Nonlinear adjustment of a rotating homogeneous atmosphere to zonal momentum forcing
Idealized numerical simulations using a simple shallow water model are performed to study a generalized Rossby adjustment problem which focuses on the nonlinear response of a rotating, uniform, homogeneous, barotropic zonal flow to meso-α and β scale zonal momentum forcing. The prescribed forcings propagate downstream at a speed (c) which is less than the basic state flow speed (U), and represent the local effects of momentum deposition/redistribution attributable to a variety of physical processes. For small Rossby number flow and t ≤ τ = 2a/(U–c), the near-field response to meso-α scale forcing in the moving frame of reference is to produce localized zonal jets of finite longitudinal and latitudinal extent whose geometries are similar to the imposed forcing structure. The perturbation mass (height) field adjusts to the wind field associated with these disturbances. Although the free surface vertical motion is dominated by transient inertia-gravity waves at early times, well-defined localized vertical motions also form in the vicinity of the forcing center. For isolated forcing, ascending and descending vertical motion occurs south and north of the forcing center, respectively. For dipole forcing, a fourcell pattern of vertical motion characterized by ascent in the southwest and northeast quadrants and descent in the northwest and southeast quadrants flanks the forcing center where a pair of easterly and westerly jets form. For t > τ, the exit region of the localized zonal jet produced by isolated forcing is advected downstream, carrying portions of the meridional perturbation winds and free surface displacement fields with it. The long term asymptotic response is a zonally elongated, synoptic scale jet due to the temporally continuous relative vorticity generated by the zonal momentum forcing. A divergent cross-stream ageostrophic flow in the jet entrance region produces an isolated region of ascending vertical motion which is compensated by weaker regions of descent to the east and west of the forcing center. The easterly jet produced by flow deceleration in the exit region of the dipole forcing is advected downstream during the same time period. A four-cell pattern of vertical motion accompanies this easterly jet. The response in the vicinity of the forcing center is an isolated meso-α scale westerly jet, with meridionally confluent flow in its entrance region and meridionally diffluent flow in its exit region. The ageostrophic circulation produces rising motion in the jet entrance region and sinking motion in the jet exit region. For moderately large Rossby number flow and meso-β scale dipole forcing, a mesoscale cyclone forms in response to fluid parcels being displaced southward into deeper fluid around a ridge in the height field. The moderately strong meso-β scale zonal wind maximum which is produced has associated vertical motions whose geometry is similar to those produced by larger meso-α scale dipole forcing. Stronger nonlinear advection allows the meso-β scale jet to form four times sooner than the westerly jet produced by smaller Rossby number meso-α scale dipole forcing.
Document Type: Research Article
Publication date: October 1, 1998