Advanced Search
Impact Factor: 5.8

Volume 28 Issue 6

Nov.  2011

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2011 >  28(6): 1433-1444

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part I: Theory and Integral Formulae

  • 1.

    NOAA/National Severe Storms Laboratory, Norman, Oklahoma, USA,Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, USA, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029


doi: 10.1007/s00376-011-0185-6

  • The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments. Classic integral formulas and their variants are used to formulate solutions for the coupled problems. In the absence of data holes, the total solution is the sum of two integral solutions. One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity, and its two components (velocity potential and streamfunction) can be constructed by applying Green's function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain. The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity, and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain. By setting either the velocity potential (or streamfunction) component to zero, the other component of the externally induced solution can be expressed by the imaginary (or real) part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution. The streamfunction (or velocity potential) for the externally induced solution can also be expressed by the boundary integral of a double-layer (or single-layer) density function. In the presence of data holes, the total solution includes a data-hole--induced solution in addition to the above internally and externally induced solutions.
  • [1] CAO Jie, Qin XU, 2011: Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part II: Numerical Methods and Test Experiments, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 1445-1458.  doi: 10.1007/s00376-011-0186-5
    [2] Botao ZHOU, Ying SHI, Ying XU, 2016: CMIP5 Simulated Change in the Intensity of the Hadley and Walker Circulations from the Perspective of Velocity Potential, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 808-818.  doi: 10.1007/s00376-016-5216-x
    [3] Jie CAO, Qin XU, Haishan CHEN, Shuping MA, 2022: Hybrid Methods for Computing the Streamfunction and Velocity Potential for Complex Flow Fields over Mesoscale Domains, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 1417-1431.  doi: 10.1007/s00376-021-1280-y
    [4] Sun Litan, Huang Meiyuan, 1994: Improving the Vorticity-Streamfunction Method to Solve Two-Dimensional Anelastic and Nonhydrostatic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 247-249.  doi: 10.1007/BF02666551
    [5] ZHANG Shuwen, QIU Chongjian, ZHANG Weidong, 2004: Estimating Heat Fluxes by Merging Profile Formulae and the Energy Budget with a Variational Technique, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 627-636.  doi: 10.1007/BF02915730
    [6] LI Nan, WEI Ming, TANG Xiaowen, PAN Yujie, 2007: An Improved Velocity Volume Processing Method, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 893-906.  doi: 10.1007/s00376-007-0893-0
    [7] Fu Baopu, 1987: VARIATION IN WIND VELOCITY OVER WATER, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 93-104.  doi: 10.1007/BF02656665
    [8] Brian HOSKINS, 2015: Potential Vorticity and the PV Perspective, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 2-9.  doi: 10.1007/s00376-014-0007-8
    [9] Yong. L. McHall, 1990: Generalized Available Potential Energy, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 395-408.  doi: 10.1007/BF03008870
    [10] Zhao Ming, 1987: ON THE PARAMETERIZATION OF THE VERTICAL VELOCITY AT THE TOP OF PLANETARY BOUNDARY LAYER, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 233-239.  doi: 10.1007/BF02677070
    [11] LIU Guimei, WANG Hui, SUN Song, HAN Boping, 2003: Numerical Study on the Velocity Structure around Tidal Fronts in the Yellow Sea, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 453-460.  doi: 10.1007/BF02690803
    [12] LI Gang, HE Guangxin, Xiaolei ZOU*, and Peter Sawin RAY, 2014: A Velocity Dealiasing Scheme for C-band Weather Radar Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 17-26.  doi: 10.1007/s00376-013-2251-8
    [13] SUN Jianning, JIANG Weimei, CHEN Ziyun, YUAN Renmin, 2005: A Laboratory Study of the Turbulent Velocity Characteristics in the Convective Boundary Layer, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 770-780.  doi: 10.1007/BF02918721
    [14] Chen Panqin, 1987: MEASUREMENTS OF THE DRY DEPOSITION VELOCITY FOR SUSPENDED PARTICLES OVER THE SUBURBS OF BEIJING, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 323-331.  doi: 10.1007/BF02663602
    [15] Yong L. McHall, 1993: Group Velocity of Anisotropic Waves-Part I: Mathematical Expression, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 393-406.  doi: 10.1007/BF02656964
    [16] Yong L. McHall, 1993: Group Velocity of Anisotropic Waves-Part II: Conservative Properties, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 407-414.  doi: 10.1007/BF02656965
    [17] Hailiang ZHANG, Yongfu XU, Long JIA, Min XU, 2021: Smog Chamber Study on the Ozone Formation Potential of Acetaldehyde, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1238-1251.  doi: 10.1007/s00376-021-0407-5
    [18] Zuohao CAO, Da-Lin ZHANG, 2004: Tracking Surface Cyclones with Moist Potential Vorticity, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 830-835.  doi: 10.1007/BF02916379
    [19] Chanh Q. KIEU, Da-Lin ZHANG, 2012: Is the Isentropic Surface Always Impermeable to the Potential Vorticity Substance?, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 29-35.  doi: 10.1007/s00376-011-0227-0
    [20] Bi Xunqiang, 1997: Parallel Computing of a Climate Model on the Dawn 1000 by Domain Decomposition Method, ADVANCES IN ATMOSPHERIC SCIENCES, 14, 569-572.  doi: 10.1007/s00376-997-0075-0
PDF

Get Citation+

shu
Export:  

Share Article

Article Metrics

Article Views: 1153 Times

PDF downloads: 873 Times

Cited by: Times
  • 加载中

    • Manuscript History

    Manuscript received: 10 November 2011
    Manuscript revised: 10 November 2011
    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

    Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part I: Theory and Integral Formulae

    • 1. NOAA/National Severe Storms Laboratory, Norman, Oklahoma, USA,Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, USA, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
    • Manuscript received: 2011-11-10
    • Manuscript revised: 2011-11-10

    Abstract: The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments. Classic integral formulas and their variants are used to formulate solutions for the coupled problems. In the absence of data holes, the total solution is the sum of two integral solutions. One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity, and its two components (velocity potential and streamfunction) can be constructed by applying Green's function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain. The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity, and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain. By setting either the velocity potential (or streamfunction) component to zero, the other component of the externally induced solution can be expressed by the imaginary (or real) part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution. The streamfunction (or velocity potential) for the externally induced solution can also be expressed by the boundary integral of a double-layer (or single-layer) density function. In the presence of data holes, the total solution includes a data-hole--induced solution in addition to the above internally and externally induced solutions.

      HTML

    Catalog

      Publish with AAS

      Contact us

      Links

      Copyright © 2018-2028 ADVANCES IN ATMOSPHERIC SCIENCES 京ICP备14024088号-7

      Supported by: Beijing Renhe Information Technology Co. Ltd  support: info@rhhz.net  

      /

      DownLoad:  Full-Size Img  PowerPoint
      Return
      Return