Gnevyshev, Vladimir G.; Shrira, Victor I. On the evaluation of barotropic-baroclinic instability parameters of zonal flows on a beta-plane. (English) Zbl 0715.76027 J. Fluid Mech. 221, 161-181 (1990). Summary: The paper is concerned with the problem of the linear stability of an arbitrary inviscid zonal flow on a \(\beta\)-plane. Based on the analysis of integral relations following from the linear boundary-value problem, new evaluations, considerably more exact than the previously known ones, of the parameter region of unstable disturbances are derived. Some new relations among these bounds are established. Cited in 3 Documents MSC: 76E20 Stability and instability of geophysical and astrophysical flows 76B60 Atmospheric waves (MSC2010) 86A10 Meteorology and atmospheric physics Keywords:linear stability; arbitrary inviscid zonal flow; \(\beta \) -plane; linear boundary-value problem PDFBibTeX XMLCite \textit{V. G. Gnevyshev} and \textit{V. I. Shrira}, J. Fluid Mech. 221, 161--181 (1990; Zbl 0715.76027) Full Text: DOI References: [1] DOI: 10.1016/0377-0265(80)90020-2 · doi:10.1016/0377-0265(80)90020-2 [2] Gnevyshev, Izv. Akad. Nauk. SSSR Atmos. Ocean. Phys. 4 pp 135– (1990) [3] Charney, J. Met. 4 pp 135– (1947) · doi:10.1175/1520-0469(1947)004<0136:TDOLWI>2.0.CO;2 [4] Romanova, Izv. Akad. Sci. SSSR, Atmos. Ocean. Phys. 23 pp 269– (1987) [5] Rayleigh, Proc. Lond. Math. Soc. 9 pp 57– (1880) [6] Miles, Rev. Geophys. 2 pp 155– (1964) [7] DOI: 10.1175/1520-0469(1964)021 2.0.CO;2 · doi:10.1175/1520-0469(1964)021 2.0.CO;2 [8] DOI: 10.1017/S0022112084000471 · doi:10.1017/S0022112084000471 [9] DOI: 10.1017/S0022112079000276 · Zbl 0395.76026 · doi:10.1017/S0022112079000276 [10] DOI: 10.1016/0377-0265(80)90013-5 · doi:10.1016/0377-0265(80)90013-5 [11] DOI: 10.1017/S0022112061000317 · Zbl 0104.20704 · doi:10.1017/S0022112061000317 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.