The applicability of two competing wave theories of the rotating shallow-water equations, the harmonic planetary waves and the trapped planetary waves, is examined by solving the equations numerically in a zonal channel on the midlatitude β-plane. The examination is carried out by initializing the numerical shallow-water solver by harmonic and trapped waves and comparing the temporal evolution to that expected from the corresponding wave theory. The simulations confirm that harmonic waves provide accurate approximations for the temporal evolution in narrow channels while trapped waves do so in wide channels. The transition from a narrow channel to a wide channel occurs when the non-dimensional number (Formula presented.) (where L is the channel width, Rd is the radius of deformation, a is Earth's radius and ϕ0 is the latitude of the centre of the channel) is increased above a threshold value that larger than 4 and that depends on the meridional mode number of the trapped wave. Numerical solutions of the nonlinear equations show that, for the same wave amplitude, trapped waves approximate the nonlinear solutions in a wide channel for much longer times than harmonic waves in a narrow channel.
|Original language||American English|
|Number of pages||8|
|Journal||Quarterly Journal of the Royal Meteorological Society|
|State||Published - 1 Jul 2016|
Bibliographical noteFunding Information:
The authors thank the two anonymous reviewers whose careful reading and detailed comments helped us to improve the style of this manuscript. This research was supported by grant of the Israeli Ministry of Science and Technology (MOST) to HU (HG).
© 2016 Royal Meteorological Society
- planetary waves
- shallow-water waves
- trapped waves