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- W2158778528 abstract "Some exact expressions are derived to describe the temporal evolution of forced Rossby waves in a two-dimensional beta-plane configuration where the background flow has constant zonal-mean velocity. The meridional length scale of the problem is assumed to be small relative to the zonal length scale and so the long-wave limit of zero aspect ratio is taken. In the case where the background flow velocity is zero, an exact solution is obtained in terms of generalized hypergeometric functions. A late-time asymptotic approximation is obtained and it shows that the solution oscillates with time and its amplitude goes to zero in the limit of infinite time. In the case of a non-zero background flow velocity, the solution is evaluated using two different procedures which give two equivalent expressions in terms of different generalized hypergeometric functions. The late-time asymptotic behaviour is investigated and it is found that the solution approaches a steady state in the limit of infinite time. We also derive a solution in the form of an asymptotic series expansion for the more general situation where a Rossby wave packet is generated by a zonally-localized boundary condition comprising a continuous spectrum of wavenumbers or Fourier modes. The exact solutions found here can be used as leading-order solutions in weakly-nonlinear analyses and other studies involving more realistic configurations for time-dependent Rossby waves or wave packets." @default.
- W2158778528 created "2016-06-24" @default.
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- W2158778528 date "2015-11-01" @default.
- W2158778528 modified "2023-10-16" @default.
- W2158778528 title "Some exact expressions for the temporal evolution of long Rossby waves on a beta-plane" @default.
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- W2158778528 doi "https://doi.org/10.1016/j.wavemoti.2015.05.002" @default.
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