Stationary Rossby wave propagation in a shear flow along a reflective boundary |
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Authors: | U Harlander A Gassmann W Metz |
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Institution: | (1) Institute for Meteorology, Leipzig, Germany, DE;(2) Institute for Meteorology, Bonn, Germany, DE |
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Abstract: | Summary
This study investigates the impact of lateral boundary conditions on the propagation and dispersion of locally excited Rossby
waves in a zonally periodic, barotropic, quasigeostrophic channel model on the β-plane. We use basic flows with either a linear
meridional shear or a jet-like profile. On the southern boundary of the channel we impose either a rigid wall or a radiation
condition, whereas the northern sidewall is permeable for Rossby waves. We compare the numerical solutions found for a reflecting
southern boundary in a weakly dissipative flow to the solutions obtained from a WKB-analysis for the corresponding unforced
nondissipative situation. Furthermore, we compare the generalized Eliassen-Palm flux vectors to the ray paths of Rossby wave
packets, obtained from WKB ray tracing. In particular, we focus our investigation on the two-dimensional structure of trapped
modal waves and wavetrains in a simple linear numerical model.
Summarizing our results, we find that along the reflective wall, trapped modal wave structures as well as reflected wavetrains
occur with characteristics (e.g., wavenumbers, turning latitudes) similar to the ones computed using asymptotic methods. In
a linear sheared flow wave packets are trapped for all zonal wave numbers in contrast to a jet-like mean flow which has a
selective effect on the waves; i.e., a turning latitudes phenomenon between the coast and the flow maximum occurs for short
waves, while long waves can propagate freely across the zonal mean flow. This comes out clearly when studying the stream lines
of the Eliassen-Palm flux vectors of the numerical model simulations. Furthermore, due to the reflected wave activity, the
dispersion of Rossby waves is influenced by the southern boundary condition not only in the vicinity of the border but also
in regions away from the boundary. These results appear to be important on the one hand for the existence of trapped Rossby
waves in large-scale oceanic shear flows along a zonally oriented coast. And, on the other hand for large-scale boundary waves
in conceptional atmospheric channel models which can lead to unwanted resonance effects.
Received July 18, 2000/Revised June 9, 2001 |
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