Abstract
Rossby wave propagation in the presence of a nonseparable Brunt-Väisälä frequency,N(y,z), and the associated geostrophic zonal flow,U(y,z), is examined in this paper. The usual quasi-geostrophic potential vorticity equation only includes vertical variations in Brunt-Väisälä frequency (i.e.N(z)). We derive a linearised quasi-geostrophic potential vorticity equation which explicitly includesN(y, z), where variations inN may occur on the internal Rossby radius length scale. A mixed layer distribution that monotonically deepens in the poleward direction leads to a nonseparableN(y,z). The resulting meridional pressure gradient is balanced by an eastward zonal geostrophic flow.
By assuming mixed layer depth changes occur slowly, relative to a typical horizontal wavelength of a Rossby wave, a local analysis is presented. The Rossby wave is found to have a strongly modulated meridional wavenumber,l, with amplitude proportional to |l|−1/2. To elucidate whether the modulations of the Rossby wave are caused by the horizontal variations inN orU we also consider the cases where eitherN orU vary horizontally. Mixed layer depth changes lead to largestl where the mixed layer is deepest, whereasl is reduced in magnitude whereU is nonzero. When bothU(y,z) andN(y,z) are present, the two effects compete with one another, the outcome determined by the size of |c|/U max, wherec is the Rossby wave phase speed. Finally, the slowly varying assumption required for the analytical approach is removed by employing a numerical model. The numerical model is suitable for studying Rossby wave propagation in a rectangular zonal channel with generalN(y, z) andU(y, z).
Similar content being viewed by others
References
Bryan, K., andRipa, P. (1978),The Vertical Structure of North Pacific Temperature Anomalies, J. Geophys. Res.,83, 2419–2429.
Darby, M. S., andWillmott, A. J. (1990),On the Generation and Propagation of Rossby Waves in an Ocean with a Zonally Shoaling Mixed Layer, J. Mar. Res. (in press).
Jennings, A.,andStewart, W. J. (1975),Simultaneous Iteration for Partial Eigensolution of Real Matrices, J. Inst. Math. Appl.15, 351–367.
Killworth, P. D. (1979),On the Propagation of Stable Baroclinic Rossby Waves through a Mean Shear Flow, Deep-Sea Res.26, 997–1031.
Lamb, P. J. (1984),On the Mixed Layer Climatology of the North and Tropical Atlantic, Tellus36, 239–305.
LeBlond, P. H., andMysak, L. A.,Waves in the Ocean (Elsevier, New York 1978) 602 pp.
Müller, P., Garwood, R. W., andGarner, J. P. (1984),Effect of Vertical Advection on the Dynamics of Oceanic Surface Mixed Layer, Annales Geophysicae2, 387–398.
Pedlosky, J. (1984),The Equations for Geostrophic Motion in the Ocean, J. Phys. Oceanogr.14, 448–455.
Stevenson, J. W. (1983),The Seasonal Variation of the Surface Mixed-layer Response to the Vertical-Motions of Linear Rossby Waves, J. Phys. Oceanogr.13, 1255–1268.
Whitham, G. B.,Linear and Nonlinear Waves (Wiley, New York 1974) 636 pp.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Darby, M.S., Willmott, A.J. On Rossby wave propagation in a meridionally stratified channel. PAGEOPH 133, 691–712 (1990). https://doi.org/10.1007/BF00876228
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00876228