. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography 422 JOURNAL OF PHYSICAL OCEANOGRAPHY Volume 5 U = U0 U = 0. Fig. 1. Schematic diagram of a Rossby wave propagating into a zonal current which is independent of longitude. While the wave's phase velocity Cp is away from the current, the group velocity Cg carries the wave energy into the current. illustrated in Fig. 2: -0km rtx I Ry (4) When lateral viscosity is present, the wave is damped as it propagates although the energy loss per wave- length is
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography 422 JOURNAL OF PHYSICAL OCEANOGRAPHY Volume 5 U = U0 U = 0. Fig. 1. Schematic diagram of a Rossby wave propagating into a zonal current which is independent of longitude. While the wave's phase velocity Cp is away from the current, the group velocity Cg carries the wave energy into the current. illustrated in Fig. 2: -0km rtx I Ry (4) When lateral viscosity is present, the wave is damped as it propagates although the energy loss per wave- length is small when Ah is small. The current is also subject to viscosity which, through the diffusion of vorticity, causes the current to spread as well as dis- sipate. We use sufficiently small values of AH in this paper that the time scales of the current are large com- pared with the wave period. 2. Numerical techniques In all the examples of Rossby waves in a current shown in this paper, the solutions are obtained by numerically integrating ordinary differential equations. All variables are first non-dimensionalized with the length scale k~x, where k= (kj+ky2)* is the wavenumber of the incident Rossby wave, and with the time scale k/0. Without viscosity, the Rossby waves are governed by the ordinary, second-order differential equation *"+|~-(c7"-/?)-£/ |¥ = 0, (5) where a—u—kM and U" are functions of the meri- dional coordinate y. The current profile U(y) consists of a constant current region U— Uo, a shear zone of width y0) and region of still water £/=0 as shown in Fig. 1. The current within the shear is a fifth-order polynomial which fits U, U' and U" continuously be- tween the two constant current regions. The boundary conditions needed to complete the problem are that ^ and *&' in the U0 region and the still region be equal to the analytic solution of (5) which represents the incident wave and waves which decay away from the shear zone. Functio
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