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-dependent, 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 perturbation 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 Ro_U = (U - c)/2af = 0.1, where a is the half-width of the prescribed zonal momentum forcing as seen by a Galilean observer traveling at the speed c < U, shows many similar characteristics with the forced shallow water flow response of Weglarz. In particular, the early response for t ≤ τ = 2a/(U - c) is characterized by a pair of easterly and westerly zonal jet streaks produced by flow acceleration/deceleration in the forcing entrance/exit region. The mass field quickly adjusts to the sub-Rossby scale (a ≪ 2d_jetN/f) perturbations in the wind field, forming a pair of high-low couplets that geostrophically support the isolated zonal jets. For t > τ, the easterly zonal jet is advected downstream a! the relative velocity U - c, leaving an isolated, meso-α-scale, westerly zonal jet streak in the vicinity of the forcing center. The ageostrophic winds characterize a mesoscale cyclonic circulation that circumvents the forcing center. The divergence associated with this circulation produces a four-cell pattern of vertical motion that flanks the core of the zonal jet streak. This pattern of steady, externally forced, vertical motion is reversed from the pattern normally inferred from traditional nonlinear quasigeostrophic jet streak dynamics because the accelerations produced by the imposed zonal momentum forcing dominate those produced by local time rate of change and linear inertial advection of the geostrophic flow.