Nonlinear adjustment of a rotating homogeneous atmosphere to zonal momentum forcing

Idealized numerical simulations using a simple shallow water model are perf ormed to study a generalized Rossby adjustment problem which focuses on the nonlinear response of a rotating, uniform, homogeneous, barotropic zonal f low to meso-alpha and beta scale zonal momentum forcing. The prescribed for cings propagate downstream at a speed (c) which is less than the basic stat e flow speed (U), and represent the local effects of momentum deposition/re distribution attributable to a variety of physical processes. For small Ros sby number flow and t less than or equal to tau = 2a/(U - c), the near-fiel d response to meso-alpha scale forcing in the moving frame of reference is to produce localized zonal jets of finite longitudinal and latitudinal exte nt whose geometries are similar to the imposed forcing structure. The pertu rbation mass (height) field adjusts to the wind field associated with these disturbances. Although the free surface vertical motion is dominated by tr ansient inertia-gravity waves at early limes, well-defined localized vertic al motions also form in the vicinity of the forcing center. For isolated fo rcing, ascending and descending vertical motion occurs south and north of t he forcing center, respectively. For dipole forcing, a four-cell pattern of vertical motion characterized by ascent in the southwest and northeast qua drants and descent in the northwest and southeast quadrants flanks the forc ing center where a pair of easterly and westerly jets form. For t > tau, th e exit region of the localized zonal jet produced by isolated forcing is ad vected downstream, carrying portions of the meridional perturbation winds a nd free surface displacement fields with it. The long term asymptotic respo nse is a zonally elongated, synoptic scale jet due to the temporally contin uous relative vorticity generated by the zonal momentum forcing. A divergen t cross-stream ageostrophic flow in the jet entrance region produces an iso lated region of ascending vertical motion which is compensated by weaker re gions of descent to the east and west of the forcing center. The easterly j et produced by Bow deceleration in the exit region of the dipole forcing is advected downstream during the same time period. A four-cell pattern of ve rtical motion accompanies this easterly jet. The response in the vicinity o f the forcing center is an isolated meso-alpha scale westerly jet, with mer idionally confluent flow in its entrance region and meridionally diffluent Bow 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-beta scale dipole forcing, a m esoscale cyclone forms in response to fluid parcels being displaced southwa rd into deeper fluid around a ridge in the height field. The moderately str ong meso-beta scale zonal wind maximum which is produced has associated ver tical motions whose geometry is similar to those produced by larger meso-al pha: scale dipole forcing. Stronger nonlinear advection allows the meso-bet a scale jet to form four times sooner than the westerly jet produced by sma ller Rossby number meso-alpha scale dipole forcing.