Volume 45 Issue 1
Jan.  2024
Turn off MathJax
Article Contents
LIU Nan, SONG Jian. Stable Radiation Baroclinic Potential Vortices Under Basic Flow Zonal Shear[J]. Applied Mathematics and Mechanics, 2024, 45(1): 120-126. doi: 10.21656/1000-0887.440168
Citation: LIU Nan, SONG Jian. Stable Radiation Baroclinic Potential Vortices Under Basic Flow Zonal Shear[J]. Applied Mathematics and Mechanics, 2024, 45(1): 120-126. doi: 10.21656/1000-0887.440168

Stable Radiation Baroclinic Potential Vortices Under Basic Flow Zonal Shear

doi: 10.21656/1000-0887.440168
  • Received Date: 2023-06-01
  • Rev Recd Date: 2023-10-02
  • Publish Date: 2024-01-01
  • In large-scale vertical shear, a new type of stably propagating baroclinic vortex was embedded, to radiate Rossby waves without attenuation. Numerical simulations were carried out based on the 2-layer model in the beta-effect plane, by means of the variation of the dispersion relation between the zonal quadratic shear flow and the stable radiation of the baroclinic fluid. The effect of the zonal quadratic shear flow on the baroclinic potential vortex instability of steady radiation, was derived. At the same time, the Rossby waves generated by the vortices cause the propagation of the meridional vortices and other coherent heat flows. For the westward flow of the subtropical ocean, with the latitude change, the approximate solution of the trigonometric function gives the numerical solution of the relevant Bessel function. The results show that, the quadratic shear flow reduces the PV gradient in the upper layer and continues to extend the life of the vortex.
  • loading
  • [1]
    AGUEDIOU H, DADOU L, CHAIGNEAU A, et al. Eddies in the tropical Atlantic ocean and their seasonal variability[J]. Geophysical Research Letters, 2019, 46(21): 12156-12164. doi: 10.1029/2019GL083925
    [2]
    GALLET B, FERRARI R. The vortex gas scaling regime of baroclinic turbulence[J]. Proceeding of the National Academy of Sciences, 2020, 117(9): 4491-4497. doi: 10.1073/pnas.1916272117
    [3]
    ARBIC B K, FLIERL G R. Coherent vortices and kinetic energy ribbons in asymptotic, quasi two-dimensional f-plane turbulence[J]. Physics of Fluids, 2003, 15(8): 2177-2189. doi: 10.1063/1.1582183
    [4]
    王爽, 菅永军. 周期壁面电势调制下平行板微管道中的电磁电渗流动[J]. 应用数学和力学, 2020, 41(4): 396-405. doi: 10.21656/1000-0887.400151

    WANG Shuang, JIAN Yongjun. Magnetohydrodynamic electroosmotic flow in zeta potential patterned micro-parallel channels[J]. Applied Mathematics and Mechanics, 2020, 41(4): 396-405. (in Chinese)) doi: 10.21656/1000-0887.400151
    [5]
    FLIERL G R. Rossby wave radiation from a strongly nonlinear warm eddy[J]. Journal of Physical Oceanography, 1984, 14(1): 47-58. doi: 10.1175/1520-0485(1984)014<0047:RWRFAS>2.0.CO;2
    [6]
    NYCANDER J, SUTYRIN G G. Steadily translating anticyclones on the beta plane[J]. Dynamics of Atmospheres and Oceans, 1992, 16(6): 473-498. doi: 10.1016/0377-0265(92)90002-B
    [7]
    PAKYARI A, NYCANDER J. Steady two-layer vortices on the beta-plane[J]. Dynamics of Atmospheres and Oceans, 1996, 25(2): 67-86. doi: 10.1016/S0377-0265(96)00475-7
    [8]
    穆穆. 两个大气动力学模式整体强解的存在唯一性[J]. 应用数学和力学, 1986, 7(10): 907-912. http://www.applmathmech.cn/article/id/3955

    MU Mu. Existence and uniqueness of global strong solutions of two models in atmospheric dynamics[J]. Applied Mathematics and Mechanics, 1986, 7(10): 907-912. (in Chinese)) http://www.applmathmech.cn/article/id/3955
    [9]
    SUTYRIN G G, DEWAR W K. Almost symmetric solitary eddies in a two-layer ocean[J]. Journal of Fluid Mechanics, 1992, 238: 633-656. doi: 10.1017/S0022112092001848
    [10]
    HELD I M, LARICHEV V D. A scaling theory for horizontally homogeneous, baroclinically unstable flow on a beta plane[J]. Journal of the Atmospheric Sciences, 1996, 53(7): 946-952. doi: 10.1175/1520-0469(1996)053<0946:ASTFHH>2.0.CO;2
    [11]
    SUTYRIN G G, RADKO T. Why the most long-lived oceanic vortices are found in the subtropical westward flows[J]. Ocean Model, 2021, 161: 101782. doi: 10.1016/j.ocemod.2021.101782
    [12]
    SUTYRIN G G, HESTHAVEN J S, LYNOV J P, et al. Dynamical properties of vortical structures on the beta-plane[J]. Journal of the Fluid Mechanics, 1994, 268: 103-131. doi: 10.1017/S002211209400128X
    [13]
    DILMAHAMOD A F, AGUIAR-GONZALEZ B, PENVEN P, et al. SIDDIES corridor: a major east-west pathway of long-lived surface and subsurface eddies crossing the subtropical South Indian Ocean[J]. Journal of Geophysical Research: Oceans, 2018, 123(8): 5406-5425. doi: 10.1029/2018JC013828
    [14]
    SUTYRIN G G. How baroclinic vortices intensify resulting from erosion of their cores and/or changing environment[J]. Ocean Modell, 2020, 156(3): 101711.
    [15]
    陈利国, 杨联贵. 推广的β平面近似下带有外源和耗散强迫的非线性Boussinesq方程及其孤立波解[J]. 应用数学和力学, 2020, 41(1): 98-106. doi: 10.21656/1000-0887.400067

    CHEN Liguo, YANG Liangui. A nonlinear Boussinesq equation with external source and dissipation forcing under generalized β plane approximation and its solitary wave solutions[J]. Applied Mathematics and Mechanics, 2020, 41(1): 98-106. (in Chinese)) doi: 10.21656/1000-0887.400067
    [16]
    YANG L, DA C, SONG J, et al. Rossby waves with linear topography in barotropic fluids[J]. Chinese Journal of Oceanology and Limnology, 2008, 26: 334-338. doi: 10.1007/s00343-008-0334-7
    [17]
    LARICHEV V D, REZNIK G M. Two-dimensional Rossby soliton: an exact solution[J]. Doklady Akademii Nauk SSSR, 1976, 231(5): 1077-1079.
    [18]
    TULLOCH R, MARSHALL J, HILL C, et al. Scales, growth rates and spectral fluxes of baroclinic instability in the ocean[J]. Journal of Physical Oceanography, 2011, 41(6): 1057-1076. doi: 10.1175/2011JPO4404.1
    [19]
    GUO C Z, JIAN S. Baroclinic instability of a time-dependent zonal shear flow[J]. Atmosphere, 2022, 13(7): 1058. doi: 10.3390/atmos13071058
    [20]
    PEDLOSKY J. Geophysical Fluid Dynamics[M]. Springer-Verlag, 1987: 710.
    [21]
    VALLIS G K. Atmospheric and Oceanic Fluid Dynamics[M]. Cambridge: Cambridge University Press, 2006: 745.
    [22]
    陈利国. 大气和海洋中两类非线性孤立波模型研究[D]. 呼和浩特: 内蒙古大学, 2020.

    CHEN Liguo. Study on two kinds of nonlinear solitary wave models in atmosphere and ocean[D]. Hohhot: Inner Mongolia University, 2020. (in Chinese))
    [23]
    KURCZYN J, BEIER E, LAVÍN M, et al. Anatomy and evolution of a cyclonic mesoscale eddy observed in the northeastern Pacific tropical-subtropical transition zone[J]. Journal of Geophysical Research: Oceans, 2013, 118(11): 5931-5950. doi: 10.1002/2013JC20437
    [24]
    CHEN G, HAN G, YANG X. On the intrinsic shape of oceanic eddies derived from satellite altimetry[J]. Remote Sensing of Environment, 2019, 228: 75-89. doi: 10.1016/j.rse.2019.04.011
    [25]
    KIZNER Z, BERSON D, REZNIK G, et al. The theory of the beta-plane baroclinic topographic modons[J]. Geophysical & Astrophysical Fluid Dynamics, 2003, 97(3): 175-211.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(5)

    Article Metrics

    Article views (134) PDF downloads(43) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return