A numerical simulation of an atmospheric vortex street
PAUL H. RUSCHER
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331, USA
Search for more papers by this authorJ. W. DEARDORFF
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331, USA
Search for more papers by this authorPAUL H. RUSCHER
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331, USA
Search for more papers by this authorJ. W. DEARDORFF
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331, USA
Search for more papers by this authorAbstract
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 Karmán 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.
- 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. Sci. 35, 2281–2301.
- 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.
- 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.
- Arakawa, A. and Lamb, V. R. 1977. Computational design of the basic dynamical process of the UCLA general circulation model. In Methods of Computational Physics, Volume 17: General circulation models of the atmosphere (ed. J. Chang). New York: Academic Press, 174–265.
- Batchelor, G. K. 1967. An Introduction to Fluid Dynamics. London: Cambridge University Press, 615 pp.
- Chen, J. H. 1973. Numerical boundary conditions and computational modes. J. Comp. Phys. 13, 522–535.
- Chopra, K. P. and Hubert, L. F. 1964. Kármán vortex streets in the Earth's atmosphere. Nature 203, 1341–1343.
- Chopra, K. P. 1965. Mesoscale eddies in wake of islands. J. Atmos. Sci. 22, 652–657.
-
Crowley, W. P.
1969. A global numerical ocean model: part I.
J. Comp. Phys.
3, 111–147.
10.1016/0021-9991(68)90009-0 Google Scholar
- Deardorff, J. W. 1973. Three-dimensional numerical modeling of the planetary boundary layer. In Workshop on Micrometeorology (ed. D. A. Haugen). Boston: American Meteorological Society, 271–311.
- Deardorff, J. W. and Willis, G. E. 1975. A parameterization of diffusion into the mixed layer. J. Appl. Meteorol. 14, 1451–1458.
- Fromm, J. and Harlow, H. 1963. Numerical solution of the problem of vortex street development. Phys. Fluids 6, 975–981.
- Gaster, M. 1969. Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech. 38, 565–576.
- Gaster, M. 1971. Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749–756.
- Gerrard, J. H. 1966. The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25, 401–413.
- Haltiner, G. J. 1971. Numerical Weather Prediction. New York: John Wiley & Sons, Inc., 317 pp.
- Hirota, I. and Miyakoda, K. 1965. Numerical simulation of Kármán vortex street behind a circular cylinder. J. Meteorol. Soc. Japan Ser. II 43, 30–41.
-
Jensen, N. O. and
Agee, E. M.
1978. Vortex cloud street during AMTEX 75.
Tellus
30, 517–523.
10.1111/j.2153-3490.1978.tb00868.x Google Scholar
- Kármán, Th. Von 1911. Über den mechanisms des widerstandes den ein bewegter körber in einer flüssigkeit erfährt. Gottingen Nachrichten Math.-Phys. 509–517.
- 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. Rev. 105, 1351–1371.
- Klemp, J. B. and Lilly, D. K. 1978. Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci. 35, 78–107.
- Klemp, J. B. and Wilhelmson, R. B. 1978. The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci. 35, 1070–1096.
- Kovásznay, 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.
- Lamb, H. 1932. Hydrodynamics, 6th ed. London: Cambridge University Press, 738 pp.
- Lavoie, R. L. 1972. A mesoscale model of lake-effect storms. J. Atmos. Sci. 29, 1025–1040.
- Lavoie, R. L. 1974. A numerical model of trade wind weather on Oahu. Mon. Wea. Rev. 102, 630–637.
- 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.
- Lilly, D. K. 1968. Models of cloud-topped mixed layers under a strong inversion. Quart. J. Roy. Meteorol. Soc. 94, 292–309.
- Lyons, W. A. and Fujita, T. 1968. Mesoscale motions in oceanic stratus as revealed by satellite data. Mon. Wea. Rev. 96, 304–314.
-
Matsuno, T.
1966. Numerical integrations of the primitive equations by a simulated backward difference method.
J. Meteorol. Soc. Japan Ser. II
44, 76–84.
10.2151/jmsj1965.44.1_76 Google Scholar
- Mesinger, F. and Arakawa, A. 1976. Numerical methods used in atmospheric models, Vol. I. GARP Publication Series, No. 17. Geneva: World Meteorological Organization/ICSU, 64 pp.
- Miyakoda, K. and Rosati, A. 1977. One-way nested grid models: the interface condition and numerical accuracy. Mon. Wea. Rev. 105, 1092–1107.
- Nitta, T. 1964. On the reflective computational wave caused by the outflow boundary condition. J. Meteorol. Soc. Japan Ser. II 42, 274–276.
- Orlanski, I. 1976. A simple boundary condition for unbounded hyperbolic flows. J. Comp. Phys. 21, 251–269.
- Overland, J. E., Hitchman, M. H. and Han, Y.-J. 1979. A regional surface wind model for mountainous coastal areas. NOAA Tech. Rept., ERL 407–PMEL 32, U.S. Department of Commerce. (Available from Superintendent of Documents, USGPO, Washington, DC 20402, USA. Order by SD Stock No. 003-017-00461-9.).
- 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.
- 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.
- 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.
- Sadourny, R. 1975. The dynamics of finite-difference models of the shallow water equations. J. Atmos. Sci. 32, 680–689.
-
Smagorinsky, J.
1963. General circulation experiments with the primitive equations: 1. The basic experiment.
Mon. Wea. Rev.
91, 99–164.
10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 Google Scholar
- Sundström, 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 Meteorological Organization/ICSU, 379–416.
- 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.
-
Trischka, J. W.
1980. Cone models of mountain peaks associated with atmospheric vortex streets.
Tellus
32, 365–375.
10.1111/j.2153-3490.1980.tb00963.x Google Scholar
- Tsuchiya, K. 1969. The clouds with the shape of Kármán vortex street in the wake of Cheju Island, Korea. J. Meteorol. Soc. Japan Ser. II 47, 457–464.
- 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. Sci. 35, 47–58.
-
Zimmerman, L. I.
1969. Atmospheric wake phenomena near the Canary Islands.
J. Appl. Meteorol.
8, 896–907.
10.1175/1520-0450(1969)008<0896:AWPNTC>2.0.CO;2 Google Scholar