A linear theory for jet streak formation due to zonal momentum forcing in a stably stratified atmosphere (original) (raw)
Zonal jets as transport barriers in planetary atmospheres
Arxiv preprint arXiv: …, 2008
The connection between transport barriers and potential vorticity (PV) barriers in PVconserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV-staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV-steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV-staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter's midlatitude weather layer and in the Earth's summer hemisphere subtropical stratosphere.
Geophysical & Astrophysical Fluid Dynamics
Two common approximations to the full Shallow Water Equations (SWEs) are non-divergence and quasi-geostrophy, and the degree to which these approximations lead to biases in numerical solutions are explored using the test bed of barotropic instability. Specifically, we examine the linear stability of strong polar and equatorial jets and compare the growth rates obtained from the SWEs along with those obtained from the Non-Divergent barotropic vorticity (ND) equation and the Quasi-Geostrophic (QG) equation. The main result of this paper is that the depth over which a layer is barotropically unstable is a crucial parameter in controlling the growth rate of small amplitude perturbations and this dependence is completely lost in the ND equation and is overly weak in the QG system. Only for depths of 30 km or more are the growth rates predicted by the ND and QG systems a good approximation to those of the SWEs, and such a convergence for deep layers can be explained using theoretical considerations. However, for smaller depths, the growth rates predicted by the SWEs become smaller than those of the ND and QG systems and for depths of between 5 and 10 km they can be smaller by more than 50%. For polar jets, and for depths below 2 km the mean height in geostrophic balance with the strong zonal jet becomes negative and hence the barotropic instability problem is ill-defined. While in the SWEs an equatorial jet becomes stable for layer depths smaller than 3-4 km, in the QG and ND approximations it is unstable for layer depths down to 1 km. These result may have implications for the importance of barotropic instability in Earth's upper stratosphere and perhaps also other planets such as Venus.
Journal of the Atmospheric Sciences, 2008
Three-dimensional numerical simulations of freely evolving stratified geostrophic turbulence on the  plane are presented as a simplified model of zonal jet formation on Jupiter. This study samples the parameter space that covers the low, middle, and high latitudes of Jupiter by varying the central latitude of the  plane. The results show that robust zonal jets can emerge from initial small-scale random turbulence through the upscale redistribution of the kinetic energy in the spectral space. The resulting flow's sensitivities to the flow's deformation radius L D and the two-dimensional Rhines length L  ϭ ͌ U/ (U is the characteristic turbulence velocity and  is the meridional gradient of the planetary vorticity) are tested, revealing that whether the outcome of the upscale energy transfer becomes dominated by jets or vortices depends on the relative values of L D and L  . The values of L  and L D are varied by tuning the -plane parameters, and it is found that the flow transitions from a jet-dominated regime in L  Շ L D to a vortical flow in L  տ L D . A height-to-width ratio equal to f /N, the Coriolis parameter divided by the Brunt-Väisälä frequency, has previously been established for stable vortices, and this paper shows that this aspect ratio also applies to the zonal jets that emerge in these simulations.
Physical review. E, 2016
Turbulence with inverse energy cascade and its transport properties are investigated experimentally in a flow associated with a westward propagating jet. Turbulence and the jet were produced by an electromagnetic force in a rotating tank filled with an electrolytic saline solution. The parabolic free surface emulated the topographic β effect which evoked the zonation. The spectral and transport flow characteristics were highly anisotropic. Turbulence is diagnosed by exploring the analogy between vertical and horizontal turbulent overturns in, respectively, stably stratified and quasigeostrophic flows which gives rise to a method of potential vorticity (PV) monotonizing. The anisotropization of transport properties of the flow is investigated using the finite scale Lyapunov exponent technique. After initial exponential particle separation, radial (meridional in geophysical and planetary applications) diffusion attains a short-ranged Richardson regime which transitions to the Taylor (...
Nonlinear adjustment of a rotating homogeneous atmosphere to zonal momentum forcing
Tellus A, 1998
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-a and b 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∏t=2a/(U−c), the near-field response to meso-a 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>t, 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-a 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-b 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-b scale zonal wind maximum which is produced has associated vertical motions whose geometry is similar to those produced by larger meso-a scale dipole forcing. Stronger nonlinear advection allows the meso-b scale jet to form four times sooner than the westerly jet produced by smaller Rossby number meso-a scale dipole forcing.
A mechanism of formation of multiple zonal jets in the oceans
2009
Multiple alternating zonal jets observed in the ocean are studied with an idealized quasigeostrophic model with the background flow imposed. Formation of the jets is governed by a spatially nonlocal mechanism that involves basin-scale instabilities. Energy of the background flow is released to the primary unstable mode with long meridional and short zonal lengthscale. This mode undergoes secondary instability that sets meridional scale of the multiple zonal jets. In a zonal channel, eddies generated by the instabilities maintain several weakly damped annular modes that significantly modify the jets and feed back on the primary instability. It is found that the jets are driven by the mixed, barotropic-baroclinic dynamics and maintained by either Reynolds or form stress forcing, depending on the direction of the background flow. The underlying dynamical mechanism is illuminated both with statistical analysis of the nonlinear equilibrium solutions and with linear stability analysis of the flow components. Finally, we find that the jets are associated with alternating weak barriers to the meridional material transport, but locations of these barriers are not unique.