Abstract
The effect of stochastic fluctuations in the background zonal velocity field on the energy dispersion of stationary wave responses to meridionally localised forcing is considered, using the non-divergent, barotropic vorticity equation. It is found that for small noise levels or large lengthscales in the noise autocovariance function, the oscillatory structure of the solutions is not altered. However, for noise levels (or autocovariance lengthscales) comparable to or larger (smaller) than those observed in the circulation at 300mb, the marginal density functions of the solution process displays a pronounced attenuation away from the stationary wave source. This indicates that fluctuations in the velocity field inhibit the dispersion of wave energy. The symmetry of the marginal PDFs about the source rather than about the equator indicates that the localisation is primarily an integrated effect of backscattering by potential vorticity gradients in regions of real refractive index, and not due to attenuation by regions of imaginary refractive index or by critical lines in the flow.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Branstator, Horizontal energy propagation in a barotropic atmosphere with meridional and zonal structure. J. Atmos. Sci., 40 (1983), 1689–1708.
G. Brunet and P. Haynes, Low-latitude reflection of rossby wave trains. J. Atmos. Sci., 53 (1996), 482–496.
L. Campbell and S.A. Maslowe, Forced rossby wave packets in barotropic shear flows with critical layers. Dyanm. Atmos. Ocean., 28 (1998), 9–37.
I.M. Held, Stationary and quasi-stationary eddies in the extratropical atmosphere: Theory. In B. Hoskins and R. Pearce, editors, Large Scale Dynamical Processes in the Atmosphere, pages 127-168. Academic Press, 1983.
B.J. Hoskins and T. Ambrizzi, Rossby wave propagation on a realistic longitudinally varying flow. J. Atmos. Sci., 50 (1993), 1661–1671.
B.J. Hoskins and D.J. Karoly, The steady linear response of a spherical atmosphere to thermal and orographie forcing. J. Atmos. Sci., 38 (1981), 1179–1196.
P. Imkeller, A.H. Monahan and L. Pandolfo, Some mathematical remarks concerning the localisation of planetary waves in stochastic background flow. In this volume, 2000.
D.J. Karoly, Rossby wave propagation in a barotropic atmosphere. Dynam. Atmos. Oceans, 7 (1983), 111–125.
J.B. Keller and G. Veronis, Rossby waves in the presence of random currents. J. Geophys. Res., 74 (1969), 1941–1951.
G.N. Kiladis, G.A. Meehl and K.M. Weickmann, Large-scale circulation associated with westerly wind bursts and deep convection over the western equatorial pacific. J. Geophys. Res., 99 (1994), 18527–18544.
G.N. Kiladis and K.M. Weickmann, Circulation anomalies associated with tropical convection during northern winter. Month. Weath. Rev., pages 1900-1923, 1992.
G.N. Kiladis and K.M. Weickmann, Extratropical forcing of tropical pacific convection during northern winter. Month. Weath. Rev., 120 (1992), 1924–1938.
G.N. Kiladis and K.M. Weickmann, Horizontal structure and seasonality of large-scale circulations associated with submonthly tropical convection. Month. Weath. Rev., 125 (1997), 1997–2013.
P.D. Killworth and M.E. McIntyre, Do rossby-wave critical layers absorb, reflect, or over-reflect? J. Fluid Mech., 161 (1985), 449–492.
L. Li and T.R. Nathan, The global atmospheric response to low-frequency tropical forcing: Zonally averaged basic states. J. Atmos. Sci., 51 (1994), 3412–3426.
L. Li and T.R. Nathan, Effects of low-frequency tropical forcing on intraseasonal tropical-extratropical interactions. J. Atmos. Sci., 54 (1997), 332–346.
A.H. Monahan and L. Pandolfo, Meridional localisation of planetary waves in stochastic zonal flows. J. Atmos. Sci., in review.
L. Pandolfo, Observational aspects of the low-frequency intraseasonal variability of the atmosphere in middle latitudes. In Advances in Geophysics, 34 (1993), 93–174. Academic Press.
L. Pandolfo and A. Sutera, Rossby waves in a fluctuating zonal mean flow. Tellus, 43A(1991), 257–265.
J. Pedlosky, Geophysical Fluid Dynamics. Springer, New York, 1987.
C. Rossby and Co-workers, Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centres of action. J. Mar. Res., 2 (1939), 38–55.
P. Sardeshmukh, C. Penland and M. Newman, Rossby waves in a fluctuating medium. In this volume, 2000.
D. Sengupta, Localization of rossby waves over random topography: Two-layer ocean. J. Phys. Oceanography, 24 (1994), 1065–1069.
D. Sengupta, L.I. Piterbarg and G.M. Reznik, Localization of topographic rossby waves over random relief. Dynam. Atmos. Oceans, 17 (1992), 1–21.
P. Sheng, Introduction to Wave Scattering, Localisation, and Mesoscopic Phenomena. Academic Press, San Diego, 1995.
R.E. Thomson, The propagation of planetary waves over a random topography. J. Fluid. Mech., 70 (1975), 267–285.
J. Vanneste, Enhanced dissipation for quasi-geostrophic motion over small-scale topography. J. Fluid Mech., 407 (2000), 105–122.
J. Vanneste, Rossby-wave frequency change induced by small-scale topography. J. Phys. Ocean., in review.
G.-Y. Yang and B.J. Hoskins. Propagation of rossby waves of nonzero frequency. J. Atmos. Sci., 53 (1996), 2365–2378.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Monahan, A.H., Pandolfo, L., Imkeller, P. (2001). Stochastic confinement of Rossby waves by fluctuating eastward flows. In: Imkeller, P., von Storch, JS. (eds) Stochastic Climate Models. Progress in Probability, vol 49. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8287-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8287-3_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9504-0
Online ISBN: 978-3-0348-8287-3
eBook Packages: Springer Book Archive