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Resonance Enhancement by Suitably Chosen Frequency Detuning

Author

Listed:
  • Denys Dutykh

    (Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France
    LAMA UMR 5127, CNRS, Université Savoie Mont Blanc, Campus Scientifique, 73376 Le Bourget-du-Lac CEDEX, France
    These authors contributed equally to this work.)

  • Elena Tobisch

    (Institute of Analysis, Johannes Kepler University, 4040 Linz, Austria
    These authors contributed equally to this work.)

Abstract

The theory of exact resonances (kinematics and dynamics) is well developed while even the very concept of detuned resonance is ambiguous and only studies of their kinematic characteristics (that is, those not depending on time) are available in the literature. In this paper, we report novel effects enforced by the resonance detuning on solutions of the dynamical system describing interactions of three spherical planetary waves. We establish that the energy variation range can significantly exceed the range of the exact resonance for suitably chosen values of the detuning. The asymmetry of system’s solutions with respect to the sign of the detuning parameter is demonstrated. Finally, a non-monotonic dependence of the energy oscillation period with respect to detuning magnitude is discovered. These results have direct implications in physics of atmosphere, e.g., for prediction of weather extremes in the Northern Hemisphere midlatitudes ( Proc. Nat. Acad. Sci. USA 2016 , 133 (25), 6862–6867). Moreover, similar study can be conducted for a generic three-wave system taken in the Hamiltonian form which makes our results applicable for an arbitrary Hamiltonian three-wave system met in climate prediction theory, geophysical fluid dynamics, plasma physics, etc.

Suggested Citation

  • Denys Dutykh & Elena Tobisch, 2020. "Resonance Enhancement by Suitably Chosen Frequency Detuning," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:450-:d:334595
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    References listed on IDEAS

    as
    1. Kartashova, Elena & Kartashov, Alexey, 2007. "Laminated wave turbulence: Generic algorithms iii," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 66-74.
    2. Elena Kartashova & Alexey Kartashov, 2006. "Laminated Wave Turbulence: Generic Algorithms I," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(11), pages 1579-1596.
    3. Gitterman, M., 2010. "Spring pendulum: Parametric excitation vs an external force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3101-3108.
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