphere
    conductivity
    wavelength
    spread F
    theses
    gravity waves
    wavelengths
    gravity wave
    nonlinearity
    ionospherics
    simulation
    electron
    gradients
    prediction

    All Science Journal Classification (ASJC) codes

    • Geophysics
    • Atmospheric Science
    • Space and Planetary Science

    Cite this

    @article{7cd64f4f60cc40899f7673ee1ccbce2a,
    title = "A preliminary investigation of the pseudo-spectral method numerical solution of the Perkins instability equations in the homogeneous TEC case",
    abstract = "A pseudo-spectral method code is developed to simulate the electrodynamic instability (spread-F) behavior of the mid-latitude ionosphere by numerically solving two of the Perkins (J. Geophys. Res. 78 (1973) 218) equations. This work follows that of Miller (On gravity waves and the electrodynamics of the mid-latitude ionosphere, Ph.D. Thesis, Cornell University, 1996) and provides extensions in both the solution method-resulting in more precise, efficient and robust solutions-and in the range of solutions investigated. In the linear instability-development stage, the simulation result is consistent with the Perkins (1973) predictions, yielding relative differences of less than 0.6{\%}. A random initial condition case like that of Miller (1996) is carried out with the result agreeing with Miller's result obtained in a different manner. In addition, the effect of non-linearity of the equation system is observed. The range of initial conditions investigated indicates that over a large wavelength range, self-similar ionospheric instability structures (Geophys. Res. Lett. 28 (2001) 4167) can be generated in conductivity and potential (the field-line integrated electron concentration is constant). Further, by using dual-wave-mode excitation with suitable parameters, saturation of the instability process is observed. Some dual-mode excitation processes are very different from the single-mode excitation case in many respects-especially in wavelength dependence. The turbulent saturation is observed in simulation to be caused by the E×B instability that requires a sharp conductivity gradient at the backside of the drift movement. On the other hand, other dual-mode excitation processes do not display a saturation state. In this case, the process converges to and then follows the path of the corresponding single-mode excitation example.",
    author = "Qina Zhou and Mathews, {John David} and Qiang Du and Miller, {Clark A.}",
    year = "2005",
    month = "3",
    day = "1",
    doi = "10.1016/j.jastp.2004.10.005",
    language = "English (US)",
    volume = "67",
    pages = "325--335",
    journal = "Journal of Atmospheric and Solar-Terrestrial Physics",
    issn = "1364-6826",
    publisher = "Elsevier Limited",
    number = "4",

    }

    A preliminary investigation of the pseudo-spectral method numerical solution of the Perkins instability equations in the homogeneous TEC case. / Zhou, Qina; Mathews, John David; Du, Qiang; Miller, Clark A.

    In: Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 67, No. 4, 01.03.2005, p. 325-335.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A preliminary investigation of the pseudo-spectral method numerical solution of the Perkins instability equations in the homogeneous TEC case

    AU - Zhou, Qina

    AU - Mathews, John David

    AU - Du, Qiang

    AU - Miller, Clark A.

    PY - 2005/3/1

    Y1 - 2005/3/1

    N2 - A pseudo-spectral method code is developed to simulate the electrodynamic instability (spread-F) behavior of the mid-latitude ionosphere by numerically solving two of the Perkins (J. Geophys. Res. 78 (1973) 218) equations. This work follows that of Miller (On gravity waves and the electrodynamics of the mid-latitude ionosphere, Ph.D. Thesis, Cornell University, 1996) and provides extensions in both the solution method-resulting in more precise, efficient and robust solutions-and in the range of solutions investigated. In the linear instability-development stage, the simulation result is consistent with the Perkins (1973) predictions, yielding relative differences of less than 0.6%. A random initial condition case like that of Miller (1996) is carried out with the result agreeing with Miller's result obtained in a different manner. In addition, the effect of non-linearity of the equation system is observed. The range of initial conditions investigated indicates that over a large wavelength range, self-similar ionospheric instability structures (Geophys. Res. Lett. 28 (2001) 4167) can be generated in conductivity and potential (the field-line integrated electron concentration is constant). Further, by using dual-wave-mode excitation with suitable parameters, saturation of the instability process is observed. Some dual-mode excitation processes are very different from the single-mode excitation case in many respects-especially in wavelength dependence. The turbulent saturation is observed in simulation to be caused by the E×B instability that requires a sharp conductivity gradient at the backside of the drift movement. On the other hand, other dual-mode excitation processes do not display a saturation state. In this case, the process converges to and then follows the path of the corresponding single-mode excitation example.

    AB - A pseudo-spectral method code is developed to simulate the electrodynamic instability (spread-F) behavior of the mid-latitude ionosphere by numerically solving two of the Perkins (J. Geophys. Res. 78 (1973) 218) equations. This work follows that of Miller (On gravity waves and the electrodynamics of the mid-latitude ionosphere, Ph.D. Thesis, Cornell University, 1996) and provides extensions in both the solution method-resulting in more precise, efficient and robust solutions-and in the range of solutions investigated. In the linear instability-development stage, the simulation result is consistent with the Perkins (1973) predictions, yielding relative differences of less than 0.6%. A random initial condition case like that of Miller (1996) is carried out with the result agreeing with Miller's result obtained in a different manner. In addition, the effect of non-linearity of the equation system is observed. The range of initial conditions investigated indicates that over a large wavelength range, self-similar ionospheric instability structures (Geophys. Res. Lett. 28 (2001) 4167) can be generated in conductivity and potential (the field-line integrated electron concentration is constant). Further, by using dual-wave-mode excitation with suitable parameters, saturation of the instability process is observed. Some dual-mode excitation processes are very different from the single-mode excitation case in many respects-especially in wavelength dependence. The turbulent saturation is observed in simulation to be caused by the E×B instability that requires a sharp conductivity gradient at the backside of the drift movement. On the other hand, other dual-mode excitation processes do not display a saturation state. In this case, the process converges to and then follows the path of the corresponding single-mode excitation example.

    UR - http://www.scopus.com/inward/record.url?scp=13444260762&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=13444260762&partnerID=8YFLogxK

    U2 - 10.1016/j.jastp.2004.10.005

    DO - 10.1016/j.jastp.2004.10.005

    M3 - Article

    AN - SCOPUS:13444260762

    VL - 67

    SP - 325

    EP - 335

    JO - Journal of Atmospheric and Solar-Terrestrial Physics

    JF - Journal of Atmospheric and Solar-Terrestrial Physics

    SN - 1364-6826

    IS - 4

    ER -