Abstract
In this paper, we first apply the assumption h = εh′ of topographic variation (h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1—3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourt-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be independent of the zonal basic westerly wind, but dependent on the meridional wavenumber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its period will belong to the 30–60-day period band. However, when the wavenumber-two topography is included, the periods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30–60-day period band can be found for zonal wavenumbers 1–3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case. When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period. The period, over a moderate range of the zonal basic westerly wind, is in the intraseasonal, 30–60-Day range.
Similar content being viewed by others
References
Anderson, J.R. and Rosen, R.D. (1983), The latitude-height structure of 40–50 day variations in the atmospheric angular momentum, J. Atmos. Sci. 40: 1584–1591.
Bernardet, P. et al. (1990), Low frequency oscillation in a rotating annulus with topography, J. Atmos. Sci., 47: 3023–3043.
Brastator, G. (1987), A striking example of the atmosphere's leading traveling pattern, J. Atmos. Sci., 44: 2310–2323.
Bretherton, F. P. (1964), Resonant interactions between waves. The case of discrete oscillation, J. Fluid Mech., 20, 457–479.
Charney, J. G. and Devore, J. G. (1979), Multiple low equilibria in atmosphere and blocking, J. Atmos. Sci. 36: 1205–1216.
Colucci, S. J., Loesch, A. Z., and Bosart, L. F. (1981), Spectral evolution of a blocking episode and comparison with wave interaction theory, J. Atmos. Sci., 38: 2092–2111.
Craik, A.D.D. (1985), Wave interactions and fluid flows, Cambridge University Press 322 pp.
Cree, W. C. and Swaters, G. E. (1991), On the topographic dephasing and amplitude modulation of nonlinear Rossby wave interactions, Geophys. Astrophys. Fluid Dyn., 61: 75–99.
Egger, J. (1978), Dynmaics of blocking highs, J. Atmos. Sci., 35: 1788–1801.
Ghill, M. and Mo, K. (1991), Intraseasonal oscillations in the global atmosphere, part I: Northern Hemisphere and tropics, J. Atmos. Sci., 48: 752–779.
**, F. F. and Ghil, M. (1990), Intraseasonal oscillations in the extratropics: Hopf bifurcation and topographic instabilities, J. Atmos. Sci., 47: 3007–3022.
Jones, S. (1979), Rossby wave interactions and instabilities in a rotating, two layer fluid on a beta-plane. Part I: Resonant interactions, Geophys. Astrophys. Fluid Dyn. 11: 289–322.
Li, G. Q. (1993), The atmospheric circulation features seen in the rotating fluid physics experiments, Acta Meteorologica Sinica, 51: 405–413.
Loesch, A. Z. (1974), Resonant interactions between unstable and neutral baroclinic waves. part I, J. Atmos. Sci., 31: 1177–1201.
Longuet-Higgins, M.S. and Gill, A. E. (1967), Resonant interactions between planetary waves, Proc. R. Soc. Lond., A229: 120–140.
Luo, D. H. (1994), Quasi-resonant interactions among barotropic Rossby waves with two-wave topography and low frequency dynamics, Geophys. Astrophys. Fluid Dyn., 76: 145–163.
Luo, D. H. (1997), Low-frequency finite-amplitude oscillation in a near-resonant topographically forced barotropic flow, Dyn. Atmos. Oceans, 26: 53–72.
Marcus, S. L., M. Ghil and Dickey, J. O. (1994), The extratropical 40-day oscillation in the UCLA general circulation model Part I: Atmospheric angular momentum, J. Atmos. Sci. 51: 1431–1445.
Nathan, T. R. and Barcilon, A. (1994), Low-frequency oscillations of forced barotropic flow, J. Atmos. Sci., 51, 582–588.
Pedlosky, J. (1979), Geophysical Fluid Dynamics, Springer, 624 pp.
Szoeke, R. A. (1983), Baroclinic instability over wavy topography, J. Fluid Mech., 130: 279–298.
Tribbia, J. J. and Ghil, M. (1990), Forced zonal basic flow over topography and the 30–60 day oscillation in the atmospheric angular momentum, NCAR Tech. Memo., 0501/89-5, NCAR, Boulder, Colorado, 26 pp.
Tung, K. K., and Lindzen, R. S. (1979), A theory of stationary long waves. Part I: A simple theory of blocking, Mon. Wea. Rev., 107: 714–734.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dehai, L. Topographically forced three-wave quasi-esonant and non-resonant interactions among barotropic rossby waves on an infinnite beta-plane. Adv. Atmos. Sci. 15, 83–98 (1998). https://doi.org/10.1007/s00376-998-0020-x
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00376-998-0020-x