Nonlinear adjustment of a rotating homogeneous atmosphere to zonal momentum forcing

Idealized numerical simulations using a simple shallow water model are performed to study ageneralized 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 stateflow speed (U), and represent the local effects of momentum deposition/redistribution attributableto 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 producelocalized zonal jets of finite longitudinal and latitudinal extent whose geometries are similar tothe imposed forcing structure. The perturbation mass (height) field adjusts to the wind fieldassociated with these disturbances. Although the free surface vertical motion is dominated bytransient inertia-gravity waves at early times, well-defined localized vertical motions also formin the vicinity of the forcing center. For isolated forcing, ascending and descending verticalmotion occurs south and north of the forcing center, respectively. For dipole forcing, a fourcellpattern of vertical motion characterized by ascent in the southwest and northeast quadrantsand descent in the northwest and southeast quadrants flanks the forcing center where a pairof easterly and westerly jets form. For t >t, the exit region of the localized zonal jet producedby isolated forcing is advected downstream, carrying portions of the meridional perturbationwinds and free surface displacement fields with it. The long term asymptotic response is azonally elongated, synoptic scale jet due to the temporally continuous relative vorticity generatedby the zonal momentum forcing. A divergent cross-stream ageostrophic flow in the jetentrance region produces an isolated region of ascending vertical motion which is compensatedby weaker regions of descent to the east and west of the forcing center. The easterly jet producedby flow deceleration in the exit region of the dipole forcing is advected downstream during thesame time period. A four-cell pattern of vertical motion accompanies this easterly jet. Theresponse in the vicinity of the forcing center is an isolated meso-α scale westerly jet, withmeridionally confluent flow in its entrance region and meridionally diffluent flow in its exitregion. The ageostrophic circulation produces rising motion in the jet entrance region andsinking motion in the jet exit region. For moderately large Rossby number flow and meso-bscale dipole forcing, a mesoscale cyclone forms in response to fluid parcels being displacedsouthward into deeper fluid around a ridge in the height field. The moderately strong meso-bscale zonal wind maximum which is produced has associated vertical motions whose geometryis similar to those produced by larger meso-α scale dipole forcing. Stronger nonlinear advectionallows the meso-β scale jet to form four times sooner than the westerly jet produced by smallerRossby number meso-α scale dipole forcing.