DOI QR코드

DOI QR Code

대류가 유도하는 중규모 흐름에 미치는 비정역학 효과

Nonhydrostatic Effects on Convectively Forced Mesoscale Flows

  • 우소라 (서울대학교지구환경과학부) ;
  • 백종진 (서울대학교지구환경과학부) ;
  • 이현호 (서울대학교지구환경과학부) ;
  • 한지영 ((재)한국형수치예보모델개발사업단) ;
  • 서재명 (서울대학교지구환경과학부)
  • Woo, Sora (School of Earth and Environmental Sciences, Seoul National University) ;
  • Baik, Jong-Jin (School of Earth and Environmental Sciences, Seoul National University) ;
  • Lee, Hyunho (School of Earth and Environmental Sciences, Seoul National University) ;
  • Han, Ji-Young (Korea Institute of Atmospheric Prediction Systems) ;
  • Seo, Jaemyeong Mango (School of Earth and Environmental Sciences, Seoul National University)
  • 투고 : 2013.03.29
  • 심사 : 2013.06.23
  • 발행 : 2013.09.30

초록

대류가 유도하는 중규모 흐름에 미치는 비정역학 효과를 조사하기 위하여 기존의 무차원화된 정역학 모형을 바탕으로 무차원화된 비정역학 모형을 개발하였다. 모형을 검증하기 위하여 정역학 방정식 계의 해석해와 비정역학성이 아주 작은 경우의 수치 실험 결과를 비교하였고, 두 결과가 거의 같음을 확인하였다. 무차원화된 비정역학 모형을 이용하여 선형 계와 비선형 계에서 대류가 유도하는 중규모 흐름에 미치는 비정역학 효과를 조사하였다. 선형 계와 비선형 계 모두에서 비정역학성 인자가 작은 경우 열원 꼭대기 위에서 연직 방향으로, 비정역학성 인자가 상대적으로 큰 경우 주 상승 기류의 풍하측에서 수평 방향으로 상승 운동과 하강 운동이 교대하는 파동 형태의 섭동장이 나타났다. 풍하측에서 나타나는 상승 운동과 하강 운동을 분석하기 위하여 선형, 정상 상태, 비점성 흐름에 대한 Taylor-Goldstein 방정식을 구하였다. 주 상승기류의 풍하측에서 교대로 나타나는 상승 하강 기류세포는 전파파의 수평 방향 전파 성분과 에바네센트파, 즉 비정역학성 인자에 의해 결정되는 임계 파장보다 파장이 짧아 연직 방향으로 전파되지 못하고 수평 방향으로만 전파되는 중력파의 중첩으로 설명할 수 있다. 선형 계에 대한 수치 실험 결과에서 나타난 상승 하강 기류 세포의 수평 방향 길이는 선형 계에 대한 방정식에서 얻은 에바네센트 파의 임계 파장 길이의 절반과 일치하였으나, 약한 비선형 계에 대한 수치 실험 결과에서 나타난 상승 하강 기류 세포의 수평 방향 길이는 선형 계에 대한 방정식에서 얻은 에바네센트 파의 임계 파장 길이의 절반보다 다소 길었다. 주 상승 기류 지역 내에서 최대 상승 기류의 위치는 비선형성과 비정역학성 정도에 따라 다르게 나타났다.

Nonhydrostatic effects on convectively forced mesoscale flows in two dimensions are numerically investigated using a nondimensional model. An elevated heating that represents convective heating due to deep cumulus convection is specified in a uniform basic flow with constant stability, and numerical experiments are performed with different values of the nonlinearity factor and nonhydrostaticity factor. The simulation result in a linear system is first compared to the analytic solution. The simulated vertical velocity field is very similar to the analytic one, confirming the high accuracy of nondimensional model's solutions. When the nonhydrostaticity factor is small, alternating regions of upward and downward motion above the heating top appear. On the other hand, when the nonhydrostaticity factor is relatively large, alternating updraft and downdraft cells appear downwind of the main updraft region. These features according to the nonhydrostaticity factor appear in both linear and nonlinear flow systems. The location of the maximum vertical velocity in the main updraft region differs depending on the degrees of nonlinearity and nonhydrostaticity. Using the Taylor-Goldstein equation in a linear, steady-state, invscid system, it is analyzed that evanescent waves exist for a given nonhydrostaticity factor. The critical wavelength of an evanescent wave is given by ${\lambda}_c=2{\pi}{\beta}$, where ${\beta}$ is the nonhydrostaticity factor. Waves whose wavelengths are smaller than the critical wavelength become evanescent. The alternating updraft and downdraft cells are formed by the superposition of evanescent waves and horizontally propagating parts of propagating waves. Simulation results show that the horizontal length of the updraft and downdraft cells is the half of the critical wavelength (${\pi}{\beta}$) in a linear flow system and larger than ${\pi}{\beta}$ in a weakly nonlinear flow system.

키워드

참고문헌

  1. Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100, 487-490. https://doi.org/10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2
  2. Baik, J.-J., and H.-Y. Chun, 1996: Effects of nonlinearity on the atmospheric flow response to low-level heating in a uniform flow. J. Atmos. Sci., 53, 1856-1869. https://doi.org/10.1175/1520-0469(1996)053<1856:EONOTA>2.0.CO;2
  3. Betz, V., and R. Mittra, 1992: Comparison and evaluation of boundary conditions for the absorption of guided waves in an FDTD simulation. IEEE Microwave Guided Wave Lett., 2, 499-501. https://doi.org/10.1109/75.173408
  4. Chun, H.-Y., 1997: Weakly non-linear response of a stably stratified shear flow to thermal forcing. Tellus, 49A, 528-543.
  5. Chun, H.-Y., H.-J. Choi, and I.-S. Song, 2008: Effects of nonlinearity on convectively forced internal gravity waves: Application to a gravity wave drag parameterization. J. Atmos. Sci., 65, 557-575. https://doi.org/10.1175/2007JAS2255.1
  6. Crook, N. A., 1988: Trapping of low-level internal gravity waves. J. Atmos. Sci., 45, 1533-1541. https://doi.org/10.1175/1520-0469(1988)045<1533:TOLLIG>2.0.CO;2
  7. Goldstein, S., 1931: On the stability of superposed streams of fluids of different densities. Proc. Roy. Soc. London, A132, 524-548.
  8. Han, J.-Y., and J.-J. Baik, 2009: Theoretical studies of convectively forced mesoscale flows in three dimensions. Part I: Uniform basic-state flow. J. Atmos. Sci., 66, 948-966.
  9. Han, J.-Y., and J.-J. Baik, 2012: Nonlinear effects on convectively forced two-dimensional mesoscale flows. J. Atmos. Sci., 69, 3391-3404. https://doi.org/10.1175/JAS-D-11-0335.1
  10. Keller, T. L., 1994: Implications of the hydrostatic assumption on atmospheric gravity waves. J. Atmos. Sci., 51, 1915-1929. https://doi.org/10.1175/1520-0469(1994)051<1915:IOTHAO>2.0.CO;2
  11. Lin, Y.-L., 2007: Mesoscale dynamics. Cambridge University Press, New York, U.S.A., 646 pp.
  12. Lin, Y.-L., and R. B. Smith, 1986: Transient dynamics of airflow near a local heat source. J. Atmos. Sci., 43, 40-49. https://doi.org/10.1175/1520-0469(1986)043<0040:TDOANA>2.0.CO;2
  13. Lin, Y.-L., and H.-Y. Chun, 1991: Effects of diabatic cooling in a shear flow with a critical level. J. Atmos. Sci., 48, 2476-2491. https://doi.org/10.1175/1520-0469(1991)048<2476:EODCIA>2.0.CO;2
  14. Nance, L. B., and D. R. Durran, 1997: A modeling study of nonstationary trapped mountain lee waves. Part I: Mean-flow variability. J. Atmos. Sci., 54, 2275-2291. https://doi.org/10.1175/1520-0469(1997)054<2275:AMSONT>2.0.CO;2
  15. Nance, L. B., and D. R. Durran, 1998: A modeling study of nonsta tionary trapped mountain lee waves. Part II: Nonlinearity. J. Atmos. Sci., 55, 1429-1445. https://doi.org/10.1175/1520-0469(1998)055<1429:AMSONT>2.0.CO;2
  16. Navon, I. M., and H. A. Riphagen, 1979: An implicit compact fourth-order algorithm for solving the shallowwater equation in conservation-law form. Mon. Wea. Rev., 107, 1107-1127. https://doi.org/10.1175/1520-0493(1979)107<1107:AICFOA>2.0.CO;2
  17. Olfe, D. B., and R. L. Lee, 1971: Linearized calculations of urban heat island convection effects. J. Atmos. Sci., 28, 1374-1388. https://doi.org/10.1175/1520-0469(1971)028<1374:LCOUHI>2.0.CO;2
  18. Pandya, R. E., and D. R. Durran, 1996: The influence of convectively generated thermal forcing on the mesoscale circulation around squall lines. J. Atmos. Sci., 53, 2924-2951. https://doi.org/10.1175/1520-0469(1996)053<2924:TIOCGT>2.0.CO;2
  19. Perkey, D. J., 1976: A description and preliminary results from a fine-mesh model for forecasting quantitative precipitation. Mon. Wea. Rev., 104, 1513-1526. https://doi.org/10.1175/1520-0493(1976)104<1513:ADAPRF>2.0.CO;2
  20. Queney, P., 1948: The problem of air flow over mountains: A summary of theoretical studies. Bull. Amer. Meteor. Soc., 29, 16-26.
  21. Raymond, D. J., and R. Rotunno, 1989: Response of a stably stratified flow to cooling. J. Atmos. Sci., 46, 2830-2837. https://doi.org/10.1175/1520-0469(1989)046<2830:ROASSF>2.0.CO;2
  22. Smith, R. B., 1979: The influence of mountains on the atmosphere. Adv. Geophys., 21, 87-230. https://doi.org/10.1016/S0065-2687(08)60262-9
  23. Taylor, G. I., 1931: Effects of variation in density on the stability of superposed streams of fluids. Proc. Roy. Soc., A132, 499-523.
  24. Wurtele, M. G., R. D. Sharman, and T. L. Keller, 1987: Analysis and simulations of a troposphere-stratosphere gravity wave model. Part I. J. Atmos. Sci., 44, 3269-3281. https://doi.org/10.1175/1520-0469(1987)044<3269:AASOAT>2.0.CO;2
  25. Wurtele, M. G., R. D. Sharman, and A. Datta, 1996: Atmospheric lee waves. Annu. Rev. Fluid Mech., 28, 429-476. https://doi.org/10.1146/annurev.fl.28.010196.002241
  26. Xue, M., and J. T. Alan, 1991: A mesoscale numerical model using the nonhydrostatic pressure-based sigma-coordinate equations: Model experiments with dry mountain flows. Mon. Wea. Rev., 119, 1168-1185. https://doi.org/10.1175/1520-0493(1991)119<1168:AMNMUT>2.0.CO;2
  27. Yang, M.-J., and R. A. Houze, 1995: Multicell squall-line structure as a manifestation of vertically trapped gravity waves. Mon. Wea. Rev., 123, 641-661. https://doi.org/10.1175/1520-0493(1995)123<0641:MSLSAA>2.0.CO;2