Summary
The eigenvalue approach is adopted to study briefly the linear barotropic instability of Rossby wave motion. It is discovered that the doubling time of barotropically unstable Rossby wave motion is quite realistic provided the amplitude of basic Rossby wave motion is calculated depending on the order of magnitude of meridional wind, permitted by the synoptic scale of motion.
The main object of the present study is to deal with the quasi-linear barotropic instability of Rossby wave motion by including the nonlinear product term of perturbation in the basic flow equation. It is found that there is a regular periodic oscillation between the basic Rossby wave motion and the perturbation zonal flow. The oscillation occurs on the time scale of “weeks” which is in agreement with observational facts.
Zusammenfassung
Eine Eigenwertmethode wurde zur Untersuchung der linearen barotropen Instabilität von Rossbywellen angewendet. Es konnte gezeigt werden, daß die Verdopplungszeit der barotrop-instabilen Rossbywellenbewegung realistische Werte ergibt, wenn die Amplitude der zugrundeliegenden Rossbywellen in Abhängigkeit von der Stärke des Meridionalwindes berechnet wird, der bei Systemen synoptischer Größenordnung auftritt.
In der vorliegenden Studie wird hauptsächlich die Instabilität von Rossbywellen unter Einbeziehung der nichtlinearen Produktterme in die Störungsglieder der Grundströmungsgleichung untersucht. Es tritt dabei eine regelmäßige, periodische Schwankung zwischen den Rossbywellen und der Störung der Zonalströmung auf. Diese Oszillation besitzt eine zeitliche Größenordnung von „Wochen” und steht somit in guter Übereinstimmung mit Beobachtungen.
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Mahanti, A.C. The oscillation between Rossby wave and zonal flow in a barotropic fluid. Arch. Met. Geoph. Biocl. A. 30, 211–225 (1981). https://doi.org/10.1007/BF02257844
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DOI: https://doi.org/10.1007/BF02257844