2002/08/08 by Young‐Suk Lee, Youngsuk Lee, Leslie Smith +1 · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Oceanographic and Atmospheric Processes #physics.ao-ph
paper · pdf · doi:10.1016/s0167-2789(03)00010-1
56 pages, 31 figures, submitted to Physica D
arxiv created 2002/08/08 · openalex publication_date 2003/04/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Floquet theory is used to describe the unstable spectrum at large scales of the beta-plane equation linearized about Rossby waves. Base flows consisting of one to three Rossby wave are considered analytically using continued fractions and the method of multiple scales, while base flow with more than three Rossby waves are studied numerically. It is demonstrated that the mechanism for instability changes from inflectional to triad resonance at an O(1) transition Rhines number Rh, independent of the Reynolds number. For a single Rossby wave base flow, the critical Reynolds number Rec for instability is found in various limits. In the limits Rh --> infinity and k --> 0, the classical value Rec = sqrt(2) is recovered. For Rh --> 0 and all orientations of the Rossby wave except zonal and meridional, the base flow is unstable for all Reynolds numbers; a zonal Rossby wave is stable, while a meridional Rossby wave has critical Reynolds number Rec = sqrt(2). For more isotropic base flows consisting of many Rossby waves (up to forty), the most unstable mode is purely zonal for 2 <= Rh < infinity and is nearly zonal for Rh = 1/2, where the transition Rhines number is again O(1), independent of the Reynolds number and consistent with a change in the mechanism for instability from inflectional to triad resonance.