Rossby wave radiation on the Β-plane by western and eastern boundary currents

The linear problem of Rossby wave radiation by meridional boundary currents is considered. The spectral problem is conditionally divided into two regions: the long-wavelength region (l < 0.5) and the short-wavelength region (l > 0.5) (where l is the meridional wavenumber normalized to the current width). It is shown that in the long-wavelength part of the spectrum (l < 0.5), a quasimonochromatic Rossby wave is radiated into the open ocean, and an asymmetry between the western and eastern boundary currents is observed. The western boundary current radiates Rossby waves with small growth increments. The wavenumber and group velocity of the radiated Rossby wave in the open ocean are practically zonal and oppositely directed (the phase propagates westward, the group velocity is directed eastward). The eastern current, conversely, radiates Rossby waves with large growth increments. The wavenumber is directed almost meridionally, and the group velocity is directed westward. Rossby waves radiated by the eastern current are an order of magnitude longer than waves radiated by the western current. In the short-wavelength region (l > 0.5), the radiation of Rossby waves into the open ocean disappears. The asymmetry between east and west also disappears. The solution, for both the eastern and western boundary currents, converges to a varicose Rayleigh mode and consists of a chain of small (compared to the current width) cyclones and anticyclones located on the outer boundary of the current (on the open ocean side). Verification of this model using the example of the Lofoten Basin in the Norwegian Sea has shown that typical nondimensional β values at mid-latitudes are closer to 0.01 rather than β = 0.5.