A Numerical Study of Transient Rossby Waves in a Wind-Driven Homogeneous Ocean

The primitive hydrostatic equations for a rectangular homogeneous ocean with a free surface on a β-plane are integrated numerically for 60 days from an initial state of rest and undisturbed depth of 400 m. A zonal wind stress (maximum 2 dyn cm−2) and a lateral eddy viscosity (108 cm2 sec−1) are assumed. A series of transient Rossby waves of approximately 1000-2000 km in length form in the central and eastern basin, and undergo a well-marked life cycle of amplification and decay as they propagate westward at ∼1 m sec−1 relative to the zonal current. The northward boundary current in the west (∼1 m sec−1) and the counter-currents in the northwest (∼10 cm sec−1) may be identified as the first stationary members of a continuing series of waves, with subsequent transients showing characteristics of reflected Rossby waves and reaching progressively smaller maximum amplitudes. The standing wave pattern (wavelength ∼600 km) in the north-west is a characteristic nonlinear effect, and is associated with the meridional tilt displayed by the transients and the resultant (nonlinear) poleward eddy transport of zonal momentum. Near geostrophic equilibrium is maintained throughout, with the meridional Ekman flow of the order of a few centimeters per second. After a spin-up period of about 12 days, the surface potential and total kinetic energy display damped oscillations with the free period of approximately 16 days, with (long) surface gravity waves not significantly present.