Yang, Huijun The central barrier, asymmetry and random phase in chaotic transport and mixing by Rossby waves in a jet. (English) Zbl 0967.76580 Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 6, 1131-1152 (1998). Summary: The central barrier, asymmetry and random perturbation in transport and mixed by Rossby waves in a jet were investigated by simple kinematic model. Two complementary methods were used: A high-resolution Lagrangian field advection model (FAM), and a finite-time Lyapunov exponential analysis. The present study revealed the following: (1) A central barrier can be formed in two Rossby waves without shear flow as well as in a jet, (2) the central barrier may occur in the region with maximum jet speed relative to the phase speed of the traveling wave, whereas the chaotic mixing most likely occurs near the critical lines; the central barrier widens as the phase speed of traveling waves relative to the jet speed increases, (3) asymmetry of wave-breaking is directly related to asymmetry of the critical line location in a jet, (4) the central barrier survives small random perturbations, (5) global bifurcation from a homoclinic orbit to a heteroclinic orbit and global chaos are two main mechanisms for the central barrier destruction. The results suggest that the small scale motions and random processes may not significantly affect the major character of Lagrangian transport and mixing by large-scale geophysical flow. Also potential vorticity mixing provides a unique kinematic and dynamic view of many features of the geophysical flow. Cited in 2 Documents MSC: 76M35 Stochastic analysis applied to problems in fluid mechanics 76B65 Rossby waves (MSC2010) 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology Keywords:Rossby waves in jet; central barrier; asymmetry; random perturbation; transport; Lagrangian field advection model; finite-time Lyapunov exponential analysis; chaotic mixing; global bifurcation; homoclinic orbit; heteroclinic orbit; global chaos PDFBibTeX XMLCite \textit{H. Yang}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 6, 1131--1152 (1998; Zbl 0967.76580) Full Text: DOI References: [1] DOI: 10.1017/S0022112084001233 · Zbl 0559.76085 [2] DOI: 10.1063/1.858052 [3] DOI: 10.1175/1520-0485(1991)021<0173:ASKMFM>2.0.CO;2 [4] DOI: 10.1175/1520-0485(1985)015<0024:TGSOB>2.0.CO;2 [5] DOI: 10.1175/1520-0485(1989)019<1177:EOCFEP>2.0.CO;2 [6] DOI: 10.1016/0370-1573(79)90023-1 [7] DOI: 10.1017/S0022112088003088 · Zbl 0645.76024 [8] DOI: 10.1063/1.858639 · Zbl 0781.76017 [9] DOI: 10.1175/1520-0469(1989)046<3416:BDOBWI>2.0.CO;2 [10] DOI: 10.1038/328590a0 [11] DOI: 10.1017/S0022112085003019 · Zbl 0676.76040 [12] DOI: 10.1175/1520-0469(1985)042<1536:VITSAA>2.0.CO;2 [13] DOI: 10.1175/1520-0485(1994)024<1641:CFMIAM>2.0.CO;2 [14] DOI: 10.1016/0021-9169(89)90071-8 [15] DOI: 10.1016/0021-9169(84)90063-1 [16] DOI: 10.1175/1520-0469(1994)051<2031:TEOFAO>2.0.CO;2 [17] DOI: 10.1063/1.858053 [18] DOI: 10.1080/03091929108227343 [19] DOI: 10.1175/1520-0469(1993)050<2462:GCMOIS>2.0.CO;2 [20] DOI: 10.1146/annurev.fl.27.010195.002223 [21] DOI: 10.1175/1520-0469(1992)049<0462:RWBMFA>2.0.CO;2 [22] DOI: 10.1175/1520-0469(1991)048<0688:PSSOTE>2.0.CO;2 [23] DOI: 10.1175/1520-0485(1992)022<0431:FEAAMJ>2.0.CO;2 [24] DOI: 10.1142/S0218127493001136 · Zbl 0922.76075 [25] DOI: 10.1142/S0218127493000830 · Zbl 0925.70164 [26] DOI: 10.1175/1520-0469(1995)052<1513:TDTOTE>2.0.CO;2 [27] DOI: 10.1175/1520-0485(1996)026<0115:TSGEIT>2.0.CO;2 [28] DOI: 10.1175/1520-0485(1996)026<2480:LMOPVH>2.0.CO;2 [29] Yang H., Nonlin. World 4 pp 323– (1997) [30] DOI: 10.1175/1520-0485(1997)027<1258:TTDCTA>2.0.CO;2 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.