A numerical simulation of an atmospheric vortex street

Paul H. Ruscher; J. W. Deardorff

doi:10.3402/tellusa.v34i6.10841

A numerical simulation of an atmospheric vortex street

Tellus

Volume 34 (1982): Issue 6

By: Paul H. Ruscher and J. W. Deardorff

Open Access

|Jan 1982

Abstract

A mesoscale mixed-layer model of the planetary boundary layer is applied to the flow past a mountain island during a cold air outbreak over the Kuroshio Current. Utilizing data taken during AMTEX '75, the governing equations are integrated in time to simulate development of a Karmxn vortex street downstream of the island of Cheju-do. The use of open lateral boundary conditions and an encroachment scheme which allows some mountain grid points to experience occasional encroachment of mixed-layer fluid as the mixed-layer deepens (and decroachment as the mixed layer thins) is also discussed.

Comparing various non-dimensional parameters on vortex-street characteristics, it is shown that the simulated vortex street resembles the observed atmospheric one rather well. Uncertainty in formulating the proper value of the eddy viscosity and the implication this has on Reynolds number comparisons are also discussed.

References

Abernathy , F. H. and Kronauer , R. E . 1962 . The formation of vortex streets . J. Fluid. Mech . 13 , 1 – 20 .
Search in Google Scholar Back to article
Agee , E. M. and Lomax , F. E . 1978 . Structure of the mixed layer and inversion layer associated with patterns of mesoscale cellular convection during AMTEX 75. J. Atmos. Sc i . 35 , 2281 – 2301 .
Search in Google Scholar Back to article
Anthes , R. A. , Keyser , D. and Deardorff , J. W . 1982 . Further considerations on modeling the sea breeze with a mixed-layer model . To appear in Mon. Wea. Rev . 110 .
Search in Google Scholar Back to article
Anthes. R. A. , Seaman , N. L. and Warner , T. T . 1980 . Comparisons of numerical simulations of the planetary boundary layer by a mixed-layer model and multi-level model . Mon. Wea. Rev . 108 , 365 – 376 .
Search in Google Scholar Back to article
Arakawa , A. and Lamb , V. R . 1977 . Computational design of the basic dynamical process of the UCLA general circulation model . In Methods of Computa-tional Physics, Volume I 7: General circulation models of the atmosphere (ed. J. Chang ,). New York : Aca-demic Press , 174 – 265 .
Search in Google Scholar Back to article
Batchelor , G. K . 1967 . An Introduction to Fluid Dynamics. London : Cambridge University Press , 615 pp.
Search in Google Scholar Back to article
Chen , J. H . 1973 . Numerical boundary conditions and computational modes . J. Comp. Phys . 13 , 522 – 535 .
Search in Google Scholar Back to article
Chopra , K. P. and Hubert , L. F . 1964 . Karman vortex streets in the Earth's atmosphere . Nature 203 , 1341 – 1343 .
Search in Google Scholar Back to article
Chopra , K. P . 1965 . Mesoscale eddies in wake of islands . J. Atmos. Sci . 22 , 652 – 657 .
Search in Google Scholar Back to article
Crowley , W. P . 1969 . A global numerical ocean model: partl. J. Comp. Phys. 3 , 111 - 147.
Search in Google Scholar Back to article
Deardorff , J. W . 1973 . Three-dimensional numerical modeling of the planetary boundary layer . In Work-shop on Micrometeorology (ed. D. A. Haugen). Boston : American Meteorological Society , 271 – 311 .
Search in Google Scholar Back to article
Deardorff , J. W. and Willis , G. E . 1975 . A parameter-ization of diffusion into the mixed layer . J. Appl. Meteorol . 14 , 1451 – 1458 .
Search in Google Scholar Back to article
Fromm , J. and Harlow , H . 1963 . Numerical solution of the problem of vortex street development . Phys. Fluids 6 , 975 – 981 .
Search in Google Scholar Back to article
Gaster , M . 1969 . Vortex shedding from slender cones at low Reynolds numbers . J. Fluid Mech . 38 , 565 – 576 .
Search in Google Scholar Back to article
Caster , M . 1971 . Vortex shedding from circular cylin-ders at low Reynolds numbers . J. Fluid Mech . 46 , 749 – 756 .
Search in Google Scholar Back to article
Gerrard , J. H . 1966 . The mechanics of the formation region of vortices behind bluff bodies . J. Fluid Mech . 25 , 401 – 413 .
Search in Google Scholar Back to article
Haltiner , G. J . 1971 . Numerical Weather Prediction . New York: John Wiley & Sons , Inc ., 317 pp .
Search in Google Scholar Back to article
Hirota , I. and Miyakoda , K . 1965 . Numerical simulation of Kirman vortex street behind a circular cylinder. J. Meteorol . Soc. Japan, Ser . 11 43 , 30 – 41 .
Search in Google Scholar Back to article
Jensen , N. O. and Agee , E. M 1978 . Vortex cloud street during AMTEX 75 . Tellus 30 , 517 – 523 .
Search in Google Scholar Back to article
Karman , Th. von 1911 . Ober den mechanisms des widerstandes den em n bewegter körber in einer flüssigkeit erfährt . Gottingen Nachrichten Math.-Phys . 509 – 517 .
Search in Google Scholar Back to article
Keyser , D. and Anthes , R. A . 1977 . The applicability of a mixed-layer model of the planetary boundary layer to real-data forecasting. Mon . Wea. Re v . 105 . 1351 – 1371 .
Search in Google Scholar Back to article
Klemp , J. B. and Lilly , D. K . 1978 . Numerical simulation of hydrostatic mountain waves . J. Atmos. Sci . 35 , 78 – 107 .
Search in Google Scholar Back to article
Klemp , J. B. and Wilhelmson , R. B . 1978 . The simulation of three-dimensional convective storm dynamics . J. A imos. Sci . 35 , 1070 – 1096 .
Search in Google Scholar Back to article
Kovisznay , L. S. G . 1949 . Hot-wire investigation of the wake behind circular cylinders at low Reynolds numbers . Proc. Roy. Soc. (London), Ser. A 198 , 174 – 190 .
Search in Google Scholar Back to article
Lamb , H . 1932 . Hydrodynamics , 6th ed. London: Cambridge University Press , 738 pp .
Search in Google Scholar Back to article
Lavoie , R. L . 1972 . A mesoscale model of lake-effect storms . J. Atmos. Sci . 29 , 1025 – 1040 .
Search in Google Scholar Back to article
Lavoie , R. L . 1974 . A numerical model of trade wind weather on Oahu . Mon. Wea. Rev . 102 , 630 – 637 .
Search in Google Scholar Back to article
Leith , C. C . 1969 . Two dimensional eddy viscosity coefficients. In Proceedings of the WMO-IUGG Symposium on Numerical Weather Prediction, Tokyo, Nov. 1968, Sec. 1, 41 - 44.
Search in Google Scholar Back to article
Lilly , D. K . 1968 . Models of cloud-topped mixed layers under a strong inversion . Quart. J. Roy. Meteorol. Soc . 94 , 292 – 309 .
Search in Google Scholar Back to article
Lyons , W. A. and Fujita , T . 1968 . Mesoscale motions in oceanic stratus as revealed by satellite data . Mon. Wea. Rev . 96 , 304 – 314 .
Search in Google Scholar Back to article
Matsuno , T . 1966 . Numerical integrations of the primitive equations by a simulated backward dif-ference method . J. Meteorol. Soc. Japan, Ser. II 44 , 76 – 84 .
Search in Google Scholar Back to article
Mesinger , F. and Arakawa , A . 1976 . Numerical methods used in atmospheric models, Vol . I. GARP Publi-cation Series , No. 17. Geneva: World Meteorological Organization/ICSU , 64 pp .
Search in Google Scholar Back to article
Miyakoda , K. and Rosati , A . 1977 . One-way nested grid models: the interface condition and numerical accuracy . Mon. Wea. Rev . 105 , 1092 – 1107 .
Search in Google Scholar Back to article
Nitta , T . 1964 . On the reflective computational wave caused by the outflow boundary condition. J. Meteorol . Soc. Japan, Ser . 11 42 , 274 – 276 .
Search in Google Scholar Back to article
Orlanski , I . 1976 . A simple boundary condition for unbounded hyperbolic flows . J. Comp. Phys . 21 , 251 – 269 .
Search in Google Scholar Back to article
Overland , J. E. , Hitchman , M. H. and Han , Y.-J . 1979 . A regional surface wind model for mountainous coastal areas. NOAA Tech. Repl., ERL 407-PMEL 32, U.S. Department of Commerce. (Available from Superin-tendent of Documents, USGPO, Washington, DC 20402, USA. Order by SD Stock No. 003-017-00461-9.)
Search in Google Scholar Back to article
Pao , H. P. and Kao , T. W . 1976 . On vortex trails over ocean islands . Atmos. Sci. (The Meteorological Society of the Republic of China) 3 , 28 – 38 .
Search in Google Scholar Back to article
Papailou , D. D. and Lykoudis , P. S . 1974 . Turbulent vortex streets and the entrainment mechanism of the turbulent wake . J. Fluid Mech. 62 , 11 - 31 .
Search in Google Scholar Back to article
Price , J. F. , Mooers , C. N. K. and Van Leer , J. C . 1978 . Observation and simulation of storm-induced mixed-layer deepening . J. Phys. Oceanog . 8 , 582 – 599 .
Search in Google Scholar Back to article
Sadourny , R . 1975 . The dynamics of finite-difference models of the shallow water equations . J. Atmos. Sci . 31 , 680 – 689 .
Search in Google Scholar Back to article
Smagorinsky , J . 1963 . General circulation experiments with the primitive equations: 1. The basic experiment. Mon . Wea. Re v . 91 . 99 – 164 .
Search in Google Scholar Back to article
Sundstrom , A. and Elvius , T . 1979 . Computational problems related to limited-area modeling. In “Numerical Methods Used in Atmospheric Models, Volume 2,” (Joint Organizing Committee, ed.). GARP Publication Series, No. 17. Geneva: World Meteoro-logical Organization/I C SU, 379 – 416.
Search in Google Scholar Back to article
Thomson , R. E. , Gower , J. F. R. and Bowker , N. W . 1977 . Vortex street formation in the wake of the Aleutian Islands . Mon. Wea. Rev . 105 , 873 – 884 .
Search in Google Scholar Back to article
Trischka , J. W . 1980 . Cone models of mountain peaks associated with atmospheric vortex streets . Tellus 31 , 365 – 375 .
Search in Google Scholar Back to article
Tsuchiya , K . 1969 . The clouds with the shape of Kirmin vortex street in the wake of Cheju Island, Korea. J. Meteorol . Soc. Japan, Ser . 11 47 , 457 – 464 .
Search in Google Scholar Back to article
Wyngaard , J. C. , Pennell , W. T. Lenschow , D. H. and LeMone , M. A . 1978 . The temperature-humidity covariance budget in the convective boundary layer. J. Atmos. Sc i . 35 , 47 – 58 .
Search in Google Scholar Back to article
Zimmerman , L. I . 1969 . Atmospheric wake phenomena near the Canary Islands . J. Appl. Meteorol . 8 , 896 – 907 .
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.3402/tellusa.v34i6.10841 | Journal eISSN: 3035-9554

Journal RSS Feed

Language: English

Page range: 555 - 566

Submitted on: Dec 1, 1981

Accepted on: Feb 23, 1982

Published on: Jan 1, 1982

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

© 1982 Paul H. Ruscher, J. W. Deardorff, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 34 (1982): Issue 6