. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography 1 2 3 u=uo 4 5 6 7 NON-DIMENSIONAL DISTANCE ACROSS CURRENT ky 0 50 1 1 1 1 |\=ooio / \ â / / 0 025 ^^ -v5 Saa^ - - - -010 1 ââ ^\ 1 1 i 12 3 NON-DIMENSIONAL 4 5 6 7 DISTANCE ACROSS CURRENT Fig. 10. The Reynolds stresses â uv and â1>2 for a Rossby wave being absorbed by a westward-flowing current, the same wave illustrated in Fig. 9. The curves indicate the dependence of these stresses on lateral viscosity. The behavior of wave
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography 1 2 3 u=uo 4 5 6 7 NON-DIMENSIONAL DISTANCE ACROSS CURRENT ky 0 50 1 1 1 1 |\=ooio / \ â / / 0 025 ^^ -v5 Saa^ - - - -010 1 ââ ^\ 1 1 i 12 3 NON-DIMENSIONAL 4 5 6 7 DISTANCE ACROSS CURRENT Fig. 10. The Reynolds stresses â uv and â1>2 for a Rossby wave being absorbed by a westward-flowing current, the same wave illustrated in Fig. 9. The curves indicate the dependence of these stresses on lateral viscosity. The behavior of waves with non- meridional group velocities is similar to that shown here. eastern part of gyres. It seems clear though that the fate of the Rossby waves depends on the relative fre- quency c= coâk-U. If a increases and |k-U| becomes sufficiently large, the waves will be reflected. If, on the other hand, a decreases to zero, the waves will be ab- sorbed and give all their momentum and some of their energy to the current. In general, whether the waves are reflected or absorbed, they exert a force on the water within the current system, tending to push the water out away from the center of the gyre. This force is a generalization of the meridional force â (v2)' and is in the direction of maximum attenuation of the waves within a given current. Since longer wavelength waves have smaller wavenumbers, those waves penetrate furthest into the currents, and they may reach the continental slope, where they are reflected back into the gyre, usually with a different wavelength. While we have used lateral viscosity in this paper, Bennett and Young (1971) chose a linear friction to study the behavior of barotropic Rossby waves in a mean flow. Instead of the diffusion term on the right- hand side of the vorticity equation (1), linear friction creates a loss term âaf, which is proportional to the vorticity. We may attribute this loss to the bottom Ekman layer. Similarly, the linear moment
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