A linear theory for jet streak formation due to zonal momentum forcing in a stably stratified atmosphere

A perturbation potential vorticity (PV) theory is developed to investigate the three-dimensional, time-depen-dent, linear geostrophic adjustment of a stably stratified, Boussinesq atmosphere that is disturbed from (i) quiescent equilibrium due to a localized, unbalanced, zonal wind anomaly and (ii) geostrophic equilibrium of the uniform zonal flow due to an isolated couplet of acceleration–deceleration forcing. This prescribed zonal momentum forcing propagates downstream at a speed c that is less than the basic-state zonal flow speed U and physically represents the parameterized effects of nonlinear inertial advection. Transient, dispersive inertia–gravity waves in all fields are essentially removed during the early stage of the response associated with the initial value problem. The steady-state equilibrium that conserves the initial per-turbation PV is a localized, geostrophic zonal jet with meridionally confluent (diffluent) flow in its entrance (exit) region. This jet is supported by a couplet of perturbation low and high pressure north and south of the zonal jet core, respectively. There exist no steady-state ageostrophic winds and vertical motions once balanced equilibrium is reached. This long-term asymptotic response characterizes a localized linear thermal wind balance among the baroclinic perturbations that will not be preserved in the nonlinear initial value problem. The forced response for a uniform, stably stratified, zonal flow whose Rossby number is RoU 5 (U 2 c)/2a