Scott, Richard K. A scenario for finite-time singularity in the quasigeostrophic model. (English) Zbl 1241.76227 J. Fluid Mech. 687, 492-502 (2011). Summary: A possible route to finite-time singularity in the quasigeostrophic system, via a cascade of filament instabilities of geometrically decreasing spatial and temporal scales, is investigated numerically using a high-resolution hybrid contour dynamical algorithm. A number of initial temperature distributions are considered, of varying degrees of continuity. In all cases, primary, secondary, and tertiary instabilities are apparent before the algorithm loses accuracy due to limitations of finite resolution. Filament instability is also shown to be potentially important in the closing saddle scenario investigated in many previous studies. The results do not provide a rigorous demonstration of finite-time singularity, but suggest avenues for further investigation. Cited in 19 Documents MSC: 76E20 Stability and instability of geophysical and astrophysical flows 86A05 Hydrology, hydrography, oceanography 86A10 Meteorology and atmospheric physics Keywords:geophysical and geological flows; instability PDFBibTeX XMLCite \textit{R. K. Scott}, J. Fluid Mech. 687, 492--502 (2011; Zbl 1241.76227) Full Text: DOI Link References: [1] DOI: 10.1103/PhysRevE.81.016301 · doi:10.1103/PhysRevE.81.016301 [2] DOI: 10.1175/1520-0469(1978)035<0774:UPVFPI>2.0.CO;2 · doi:10.1175/1520-0469(1978)035<0774:UPVFPI>2.0.CO;2 [3] DOI: 10.1063/1.869184 · Zbl 1185.76841 · doi:10.1063/1.869184 [4] DOI: 10.1002/qj.49712354015 · doi:10.1002/qj.49712354015 [5] DOI: 10.1175/1520-0469(1995)052<3247:IOSAUT>2.0.CO;2 · doi:10.1175/1520-0469(1995)052<3247:IOSAUT>2.0.CO;2 [6] DOI: 10.1080/03091929.2010.485997 · doi:10.1080/03091929.2010.485997 [7] DOI: 10.1175/1520-0469(1994)051<2756:QDOTT>2.0.CO;2 · doi:10.1175/1520-0469(1994)051<2756:QDOTT>2.0.CO;2 [8] DOI: 10.1016/0167-7977(89)90004-X · doi:10.1016/0167-7977(89)90004-X [9] DOI: 10.1175/1520-0469(1982)039<0707:CMOFDB>2.0.CO;2 · doi:10.1175/1520-0469(1982)039<0707:CMOFDB>2.0.CO;2 [10] DOI: 10.1073/pnas.0501977102 · Zbl 1135.76315 · doi:10.1073/pnas.0501977102 [11] DOI: 10.1175/1520-0469(1972)029<0011:AFMMFA>2.0.CO;2 · doi:10.1175/1520-0469(1972)029<0011:AFMMFA>2.0.CO;2 [12] DOI: 10.1017/S0022112095000012 · Zbl 0832.76012 · doi:10.1017/S0022112095000012 [13] DOI: 10.2307/121037 · Zbl 0920.35109 · doi:10.2307/121037 [14] DOI: 10.1016/j.jcp.2009.01.015 · Zbl 1159.76031 · doi:10.1016/j.jcp.2009.01.015 [15] DOI: 10.1016/S0375-9601(98)00108-X · Zbl 0974.76512 · doi:10.1016/S0375-9601(98)00108-X [16] DOI: 10.1017/S0022112091000915 · Zbl 0728.76045 · doi:10.1017/S0022112091000915 [17] DOI: 10.1088/0951-7715/7/6/001 · Zbl 0809.35057 · doi:10.1088/0951-7715/7/6/001 [18] DOI: 10.1016/0167-2789(95)00102-A · Zbl 0899.76103 · doi:10.1016/0167-2789(95)00102-A [19] DOI: 10.1016/0960-0779(94)90140-6 · Zbl 0823.76034 · doi:10.1016/0960-0779(94)90140-6 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.