Stability of Rossby–Haurwitz waves. (22nd December 2019)

• Record Type: Journal Article
• Authors: Bénard, P.
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 146:Number 727(2020)
• Page Start: 613
• Page End: 628
• Publication Date: 2019-12-22
• Subjects: application/context -- atmosphere -- climate -- dynamic/processes -- dynamical Stability, geophysical sphere -- rossby waves, tools and methods; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.3696
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract: Exploiting a factorized form of the linear perturbation equation valid around Rossby–Haurwitz waves in the nonlinear barotropic vorticity equation system on the sphere, an elementary discrete numerical method for analysing the stability of these waves is proposed. In contrast with former approaches based on wave‐interaction theory and its cumbersome triad‐interaction coefficients, the discrete analysis proposed here is inspired by the spectral‐transform technique, where nonlinearities are treated in physical space. This approach, based only on standard linear algebra techniques, is simpler than former ones and allows a large number of degrees of freedom to be retained in perturbation space. The merits and possible limitations of the method are discussed; some validations and results are presented. Abstract : Maps of the most unstable modes for the Rossby‐Haurwitz wave (m = 4, n = 5) at the onset of instability (left) and at a twice larger amplitude (right). Abscissae: longitude (in degrees); ordinates: latitude (in degrees). For each mode, only half of the longitude domain is represented. The amplitude of both unstable modes is normalized to span the interval [−1, 1].